Mba Center Book.pdf

Total PrepKit for the GMAT Copyright © 2001-2007 by the MBA Center Publications All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information and retrieval system, without the written consent of The MBA Center, except where permitted by law.

© The MBA Center

CONTENTS I. INTRODUCTION THE MBA CENTER GMAT COURSE ...................................................7 WHAT IS THIS THING CALLED

THE

GMAT?.......................................11

STEP 1 THE MBA CENTER APPROACH TO

THE

GMAT CAT .................19

II. LESSONS QUANTITATIVE SECTION INTRODUCTION ............................................................................35 STEP 2 MATH REVIEW....................................................................41 STEP 3 PROBLEM SOLVING............................................................105 3.1 Lesson ..................................................................................109 3.2 Homework/Practice Test.......................................................131

STEP 4 PROBLEM SOLVING WORKSHOP ...........................................139 STEP 5 DATA SUFFICIENCY ............................................................149 5.1 Lesson ..................................................................................151 5.2 Homework/Practice Test.......................................................179

STEP 6 DATA SUFFICIENCY WORKSHOP ............................................189 VERBAL SECTION INTRODUCTION ..........................................................................197 STEP 7 GRAMMAR

AND

STYLE REVIEW .............................................203

7.1 Lesson ..................................................................................205 7.2 Homework/Practice Test.......................................................251

STEP 8 GRAMMAR WORKSHOP .....................................................257 STEP 9 SENTENCE CORRECTION .....................................................267 9.1 Lesson ..................................................................................269 9.2 Homework/Practice Test.......................................................305

STEP 10 SENTENCE CORRECTION WORKSHOP ...................................317

© The MBA Center

STEP 11 CRITICAL REASONING ......................................................327 11.1 Lesson ................................................................................329 11.2 Homework/Practice Test.....................................................357

STEP 12 CRITICAL REASONING WORKSHOP ......................................369 STEP 13 ANALYTICAL WRITING ASSESSMENT .....................................379 13.1 Lesson ................................................................................381 13.2 Homework/Practice Test.....................................................401

STEP 14 ANALYTICAL WRITING ASSESSMENT WORKSHOP .....................403 STEP 15 READING COMPREHENSION ...............................................407 15.1 Lesson ................................................................................409 15.2 Homework/Practice Test.....................................................435

STEP 16 READING COMPREHENSION WORKSHOP ...............................447

III. APPENDICES BEFORE

THE

GMAT ....................................................................457

MBA ADMISSIONS......................................................................463

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© The MBA Center

© The MBA Center

The MBA Center GMAT Course

© The MBA Center

© The MBA Center

The MBA Center GMAT Course

TOUR GUIDE: THE MBA CENTER GMAT COURSE The MBA Center GMAT course is a sophisticated global package that helps our students prepare for the GMAT Computer Adaptive Test. The package contains the present manual with lessons, strategies, drills, and practice questions and is accompanied by online resources on our website - www.mba-center.net: a GMAT Diagnostic Test, GMAT Study materials, and the latest news about the GMAT and the MBA admissions process on our website www.mba-center.net.

Point 1: Getting ahead… This first point requires personal reading, inquiries, self-evaluation, and an introduction to our general strategies – in other words, getting acquainted with the GMAT CAT. This is what we advise you do to:

Point 1 should not last more than 2 weeks.

Take our FREE online GMAT Diagnostic Test at www.mba-center.net. This online test is tailored to identify your individual strengths and weaknesses on different key points tested on the GMAT. Alternatively, you can also take the same test at any MBA Center, free of charge. Read the chapter "What Is This Thing Called the GMAT?" You should do this before your first lesson. It will give you information on the origin and purpose of the GMAT, its format and most recent changes, and samples of the types of questions being tested. Check out our website www.mba-center.net. It features the most recent information on the GMAT CAT, as well as comments from our students who have taken our preparation course and the test. You are also welcome to take advantage of our free online introductory lessons to the GMAT (see the website section "Free Study Materials"). Attend your first class with the lesson "The MBA Center Approach to the GMAT CAT," where your instructor will teach you how to use GMAT CAT to your advantage. These general strategies are the first and most immediate way to increase your score. They also form the basis for the more specific strategies that follow, and are further developed at each step of our GMAT preparation.

Point 2: Getting started... Preparing for the GMAT is a demanding process. In order to make your job easier, we provide access to the most updated, complete, and modern test prep technology, including: The Study Book: This textbook contains 16 steps illustrated by examples and strategies. Our lessons provide in-depth analysis of section structures and question types for all sections of the GMAT: the Analytical Writing Assessment, Problem Solving, Data Sufficiency, Sentence Correction, Critical Reasoning, and Reading Comprehension.

Point 2 should not last more than 10 weeks.

Online Forum: the MBA Center Forum, forum.mba-center.net, is a great way of getting answers to your questions, as well as getting feedback and opinions from those who have already taken the test. Practice Exercises: Don't forget to apply the theories you learn from the book, the class, and the website when working with practice tests and other study materials.

© The MBA Center

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Total PrepKit for the GMAT®

Introduction

Point 3: Winning!

Point 3 should not last more than 4 weeks.

10

After you have completed your course, the best key to improving your score is to practice with simulated GMAT CATs. You can download additional materials from the official GMAT website: www.mba.com. Also, check regularly the website of the MBA Center: www.mba-center.net, as well as your local MBA Center to find out what additional GMAT practice CATs they may have available in their computer lab.

© The MBA Center

What Is This Thing Called the GMAT?

© The MBA Center

© The MBA Center

What Is This Thing Called the GMAT?

WHAT IS THIS THING CALLED THE GMAT? A LITTLE GMAT HISTORY The GMAT was first administered in the United States in 1954. That first test was very different from today’s GMAT. The older test was on paper, had no Analytical Writing Assessment or Critical Reasoning questions, and was based on the pre-collegiate Scholastic Aptitude Test (SAT). Since then, generations of test takers suffered taking the pencil-andpaper exam. In October 1997 that old familiar format was changed to the new Computer Adaptive Test (CAT). Since the early 1990’s, psychometricians at Graduate Management Admissions Council (GMAC) had been working to improve and modernize their standardized tests using research data and techniques gathered from years of experimentation with artificial intelligence. Today, the GMAT, as well as the TOEFL, GRE, and other tests, have been computerized.

WHO IS RESPONSIBLE

FOR THE

For more information, please see the GMAC's official website, www.gmac.com, as well as the official website of the GMAT, www.mba.com.

GMAT?

An organization known as GMAC, the Graduate Management Admission Council, delivers the GMAT CAT. Since January 2006, the content of the GMAT has been designed by ACT, Inc. and the test sessions are administered by Pearson VUE, subsidiary of Pearson PLC. GMAC is involved in "developing business education" and promoting its more than 130 business school members. GMAC is not a government agency, though it is a body of more or less academic folks whose work can have a significant influence on your life and career. The fact is, if you want to attend an MBA program almost anywhere in the world, you have little choice but to take the GMAT.

WHAT DOES

THE

GMAT MEASURE?

You might think that the GMAT measures something like your probability of success in business school, or that it assesses your level of education or intelligence. It does neither. The GMAT is not a success-predictor or an IQ test. It has its limitations. Research shows that the test cannot predict with certainty the success, failure, or grades of an individual in an MBA program. Furthermore, the GMAT, however respected, cannot and does not take into consideration other factors critical to professional success such as creativity, business acumen, negotiating skills, exemplary work ethic etc... What does the GMAT measure? The GMAT is best at measuring one’s ability to take a standardized test.

WHAT IS

THE

CAT LIKE?

The Tutorial The test begins with a mandatory computer tutorial. The tutorial will methodically guide you through the (new) format of the test, including the various computer functions necessary for the test, such as: how to select answers, advance to the next question, show or hide the clock, access the HELP mode, and use word processing functions. One trip through this tutorial in your practice should be enough to get you going, since GMAT CAT commands and functions are intentionally easy to use.

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Total PrepKit for the GMAT®

Introduction

GMAT CAT – Tutorial End

When finished reading tutorial click on the icon below

CAT TUTORIALS How to Use the Mouse How to Answer How to Use Testing Tools How to Scroll

Test

Section

Quit

Exit

Dismiss Tutorial Answer

Time Time

Help

Confirm

Next

The Analytical Writing Assessment (AWA) After you have completed the mandatory (and somewhat insulting) tutorial you’re instructed to write two essays of 30 minutes each: one called Analysis of an Issue and one called Analysis of an Argument. The task itself is to write a clear, concise, and cogent short essay (3 to 5 paragraphs or so) for each analysis topic. Of the two topics, the first is typically the Analysis of an Issue question which might ask you to evaluate a statement (on business, government and business, or personal success issues) or to consider a point of view, or opinion. Whether statements or opinions, business or personal, Issues are broad, topical subjects – such as those you might find in a newspaper or magazine. (See the Official Guide for the GMAT Review or www.mba.com for samples.) Your Analysis of an Issue essay should be a logical, thoughtful assessment of the Issue resented in which you might either deconstruct and analyze a statement or discuss whether or not you agree with an opinion. Inclusion of personal experiences and examples is strongly encouraged for essays on this question type, a luxury not allowed on the Analysis of an Argument. The Analysis of an Argument question type also presents you with only one subject, or argument, to analyze and write about. This time the subject is a formal argument composed of premises and conclusions which is no different than the arguments you’ll find in the Critical Reasoning section. You might evaluate arguments based on basic principles of market economics, business, and entrepreneurship, or on education, lifestyle, or health topics. Whatever the subject matter, your interpretation and your essay should stick very closely to the logic of the argument presented to you. The Analysis of an Argument is the more strict of the two essays, and including personal experiences in this essay is discouraged. The Analytical Writing Assessment primarily tests your ability to analyze an issue or an argument and to write a logical and well-organized essay. For more information and our strategies for this section of the test, see the Analytical Writing Assessment lesson in Step 13 of this book. The Quantitative And Verbal Sections The AWA is followed by the two computer-adaptive, multiple-choice test sections, Quantitative and Verbal. We recommend you take the optional break between the two sections on the test day. The Quantitative Section is the mathematics section of the test and contains 37 questions to be completed in 75 minutes. Two types of questions which test fundamental mathematical principles appear in this section, Problem Solving and Data Sufficiency. The

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© The MBA Center

What Is This Thing Called the GMAT?

same mathematical principles (Arithmetic, Algebra, Geometry, and Word Problems) are tested by both question types, though in two very different ways. Problem Solving and Data Sufficiency questions are intermixed in the Quantitative section. You will get one or two or three Problem Solving questions, followed by one or two Data Sufficiency questions, and then back to Problem Solving. In all, of the 37 Quantitative questions, approximately 24 will be Problem Solving and approximately 13 will be Data Sufficiency. And here are the vital statistics for the Verbal Section: a total of 41 questions to be completed in 75 minutes. Two of the Verbal question types — Critical Reasoning and Sentence Correction — are in the Verbal section, much as the two Quantitative question types are intermingled throughout, the Quantitative section. That is, you may get one, two Sentence Correction questions, followed by one or two Critical Reasoning questions, then perhaps another Sentence Correction item. However, questions of the third Verbal type — Reading Comprehension — are grouped. Each Reading passage is accompanied by a set of three to six questions in a row, all relating to that passage. It is a fact that about 8 of the 37 Quantitative questions and about 11 of the 41 Verbal questions will actually not count towards your score. These are called experimental questions or equating items — they are used only for research purposes. Unfortunately, there is no way to know which questions are unscored. You must approach each question as if it counts.

Not all the questions count.

THE SCORING SYSTEM Clear away the haze and recall your youthful school days. The heady days of wealth and responsibility seemed very far away. The tests were multiple choice (multiple guess), and only the number of questions you answered correctly determined your score. The GMAT CAT scoring philosophy is altogether different. Your score is calculated according to your accuracy (answer right or answer wrong) and the level of difficulty of each question. The first question of each section is of medium difficulty (score value: 500 points). If this first question is answered correctly, the level of difficulty for the next question will increase. The more questions you answer correctly, the more difficult the next questions become. In this way the program will rapidly determine your approximate level and fine tune it afterwards. Thus, the harder the question, the higher the point or score value for that question. Likewise, the easier the question, the lower the point value assigned that question. If you respond incorrectly to a question, the next question will be easier and have a lower score value, and vice versa. A high GMAT score, therefore, indicates that a given test taker has correctly answered more questions at higher levels of difficulty than another test taker with a lower GMAT score, and therefore has a higher GMAT level. The same scoring operation applies to each section of the CAT. Your overall GMAT score is worked out by combining your two section scores (Verbal and Quantitative). In order to provide an admissions officer with a detailed indication of your testing level and abilities, your official score report also includes scaled scores ranging from 0 to 60 for each section, percentile rankings of your performance on each section and on the GMAT as a whole (this percentile ranking is a comparison between you and other test takers), and finally a separate AWA grade. Analytical Writing Assessment scores range from 1 to 6. Your essays are graded not by computer but by human graders – teaching assistants working for the GMAC. After finishing your test, you’ll immediately receive an unofficial score for the computer-adaptive portions of the test only. Your AWA score and your official GMAT CAT test score come together by mail in about 15 days.

© The MBA Center

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Total PrepKit for the GMAT®

Introduction

FREQUENTLY ASKED QUESTIONS ABOUT THE GMAT CAT The results of our website open forum are in: here is a transcript of the most frequently asked questions about the GMAT CAT and our answers. Q: Should I answer questions wrong on purpose so the test gets easier? A: Absolutely not! If you answer a question wrong, the computer will give you an easier question but your score will go down as a result. If you want a good score (you know you do!) you must answer as many questions correctly as possible. The harder the question, the higher the point value. This is crucial information! Since the CAT scoring algorithm very rapidly determines your testing level, answering correctly without hesitation from the first question on is extremely important so that you start off with a high score. It’s much easier to maintain a high score than it is to raise a low score. Q: How much does the level of difficulty change from question to question? A: In the beginning, quite a lot. Near the end, not so much. This is an important quirk in the system. The objective of the CAT is to quickly determine (right from the beginning) your approximate testing level and then fine-tune it while you continue the test. To illustrate: a right answer on the first question results in an increase of 50 points, a right answer on the second, an increase of 40 points – on the second-to-last question a right answer nets you an increase of only 10 points. So, if you answer the first few questions correctly, you’ll swiftly receive more difficult (higher score value) questions and can therefore raise your score. Q: Does my performance on one section affect the level of difficulty of the questions in the other sections? A: No. Each section is scored separately and begins with a question at the 500-level score value. If, for example, the Quantitative Section is the first section of the test, and if you get all the questions wrong, you’ll still begin with a question valued at 500 on the Verbal Section. Q: Is the computer program that precise? A: At The MBA Center, we don’t think so: it’s about as precise as the pencil-and-paper test. Standardized tests, even on computer, cannot be 100 percent accurate in their estimation of the level of difficulty of a given question. Some students consider difficult questions to be easy, other students consider easy questions to be difficult – it varies from test to test, student to student. However, the Adaptive Scoring System comes closer to identifying a personalized testing level than did the pencil-and-paper test. Q: Can I skip a question? A: No. Unlike the old test, on the CAT you cannot skip a question and come back to it. Neither can you change your responses. In order to advance to the next question you must enter your answer and then confirm it. The explanation is simple: the computer selects a question for you which depends on an algorithm that takes into consideration all of your answers thus far – if you could go back and change an answer, the continuity of the algorithm would be broken.

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© The MBA Center

What Is This Thing Called the GMAT?

ADVANTAGES AND DISADVANTAGES OF THE GMAT CAT The Computer Adaptive Test format was introduced in order to update the old format using the capabilities of high technology and to add new sections to the GMAT. Now that some time has passed since the introduction of the CAT, certain conclusions can be drawn regarding the advantages and disadvantages of the new test. Good CAT The most important advantage of the new CAT is flexibility. For example, the CAT version of the GMAT is offered continuously throughout the year. Unlike the pencil-andpaper test, you do not have to wait months between test dates. Test sessions are offered three weeks out of every month, and you can register easily by phone or by mail. This flexibility is particularly beneficial for students who plan to prepare thoroughly for the test and would like to make a convenient study schedule for themselves. Now, you can take the test when you want to, would like to, or need to. Another advantage of the new test is that you can take it as many times as you’d like. But keep in mind that you must wait until one calendar month has passed before repeating the test. If you took the test on March 20th, for example, you could take it again beginning April 1st. Door number 3....? Something else advantageous? You should be pleased to hear that 20 percent more time is allocated per question on the new test than on the old. Because you cannot skip questions to save time on the CAT, as you could on the old test, you now get 20 percent more time. In the days of the pencil-and-paper test, you had to wait six weeks for your official score. Now, the computer has an unofficial score for you immediately following the test. Since you’re being scored by the computer every step of the way, it “knows” your score the minute you finish. For your official score you’ve still got to wait by the mailbox. It’s mailed to you in about 15 days along with your AWA results.

Bad CAT The bad CAT: if you’re not computer-literate, you have a distinct disadvantage. Fortunately, the commands required to use the CAT are not difficult to learn, and you can practice them on preparation software available. We recommend that you spend time practicing with a computer well before the date of your test. A second disadvantage of the CAT is that your essays, the Analytical Writing Assessment, must be typed on a computer. If you use computers all the time, typing your essays on the CAT is little different from using any of the more popular word processing programs. However, if you do not know what “word processing” is and sense anxiety coming on as a result, then reduce stress by practicing on a computer well before the test. (Note: The actual test is taken using an American keyboard.) For some test takers, not being able to skip questions on the CAT as you could on the pencil-and-paper test is a disadvantage. If you have not yet learned how to think like the test, such as knowing when to make educated guesses to save yourself time and frustration, you may worry about having to answer every question. Our lessons include alternative approaches to skipping questions and we recommend that you practice them in class and on your own. Strategy is very important on the CAT. For instance, you’ll never know the level of difficulty of the questions on the actual test. But, you still must learn to answer easy questions correctly in order to increase the level of difficulty and the score value of following questions, and therefore raise your overall score as high as possible.

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Total PrepKit for the GMAT®

Introduction

On Reading Comprehension passages in particular, new strategy must be employed. On the old test, an excellent strategy was to make notes in the test booklet, but you cannot do this on the CAT. Why? Well, though some have tried, you cannot write on the monitor screen on which you view the test. Since on this new test the old ways don’t apply, new ones must be adopted. For instance, taking full advantage of the note-taking materials available on test day to take notes on Reading Comprehension passages while you scroll up and down with the mouse looking for what you need. Finally, cost is an additional disadvantage of the CAT. It’s about 50 percent more expensive than the old test – you’ll find this out when you register.

HOW DO ADMISSIONS OFFICERS USE GMAT CAT SCORES? Our inquiries make one thing perfectly clear: there is no universal or uniform use of GMAT scores. For example, Rotterdam, Erasmus considers only the Verbal Section of the test as a relevant selection tool, using it primarily to evaluate your English abilities. Schiller International University, on the other hand, has found a high correlation between GMAT math scores and eventual success in their MBA program and therefore concentrates on the Quantitative score to select, or “weed out,” applicants. Further, HEC Montreal considers the overall GMAT score to be a good indicator of future success in their MBA curriculum, especially for applicants with little or no scientific background. You might also consider the policy of certain schools toward applicants who have taken the GMAT several times. Harvard Business School, for instance, does not discriminate against the applicant and simply accepts the highest score. Wharton, however, averages the scores submitted. The best tactic, in general, is to achieve the highest score possible the first time you take the test. Another important issue is the score policy of your target school(s), and how the GMAT is treated by admissions officers in their evaluation. Studies show that a very strong correlation exists between the average GMAT score of an MBA class in a given school and that school’s rank. According to Business Week, the average GMAT score in the top 10 United States MBA programs ranges from 637 to 710. Although it is true that the GMAT is just one criterion for admissions among others (personal essays, letters of recommendation, professional and academic background, interviews...), the test remains one of the most important criteria, if not the most important. One other thing is certain: the higher the ranking of the school, the more closely considered your GMAT score will be. Indeed, Business Week reports that the GMAT counts for 20 percent of the admissions criteria at the top schools, while U.S. News and World Report puts the figure at 30 percent. For recognition and credibility, it is to their advantage that highlycompetitive and well-known business schools require a high GMAT score. For slightly less competitive schools, the GMAT score and evaluation policy is typically more flexible. For any school you consider, we advise contacting the admissions office and asking for their GMAT admissions policy. Our website, www.mba-center.net, is also a resource for information regarding average GMAT scores, MBA program rankings, admissions criteria and more.

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© The MBA Center

Step 1 The MBA Center Approach to the GMAT CAT

© The MBA Center

Total PrepKit for the GMAT®

Step 1

GENERAL OUTLINE The GMAT is said to be a test that assesses your ability to succeed in an MBA program. GMAC claims that it is impossible to prepare for the GMAT. However, a standardized test means standardized content and after taking one or two practice tests, you will see that success on the GMAT very much depends on strategy, practice, and a thorough understanding of the precise areas of math and verbal skills tested. The GMAT is a test that lends itself to strategy because it is a test made with strategy in mind. For this reason, a strategic overview of each section of the test is part of each lesson. Studying for the GMAT is not like studying for a final exam for which you have notes to memorize and that is all. The concepts and methods necessary for a high score on the GMAT cannot be learned by rote, but they can be mastered by practice. Improving your GMAT score requires a method, instruction, and practice to answer every type of question, even the most obscure. The adaptive format means strategy is important, since the difficulty level of the questions fluctuates throughout the greater part of the test. What is more, the change to the adaptive format means that it is essential to be informed about how to use it, so that you anticipate, not react to, the test.

THE

FOLLOWING TOPICS WILL BE COVERED IN THIS LESSON:

The CAT Principle Using Your Time Strategically The Wrong Answer Factory The Process Of Error Identification Guessing

KEY

WORDS

Computer Adaptive Test. A type of test that adjusts the difficulty level of each question to the testing capabilities of each test taker. Test questions for a computer-adaptive test are selected from a large database and are classified by content and level of difficulty. The main purpose of the adaptive program is to assess each test taker’s level of ability by adapting the level of difficulty of the questions. Process of Error Identification. This technique helps you find the “best answer” by eliminating answer choices you are sure are wrong. The Process of Error Identification allows you to choose the “best answer” even when you aren’t sure what it is, and should be used systematically. Using the Process of Error Identification is the most efficient method of identifying and eliminating wrong answer choices and should be used in combination with your knowledge of Phineas the test writer’s techniques and the Wrong Answer Factory principles that follow. Phineas and the Wrong Answer Factory. It’s time you met Phineas, a test writer and part of the Wrong Answer Factory – the name we have given to the test makers to explain how wrong answer choices are constructed according to standardized types, a principle no standardized test is exempt from. Phineas isn’t extraordinary. He’s smart enough guy; he probably did well on his SATs, went to a respectable college where he enjoyed his studies, and possibly continued them for a while afterward. Eventually, thought, Phineas realized that academics weren’t for him, fished around for a career, and discovered that he wasn’t really qualified for much. So he started writing tests because the salary was decent and it beat waiting tables. The job was relatively stress-free; it left him time to relax and hang out with friends. Phineas is not such a bad guy; really, you might even like him, if it weren’t for one small item:

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© The MBA Center

The MBA Center Approach

He’s out to sucker you. “There’s a sucker born every minute,” Phineas reminds himself as he sets down each day to write his questions. He proceeds to attempt to sucker test takers. How does he do this? Like all pathologicals, Phineas is pretty predictable. One of his basic tricks is to make very simple concepts appear very difficult, mostly by expressing them in obscure language and syntax. He's generally quite successful (you would be too if this were all you had been doing for years), but the keyword above is "appear." These concepts appear difficult, but remain simple. And after you decipher Phineas' jargon and methods, the questions he poses will no longer appear very complex. Another of Phineas' ruses is to provide answer choices to difficult questions that leap off the page and look correct. Phineas loves the idea of sucker test takers falling for this one. But with practice you can learn to recognize these choices and eliminate them quickly. How do you avoid being a sucker? One way is to learn exactly the types of wrong answer choices that Phineas will use, and we’ll do that shortly.

Meet Phineas* Facing and unknown opponent is always scary. Learn how Phineas thinks, how he writes questions, and what traps he lays for the unwary test taker.

* All characters in this book are purely fictitious. Any similarity to real people, living or dead, is purely coincidental.

THE CAT AND YOU Except for the Analytical Writing Assessment and the Reading Comprehension questions, all the questions on the computer test are adaptive. A good understanding of the principle and use of adaptivity on the updated test is highly recommended to improve your score. 1) The CAT Principle The adaptivity principle on the GMAT means that the more correct answers you choose on certain questions (the first 7 or so), the higher the level of difficulty and the score value of the following questions. If you answer certain questions correctly, then harder questions will follow. Likewise, if you don’t answer certain questions correctly, the next questions you receive will be easier and your score will go down. Your objective is to reach the higher score value questions with as much certainty as possible. Two more things: 1. Higher scores come from the value, not the number, of questions you answer correctly. 2. The test was designed to quickly determine your individual testing level, within the first few questions of any adaptive section, and fine tune it as you go along.

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Total PrepKit for the GMAT®

Step 1

The CAT Principle CONTINUOUS SCORING The CAT adjusts your score after each question. Note on the graph that your score jumps from 40 to 50 points per question in the beginning, but only 10 to 20 points per question near the end.

Score V600

600

V590

X590

V580 X560

V550

550

500

*This graph is only a rough approximation. It does not use the actual CAT algorithm

1

2

3

4

5

6

Questions

Comments The graph above gives you an idea of the CAT adaptivity principle as it would look if it were plotted out in the traditional manner. While answering the first few questions, the computer is tracking you and raising and lowering your score by as much as 30 to 50 points. After 7 or 8 questions, the tracking system has formed its general impression of your testing abilities and as it continues to adapt the test to you, the following questions vary by only 10 points or so.

CAPITAL QUIZ Directions: Time for some practice with the CAT adaptivity principle. On this quiz there are 10 questions which ask about the capital city of a country. Select the right answer from among the 4 answer choices. Your first right answer is worth 4 points. After that, the points per question range from 1 to 7 according to its level of difficulty. For every right answer, you move up to the next question on the ladder; for every wrong answer, move down one step. Use your quantitative skills to figure out your score at the end. Go to town! Although our games simulate the adaptivity principle of the CAT, your experience on the actual test may be slightly different.

Q1-What is the capital of the US? New York Washington D.C. Los Angeles Detroit Score value 4 Q2-What is the capital of Finland? Stockholm Oslo Copenhagen Helsinki Score value 5

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Q6-What is the capital of the United Kingdom? Manchester Glasgow London Nottingham

Score value 2

Q7-What is the capital of Madagascar? Moroni Lumbashi Antanarivo Fianarantsoa

Score value 7 © The MBA Center

The MBA Center Approach

Q3-What is the capital of China? Honk Kong Canton Shanghai Beijing

Q8-What is the capital of Australia? Canberra Melbourne Sydney Brisbane

Score value 3

Q4-What is the capital of California?

Q9-What is the capital of France?

Los Angeles San Francisco San Diego Sacramento Score value 6

Paris Brussels Rome Marseilles

Q5-What is the capital of Canada? Ottawa Toronto Montreal Vancouver

Score value 5

Score value 3

Q10-What is the capital of Japan? Nagoya Tokyo Nagasaki Beijing

Score value 4

Score value 1

Q7 v v v Q1

Q2

Q4

Q8

x

v Q5

x

v

x

x

v

Q9

Q3 v = right answer x = wrong answer

x

Q6 x Q10

Answers:1-Washington; 2-Helsinki; 3-Beijing; 4-Sacramento; 5-Ottawa; 6-London; 7-Antananarivo; 8- Canberra; 9-Paris; 10 Tokyo. © The MBA Center

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Total PrepKit for the GMAT®

Step 1

2) Learn how to pace yourself Since your testing level is determined during the first few questions of the test, our first piece of advice is to spend the most time and effort on the first seven questions, and less on the ones that follow. Adjust your strategy to the strategy of the test. A safe time to guess is on the last question. It will hardly affect your score.

Time

Questions 5

25

37

3) Draw a grid Instead of letters for answer choices on the computer test you’ll see small white bubbles, perfect for pointing your mouse toward. Since you cannot write on the monitor screen, you cannot cross out wrong answers. Our technique and our advice to make things easier is to draw a grid like this one:

1

2

3

4

X

A B

X

C

X

D

X

6

7

8

9

10

11

12

13

14

15

16

X

X

X X

X

5

X X

X

X X

X

X

X

E On test day, use the time (as long as 30 minutes) during the mandatory CAT-tutorial (which you will know long before the exam) and during the optional 5-minute break between the Quantitative and Verbal sections to draw yourself one of our helpful grids. Two advantages to the grid: 1. You can eliminate wrong answers easily and focus on remaining possible answer choices. This is very effective for Reading Comprehension questions for which you must scroll up and down and move back and forth between the questions and the passage. On the test, it’s easy to forget which answer choices you’ve recognized as wrong and waste time looking back at the screen to make sure. 2. You can cross out an answer choice, and have a record of it, as soon as you see that it’s incorrect. This is an especially useful system on Problem Solving and Data Sufficiency questions in which some answer choices can be eliminated immediately.

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The MBA Center Approach

SPECIFIC STRATEGIES 1)The Wrong Answer Factory The power of good guesswork is one reason why multiple-choice tests are rarely given in school. That it is possible to guess the right answer without knowing the right answer is usually bad news in the testing business. On the GMAT CAT, you do have the power to guess even though every effort has been made to make it difficult for you. Wrong answer choices are constructed in certain ways to tempt you and to discriminate between someone who knows the right answer (and strategies) from someone who doesn’t. Phineas’ Wrong Answer Factory realizes that most people who take the test make the same mistakes: errors in calculation, jumping to conclusions, and overcomplicating simple problems. Knowledge is power: if you know how wrong answers are made and what they’re made of, you’ll avoid being the victim of the tricks and traps waiting for you. Given a little time, a little coursework, and a little practice, you’ll be eliminating wrong answers with deadly accuracy.

Lighten your testprep load: Once you learn what traps the Wrong Answer Factory comes up with, you can spot them and eliminate wrong answers without solving the problem.

Take a look at this math problem: GMAT CAT – Section 3 : Quantitative

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It takes Susan three hours to mow her lawn. If her friend Melinda helps her, they can mow the same lawn in 1 hour. How long does it take Melinda to mow the lawn alone? ! ! ! ! !

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01:15

(A) (B) (C)1 1/2 hours (D) (E)

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Answer Time Time

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Phineas knows the right answer first. He has four more plausible answers to write and he knows how the average test taker thinks.

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Total PrepKit for the GMAT®

Step 1

Here is the final version: 01:15

GMAT CAT – Section 3 : Quantitative

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It takes Susan 3 hours to mow her lawn. If her friend Melinda helps her, they can mow the same lawn in 1 hour. How long does it take Melinda to mow the lawn alone? (A) (B) (C) (D) (E)

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1 2 1 3 4

hour hours 1/2 hours hours hours

Answer Time Time

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Phineas got wise by reading score and experimental section reports and he knows the average test taker is attracted by solutions that can be easily found. For instance, Phineas knows that some test takers will just subtract: 3 – 1 = 2. That’s why he created choice (B). And Phineas knows that other test takers will just add: 3 + 1 = 4. That’s why he created choice (E). Weaker test takers are often attracted by a number already seen in the problem and might choose (A) or (D). These are totally wrong, eliminate them.

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The MBA Center Approach

In the previous example you saw that Phineas creates traps for those who oversimplify a difficult problem. The Wrong Answer Factory principles also apply to Verbal questions: GMAT CAT – Section 4 : Verbal

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Trumpeting the victory of her team in the volleyball semifinals, the coach’s attitude was one of exuberance and guarded optimism.

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! (A) the coach’s attitude was one of exuberance and guarded optimism. ! (B) the coach’s attitude reflected her exuberance and guarded optimism. ! (C) the attitude of the coach was exuberant and guardedly optimistic. ! (D) the coach displayed an attitude of exuberance and guarded optimism. ! (E) the coach displayed an attitude of exuberance which was guardedly optimistic.

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01:15

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CAT and Process of Error Identification The Identification process will help you overcome one of the greatest challenges on the GMAT CAT: time.

If you analyze the structure of the sentence, you can determine that it begins with a participial phrase (-ing form). Then there is a comma and underlined text. The grammar problem is that the subject of the participle “trumpeting” is supposed to follow the comma. Have a look at the Wrong Answer Factory at work in this question. Choice (A) is wrong because the coach’s attitude is supposed to be the subject of the participle, which is impossible here. Choice (B) should be avoided because it reproduces the same error. Choice (C), although it offers different wording, reproduces the same type of error (illogical connection between participle, “Trumpeting,” and subject “the attitude of the coach,” as in (A) and (B)). Choice (E) fixes the initial mistake because it is the coach that is trumpeting the victory and not the “coach’s attitude” or “the attitude of the coach”. However choice (E) introduces a new mistake with “which was guardedly optimistic” and breaks the parallelism. Only choice (D) is valid, since it correctly refers to the participle “Trumpeting” and retains the parallelism. 2) Looking for wrong answers is as effective as looking for right answers. On a Multiple Choice Question test the right answer is always in front of you. By employing common sense and an understanding of how the Wrong Answer Factory works, you can identify and eliminate wrong answers, leaving the right answer ready to choose. Let’s look at an example: What is the capital of Madagascar? (A) (B) (C) (D)

Los Angeles Madrid Antanarivo Bangkok

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Step 1

Unless you spent time in Madagascar, or study maps in your spare time, there is little chance that you know the answer to this question. However, you may be able to eliminate answer choices (A) and (B) since there is a good chance that you know Los Angeles is in the USA, Madrid is in Spain, and neither is in Madagascar. If you know a little more geography you might know that Bangkok is in Thailand, and bingo you pick up the right answer just by eliminating the wrong answers. On a Multiple Choice Question test looking for wrong answers can be just as effective as looking for right answers. Let’s take an example from the GMAT to illustrate this principle: GMAT CAT – Section 3 : Quantitative

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A bookstore makes a gross profit of 15% of the wholesale cost on a certain book it carries. If each book is sold by the bookstore for a retail price of $23, what is the wholesale price of the book? ! ! ! ! !

(A) (B) (C) (D) (E)

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$10.00 $11.50 $19.55 $20.00 $23.00

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Suppose you don’t know the formula to solve this problem, or you don’t know the difference between wholesale cost and retail price and cannot come up with the answer on your own. It’s time to start eliminating. The Process of Error Identification should be learned and practiced. It allows you to eliminate answer choices even when you do not know which choice is best.

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The MBA Center Approach

3) Guessing Good guesswork is still important no matter how much other preparation you do. Sometimes the best you can do is eliminate two or three answer choices, and move on to the next question. You should use guesswork for two reasons: first, you cannot skip a question on the GMAT CAT; second, and more importantly for a high test score, your testing level is constantly checked and adapted. By a certain point on the test, your testing abilities have been generally determined and if you’ve done well up to that point you’ll be given difficult questions with high score values. If you become stuck, especially toward the end of a section, use strategic guesswork for a correct answer and move on into higher-score territory. For quantitative questions calculation is not always necessary to eliminate wrong answers. You can also use common sense to eliminate answer choices that are obviously incorrect or do not belong.

MEDIUM

QUESTIONS:

Questions of medium difficulty are easy enough to understand but difficult to answer because the answer choices are deliberately tricky – read answer choices completely and don’t be hasty.

Look at this example: GMAT CAT – Section 3 : Quantitative

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If Lorenzo walks to work at 3 miles per hour and returns along the same route at 2 miles per hour, what is his average speed, in miles per hour for the round trip? ! ! ! ! !

(A) (B) (C) (D) (E)

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01:13

2.0 2.2 2.4 2.5 3.0

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Suppose you do not know how to solve this problem, or that you have little time left. Thanks to the Wrong Answer Factory we can eliminate (A) and (E), which reuse numbers already seen in the initial statement, as well as (D), because it is an obvious average between 2 and 3. You still have two options left, (B) and (C), and if you are still unsure of the answer, guess and move on to the next.

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Step 1

4) Easy and difficult questions test the same material. Two questions may test the same material, but vary in level of difficulty. Sometimes, this is because of traps within the question itself, other times it’s because the answer choices have been altered to make them easier or harder. Of these two sentences which is the easier to fix? Sentence 1: Both Christina and Marion is hungry. Sentence 2: Both Christina and Marion, one having chosen not to eat with Jonathan because he always eats greasy fried food and the other having made the same choice because she refuses to be seen in public with Jonathan, wants food. Well, it should be apparent at a glance that Sentence 2 seems to have a lot of information written in a very confusing manner, and that Sentence 1 is a very simple statement of fact with just one small easily recognizable error. Did you spot what it was? The same grammatical rule, subject-verb agreement, was tested in both sentences. (Subject-verb agreement is a common testing point in the Sentence Correction section.) However, the error was much easier to spot in Sentence 1 than in Sentence 2, which was intentionally written to confuse you. You can quickly see in Sentence 1 that there are two actors, Christina and Marion, and therefore that the singular verb “is” must be changed to the plural verb “are” in order to correct the subjectverb agreement error. The second sentence, which frankly is far more Phineas-like, contains some information we don’t care about (for example, the bit about ”greasy fried food”) and a misleading singular noun, ”Jonathan”, which tries to mask the subject-verb agreement error at the end. The same type of correction as in Sentence 1 needs to be made here: the singular verb ”wants” should be changed to the plural verb ”want”. Just as important as correcting the grammatical error is noticing how Phineas can turn an easy question into a hard one just by adding extra clauses and information. When you see a question that seems wordy and difficult, try to reduce it to its essential parts. (In the sentences above these were simply the subjects, Christina and Marion, and the respective verbs is/are and wants/want). Here are two reasons why you should reduce: - Easy and difficult questions often test the same problems. - You’ll be able to choose the best answer more quickly and more accurately when you do.

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The MBA Center Approach

CAT AND LEVEL OF DIFFICULTY Using the level of difficulty of a question to your advantage is an excellent strategy for the GMAT. With some practice you’ll begin to recognize which questions are easy, medium, or difficult. Keep in mind that: -

The The The The

Computer Adaptive Test starts with medium questions. difficulty level of each question varies a lot at the beginning. material tested on the GMAT does not vary significantly from question to question. presence or absence of a trap makes a question more or less difficult.

For instance, if you recognize a difficult question and realize a possible answer came too easily to you, then you’ve probably made one of the three common mistakes, and a trap was set for you by Phineas. On the other hand if a question seems easy and an answer seems clearly right, then trust your instincts: easy questions have no real traps. Consider these two questions: Question 1 GMAT CAT – Section 3 : Quantitative

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A machine manufactures 10 nails per hour for three hours. Then the machine is sped up and produces 20 nails per hour for three hours. The machine, over the 6 hours, produces an average of how many nails per hour?

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(A)12 (B)15 (C)16 (D)20 (E)90

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01:12

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Question 2 GMAT CAT – Section 3 : Quantitative

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If a book that is usually sold for $23.95 is now on sale for $19.95, then the price decrease is closest to:

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(A) 10 (B) 16 (C) 20 (D) 25 (E) 30

% % % % %

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! ! ! ! !

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01:11

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These questions probably appear, at a glance, to have about the same level of difficulty. An intuitive answer to question 1 would be 15, and is effectively the best answer. An intuitive answer, to the second question would be 20%, and is wrong. © The MBA Center

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Step 1

HOW TO USE THE LEVEL OF DIFFICULTY: Question 1 is an easy question (score value 450), and you can trust your instinct if you chose (B). Question 2 is of medium difficulty, and if you thought 20 percent was the right answer don’t trust your instinct (unless you score 700 on your diagnostic test). If you do not know how to solve this question you can always use the Process of Error Identification. Choices (D) and (E) are wrong because the percentage decrease is too high. Choice (A) is wrong because the percentage decrease is too low. Understanding how the Wrong Answer Factory works, you might recognize Phineas’ trap: the possible confusion between a percentage increase from $19.95 to $23.95, which is 20%, and a percentage decrease from $23.95 to $19.95, which is less than 20%: (23.95 19.95)/23.95. The only possible answer is (B).

SUMMARY The GMAT CAT is not a linear test. It adapts to the level of each test taker who receives points according to the difficulty level of the question. The computer adds or subtracts more points at the beginning of an adaptive section and fewer at the end. Your effort and concentration should be greater at the beginning when questions directly affect your final score. Since the Process of Error Identification is a very effective method and you cannot write on the monitor screen when eliminating wrong answers, our advice is to take the time to draw a scoring grid. Phineas offers you the same chances to make mistakes throughout the test. Learn how to recognize the most common traps. Once familiar with Phineas’ tricks, you’ll find that looking for wrong answers can be as effective as looking for right answers. Use the level of difficulty to your advantage. On difficult questions, Phineas always uses traps we’ve explained by Wrong Answer Factory principles: Consider answer choices very carefully. On easier questions the traps set by Phineas are not difficult to spot: Use your instinct.

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II. LESSONS

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Quantitative Section Introduction

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Total PrepKit for the GMAT®

Quantitative Section

GENERAL OUTLINE

The Quantitative Section of the GMAT CAT is designed to test your ability to think and reason quantitatively. There are two types of questions in this section: Problem Solving and Data Sufficiency. Both of these question types test your mastery of basic mathematics and your ability to solve complex problems. This introduction is designed to familiarize you with the Quantitative Section of the GMAT CAT and the material covered. The lessons which follow this preview will discuss Problem Solving and Data Sufficiency questions in greater detail and will give you specific strategies to help you improve your score on the Quantitative Section of the GMAT CAT.

THE

FOLLOWING TOPICS WILL BE COVERED IN THIS LESSON:

The GMAT Quantitative Section: General GMAT Math: An Overview CAT Strategy Guessing And The CAT

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Introduction

THE GMAT QUANTITATIVE SECTION: AN OVERVIEW The Quantitative Section of the GMAT CAT is a 75-minute section designed to test your mastery of basic mathematical concepts and your ability to reason quantitatively. In this section there are 37 multiple-choice questions which fall into two distinct categories: Problem Solving and Data Sufficiency. Problem Solving questions are simply math problems in a multiple-choice format. Data Sufficiency questions are similar to Problem Solving questions, but you are not required to arrive at a solution. Instead, you must determine whether the information in the question is sufficient to solve the problem. These two types of questions are intermingled throughout the Quantitative Section and are presented in random order. You should expect approximately 23 Problem Solving and 14 Data Sufficiency questions in this section. However, because the number of each question type is decided by the computer, the actual allocation of questions may vary. Although Problem Solving and Data Sufficiency questions generally test the same skills and require the same basic knowledge of mathematics, they will be taught separately in this course because they require very different strategies and techniques. What The Quantitative Section Tests The Quantitative Section of the GMAT requires knowledge of only a limited range of fairly low-level math concepts. These concepts are the same for every GMAT and are tested in similar ways on each test. The most commonly tested math topic on the GMAT is arithmetic. Virtually all of the Problem Solving and more than three-quarters of the Data Sufficiency questions require at least some knowledge of basic arithmetic. Algebra is the second most commonly tested topic in the Quantitative Section; over half of the questions include algebra in some form or another. Geometry is the third most commonly tested math topic; approximately 15 percent of all GMAT math problems relate to geometry. A few problems in the Quantitative Section relate to topics such as logic, data interpretation (graphs), and sets. Many GMAT math problems, particularly word problems, combine two or more math topics. Unfortunately, many people who take the GMAT have forgotten the basic math skills tested. You probably learned most of the math covered before you left high school, which was a long time ago. Don’t worry though, you have time now to brush up on the necessary math before you take the test. All of the math topics tested on the GMAT are covered in the Comprehensive Math Review for the GMAT, which is Step 2 in this book. We recommend that you look through the math review and become familiar with the math covered before you begin the Problem Solving and Data Sufficiency lessons which follow.

THE CHALLENGE The Quantitative Section tests not only your mastery of basic math, but also your ability to reason through complex problems quickly and accurately. Generally, the difficulty in solving GMAT math problems is not calculating the answers, but sorting through the information given in the questions and quickly finding the best approach to solving them. The typical question in this section combines several simple math concepts in a way designed to confuse the test taker. Your task then is to identify the math concepts tested and work through the problem logically, and above all, quickly. The principal challenge of the Quantitative Section of the GMAT is time. If you were given an unlimited amount of time, you could probably solve all or nearly all of the questions. However, the time given is very limited and most test takers have difficulty finishing the section in the time allowed. For this reason the MBA Center method stresses both mastery of the necessary mathematics and employment of the time-saving strategies in the Problem Solving and Data Sufficiency lessons which follow.

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Total PrepKit for the GMAT®

Quantitative Section

GMAT MATH The Quantitative Section of the GMAT CAT, like the Verbal Section, is adaptive. This means that the computer determines your ability and selects questions that match your level. How The CAT Works When you begin the Quantitative Section of the GMAT CAT, the computer will give you a question (either Data Sufficiency or Problem Solving) of medium difficulty, in other words, a question that roughly half of all test takers get right and roughly half get wrong. If you answer the first question correctly the computer will give you a harder question. Likewise, if you answer the first question incorrectly the computer will give you an easier question. This process is then repeated for the rest of the section. As you progress through the section each successive jump gets smaller and smaller as the computer focuses in on your level. In theory, you will eventually arrive at a point where every question will be about at your level. The score you receive for the section depends not on the number of questions you answer correctly, but on the level of difficulty of those questions. The idea is to award more points for difficult questions than for easy ones. Therefore, correct answers to difficult questions increase your score more than do correct answers to easy questions. CAT Strategy In order to maximize your score on the Quantitative Section of the GMAT, it is important to keep in mind how the CAT arrives at a score. Remember, the computer tries to find your level of ability and present you with questions accordingly. Early in the section the computer makes large jumps in order to find your general level of ability. As the section progresses, the jumps get smaller and smaller as the computer focuses in on your level. Because your final score depends on the level of difficulty of the questions you answer correctly, it is important that you answer the early questions correctly in order to get quickly to the harder, more valuable questions.

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Introduction

Time Management On The CAT Because of the incredible time pressure on the CAT, it is important that you have a strategy for managing time. Use the chart below to help pace yourself on the Quantitative Section of the CAT. Those test takers who are weaker at math may want to spend a bit more time on the first eight questions to make sure they are answered correctly. Likewise, test takers who are stronger at math should move a bit more quickly through the early questions in order to conserve time for the difficult questions later in the section.

Time

Questions 5

25

37

Out of the Blocks — Questions 1–8 The first eight questions are by far the most important for determining your score. Because the CAT is making large jumps at this stage of the test, a wrong answer is far more damaging to your score than is a wrong answer later on in the section. You can spend a bit more time per question here than you can later in the test. Take your time, check your work and avoid guessing. Try to finish the first eight questions before twenty minutes have elapsed in the section. Cruising — Questions 9–25 These questions are still quite important, but a wrong answer here won’t be as damaging to your score as a wrong answer in the first eight questions. You should move quickly and efficiently. Make an honest attempt to answer all of these questions, but if you get stuck, go ahead and guess. You should be done with these questions before an hour has elapsed in the section. The Final Stretch — Questions 26–37 These last twelve questions don’t influence your score as much as the previous questions. You should answer each of these questions quickly and don’t hesitate to guess if you find the question too difficult. When you get the 5-minute warning, answer the rest of the questions.

GUESSING AND THE CAT Guessing is especially important on the CAT for two reasons: 1) You can’t skip questions on the CAT. The computer will not let you move on to the next question until you answer the question you are currently on, so if you don’t know the answer to a question, you must guess. Don’t worry. There isn’t a guessing penalty on the CAT. 2) Because the computer adapts to your level, you should find that nearly every question on the test is difficult. For this reason you will have to guess more often than you would on the pencil-and-paper test.

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Total PrepKit for the GMAT®

Quantitative Section

Because guessing is necessary on the CAT, it is important that you become good at it. By using the techniques and strategies described in the Problem Solving and Data Sufficiency lessons, you will be able to eliminate several wrong answer choices and improve your chances of guessing the correct answer. Answer every question in the section even if you have to guess. When time expires, every question left unanswered in the section is considered wrong. For this reason it is important that you answer every question in the section, even if you have to take random guesses at the end. Remember there is no penalty for getting a question wrong, and if you take a random guess on a question you have at least a 20 percent chance of getting it right. So make sure to allow enough time at the end to guess on the final questions. You should of course try to eliminate any wrong answers you can, but if you can’t, just take a guess.

A FEW FINAL WORDS

ON THE

CAT

Taking notes is very important Materials for taking notes are provided at the test center. You can use it in any way you find useful, including solving equations and drawing diagrams. Be careful to transfer information carefully and accurately from the computer screen to your notes. We recommend that you practice using note-taking materials when you take the practice GMAT CATs. Calculators are not permitted on the GMAT You are not permitted to use a calculator when taking the GMAT. Because many of the questions require you to do calculations, you should practice calculating in your notes before you actually take the test.

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Step 2 Math Review

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Total PrepKit for the GMAT®

Step 2.1 Lesson

GENERAL OUTLINE

The Quantitative Section of the GMAT CAT requires a good understanding of the basic concepts of arithmetic, algebra, and geometry, and the ability to apply those concepts efficiently and accurately. For many test takers (perhaps a majority) the math tested is ancient history. This chapter provides a quick review of the key math concepts frequently tested on the GMAT. We advise you to brush up on the math covered in this lesson before you move on to the Problem Solving and Data Sufficiency lessons which follow. This lesson is a basic math review, not a math course; test takers who are particularly weak in math may wish to consult a math textbook for a more thorough discussion of the math topics discussed.

THE

FOLLOWING TOPICS WILL BE COVERED IN THIS LESSON:

Number Properties Fractions Percents Average, Median, And Mode Exponents And Square Roots Equations Quadrilaterals Triangles Circles Phineas’ Favorite Word Problems

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Math Review

1. NUMBER PROPERTIES Real numbers — numbers that have locations on the number line. All numbers on the GMAT are real numbers. Greater than — to the right on the number line (symbol: >). Less than — to the left on the number line (symbol: <). Positive — greater than 0 (to the right of 0 on the number line). Negative — less than 0 (to the left of 0 on the number line). Q: Which is greater: –8 or –15? A: –8 is to the right of –15 on the number line, and so –8 > –15.

If you know what imaginary and complex numbers are, you can forget about them while you’re taking the GMAT.

Integers — the positive whole numbers, zero, and the negative whole numbers — numbers that can be expressed without a decimal or fraction. The integers: . . . –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, . . . Digits — the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, used in combination to represent integers greater than 9 and less than –9. Some positive 2-digit numbers: 10, 11, 12, 13, 29, 36, 63, 77, 90 In a whole number, the rightmost digit is the units’ digit or ones’ digit. The next digit to the left is the tens’ digit. Continuing to the left the digits are the hundreds’, thousands’, and so on. The digits, if any, to the right of the decimal point are the tenths’, hundredths’, thousandths’, and so on. The 4 Basic Operations — addition subtraction multiplication division

Symbol

Result

+ – × or • ÷ or fraction bar

sum difference product quotient

Ex: The sum of 2 and 7 is 9. The product of 2 and 7 is 14. Even numbers — integers that are divisible by 2. The even numbers: . . . –10, –8, –6, –4, –2, 0, 2, 4, 6, 8, 10,. . . Odd numbers — integers that are not divisible by 2. The odd numbers: . . . –9, –7, –5, –3, –1, 1, 3, 5, 7, 9, . . . You can predict whether a sum, difference, or product will be even or odd. EVEN ± EVEN = EVEN EVEN ± ODD = ODD ODD ± ODD = EVEN

EVEN × EVEN = EVEN EVEN × ODD = EVEN ODD × ODD = ODD

There is no need to memorize these rules. Just remember that such rules exist. You can use any even and odd numbers to remind yourself. Q: Is the product of two odd numbers even or odd? A: Think of any two odd numbers, say 3 and 5. The product of 3 and 5 is 15, which is odd, and so you can say that the product of any pair of odd numbers is odd. If integer A divided by integer B equals an integer, you can say that A is a multiple of B, and you can say that B is a factor of A. Ex: Some multiples of 10 are: 10, 20, 350, 970, –10, –440, and 0. Ex: The factors of 10 are: 10, 5, 2, 1, –1, –2, –5, and –10. Remainder — the integer that is left over after division. If positive integer A is not a multiple of positive integer B, then when you divide A by B you will get a quotient and a remainder.

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Note that you cannot predict the even/oddness of a quotient. When you divide an even by an even, for example, the result might be even (8 ÷ 2 = 4), or it might be odd (10 ÷ 2 = 5), or it might not be an integer at all (10 ÷ 4 = 2.5).

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Step 2.1 Lesson

Ex: When you divide 37 by 5, the quotient is 7 with a remainder of 2. Ex: When you divide 9 by 23, the quotient is 0 with a remainder of 9. Sometimes the best way to do a remainder problem is to use a specific case. Q: When positive integer A is divided by 7, the remainder is 3. What is the remainder when 4 times A is divided by 7? A: Think of a positive integer that would leave a reminder of 3 when divided by 7. One such number is 10. Multiply 10 by 4 and you get 40. Divide 40 by 7 and you get 5 with a remainder of 5. So the answer is 5. By definition, 1 is not a prime number.

Prime number — a positive integer that has exactly two distinct factors, 1 and itself. The smallest prime number is 2 — its only factors are 1 and 2. The next ten prime numbers are 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.

Note that 2 is not only the smallest prime number, but also the only even prime number.

There is no easy way to recognize a prime number. To test a number for primeness, you just have to keep trying to divide it by prime numbers. Q: Is 187 a prime number? A: Try dividing 187 by prime numbers, starting with the smallest one, 2. Here’s where the divisibility tests come in handy. 187 is not divisible by 2 (its last digit is not even). It’s not divisible by 3 (the sum of its digits is 16, which is not a multiple of 3). It’s not divisible by 5 (its last digit is not 5 or 0). It’s not divisible by 7 (187 w 7 = 26 with a remainder of 5). It is divisible by 11 (187 w11 = 17). Therefore 187 is not prime. Note that you need to try dividing by prime numbers only. Q: Is 191 a prime number? A: 191 is not divisible by 2 (its last digit is not even). It’s not divisible by 3 (the sum of its digits is 11, which is not a multiple of 3). It’s not divisible by 5 (its last digit is not 5 or 0). It’s not divisible by 7 (191 w 7 = 27 with a remainder of 2); by 11 (191 w 11 = 17 with a remainder of 4); by 13 (191 w 13 = 14 with a remainder of 9); or by 17 (191 w 17 = 11 with a remainder of 4). Therefore 191 is prime. When can you stop dividing by prime numbers? When you get a quotient smaller than the prime number you’re dividing by. Prime factorization — the expression of a positive integer as a product of prime numbers. The prime factorization of 36, for example, is 3 s 3 s 2 s 2. To determine an integer’s prime factorization, break it down into factors bit by bit until all the factors are prime. Q: Find the prime factorization of 1,650. A: Break 1,650 down into factors bit by bit. You might first break it down this way: 1,650 = 165 s 10 Then you could reexpress 165 as 5 s 33 and 10 as 2 s 5: 165 s10 = 5 s 33 s 2 s 5 All that’s left now is to reexpress 33 as 3 s 11: 5 s 33 s 2 s 5 = 5 s 3 s 11 s 2 s 5 That’s the prime factorization. To put it in standard form, put the prime factors in order from least to greatest: 1,650 = 2 s 3 s 5 s 5 s 11

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Math Review

Common multiple — a number that is a multiple of two or more given integers. Ex: The number 12 is a common multiple of 2, 3, 4, and 6. Least common multiple (LCM) — the least positive integer that is a multiple of all the integers in a given set. To determine the LCM of a set of integers, break each integer in the set down into its prime factorization. Next, eliminate duplicate prime factors, leaving only those duplicate factors that are raised to the highest power. Multiply the remaining factors and the LCM is the product. Q: What is the least common multiple of 3, 4, 9, and 27? A: Break each number down into its prime factors: 3 is a prime number, so its prime factorization is simply 3; 4 = 2 × 2, or 22; 9 = 3 × 3, or 32; and 27 = 3 × 3 × 3, or 33. Next, eliminate duplicate factors, leaving only those duplicates which are raised to the highest power. You have a 33, so you can eliminate the 3 and 32, leaving you with 22 × 33 = 108, which is the LCM. When you want to find the LCM of two integers, sometimes the easiest approach is to check out successive multiples of the larger integer until you find one that is also a multiple of the smaller integer. Q: What is the least common multiple of 24 and 32? A: Take the larger integer, 32, and keep multiplying it until you find a multiple that is also a multiple of 24. 32 × 2 = 64, which is not a multiple of 24. 32 × 3 = 96, which is a multiple of 24. The LCM of 24 and 32 is 96. Common factor — a number that is a factor of two or more given integers. Ex: 4 is a common factor of 32 and 40. Greatest common factor (GCF) — the greatest integer that divides with no remainder into two or more given integers. Ex: 1, 2, 4, and 8 are all the positive common factors of 32 and 40. Of these, 8 is the greatest common factor. The greatest common factor is equal to the overlap in the prime factorizations. Q: What is the greatest common factor of 48 and 84? A: First figure out the two prime factorizations: 48 = 2 × 2 × 2 × 2 × 3 and 84 = 2 × 2 × 3 × 7 Then find the overlap. Both factorizations have at least two 2’s and a 3, so the overlap is: 2 × 2 × 3 = 12 Thus the greatest common factor is 12. Sometimes you’ll find two prime factorizations that have no overlap, in which case the greatest common factor is 1. Q: What is the greatest common factor of 48 and 49? A: First figure out the two prime factorizations: 48 = 2 × 2 × 2 × 2 × 3 and 49 = 7 × 7 These two have no prime factors in common. Therefore the greatest common factor is 1. Integers with no common factor greater than 1 are called relative primes.

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You might have known immediately that the GCF of 48 and 49 is 1, because consecutive integers are always relative primes.

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Total PrepKit for the GMAT®

Step 2.1 Lesson

PRACTICE QUESTIONS 1-10 (NUMBER PROPERTIES) 1. What is the product of the greatest 2-digit multiple of 7 and the greatest 2-digit prime number? (A) (B) (C) (D) (E)

9,312 9,408 9,506 9,603 9,702

2. If the sum of two integers A and B is even, which of the following must be even? I. II. III. (A) (B) (C) (D) (E)

A×B A÷B A–B I only II only III only I and III only I, II, and III

3. What is the smallest positive integer that is a multiple of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10? (A) 360 (B) 630 (C) 840 (D) 1,260 (E) 2,520 4. When positive integer X is divided by 9, the remainder is 5. What is the remainder when 4 times X is divided by 6? (A) (B) (C) (D) (E)

1 2 3 4 5

5. Which of the following has the greatest number of distinct prime factors? (A) 30 (B) 32 (C) 34 (D) 36 (E) 38

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Math Review

AB +BA CDC 6. In the correctly worked computation above, A, B, C, and D represent distinct nonzero digits. What is the value of A + B + C + D? (A) (B) (C) (D) (E)

14 16 18 20 It cannot be determined from the information given.

7. What is the units’ digit of (493)(915)(381)(756)(29)? (A) (B) (C) (D) (E)

0 1 4 5 6

8. If p and q are distinct integers, and the sum of p and q is zero, which of the following statements must be true? (A) (B) (C) (D) (E)

The The The The The

product product product product product

of of of of of

p p p p p

and and and and and

q q q q q

is is is is is

even. odd. negative. zero. positive.

9. When positive integer X is divided by 9, the remainder is 6. When positive integer Y is divided by 10, the remainder is 8. What is the remainder when X × Y is divided by 6? (A) (B) (C) (D) (E)

0 1 2 3 4

10. If the sum of two prime numbers a and b is prime, which of the following must be true? I. a – b is odd. II. ab is even. III. a ≠ b (A) (B) (C) (D) (E)

III only I and II only I and III only II and III only I, II, and III

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Total PrepKit for the GMAT®

Step 2.1 Lesson

2. FRACTIONS A fraction is a number written in the form N in which the top number N D is called the numerator and the bottom number D is called the denominator. The denominator tells you into how many equal parts a whole is divided, and the numerator tells you how many of those parts you’re considering. Equivalent fractions look different, but they’re equal in value. Any fraction can be expressed as an equivalent fraction simply by multiplying the numerator and the denominator by the same number. Ex: The fraction 2 is equivalent to 4 and 6 . 5 10 15 To reduce a fraction, divide the numerator and denominator by their greatest common factor. When the numerator and denominator have no common factor greater than 1, the fraction is expressed in its lowest terms. Q: Reduce 16 . 24 A: The greatest common factor of 16 and 24 is 8. Divide both the numerator and denominator by 8 and you end up with 2 . 3 To add or subtract fractions, convert the fractions to equivalent fractions with the same denominator and add or subtract the numerators. Q: 1 + 1 = ? 2 3 A: Convert each fraction to an equivalent fraction with a denominator of 6: 1 + 1 = 3 + 2 2 3 6 6 Now add the numerators and put the sum over the 6: 3 + 2 = 3+2 = 5 6 6 6 6 Q: 3 – 1 = ? 4 6 A: Convert each fraction to an equivalent fraction with a denominator of 12: 3 – 1 = 9 – 2 4 6 12 12 Now subtract the numerators and put the difference over the 12: 9 – 2 = 9–2 = 7 12 12 12 12 To multiply fractions, multiply the numerators and multiply the denominators. Q: 1 s 2 = ? 6 3 A: Multiply the numerators (1 s 2 = 2), and multiply the denominators (6 s 3 = 18): 1 s 2= 1s2 = 2 = 1 6s3 6 3 18 9

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Math Review

You can sometimes avoid big numbers and a lot of simplification by canceling common factors before you multiply. Look for factors common to the numerator of one fraction and the denominator of the other. Q: 14 × 30 = ? 45 49 A: You could just go ahead and multiply the numerators and multiply the denominators: 14 × 30 = 420 45 49 2205 The result 420 can be simplified. But it would have been easier 2205 to cancel out common factors before multiplying. The numerator of 14 and the denominator of 30 are both multiples of 7, so you can 45 49 cancel a factor of 7 from each: 14 × 30 = 2 × 30 45 49 45 7 Similarly, the denominator of the first fraction and the numerator of the second are both multiples of 15, so you can cancel a factor of 15 from each: 2 × 30 = 2 × 2 = 4 45 7 3 7 21 To divide fractions, first flip the second fraction (the one after the ÷ sign), and then multiply. Q: 1 ÷ 2 = ? 6 3 A: First flip the second fraction, and then multiply: 1 ÷ 2 = 1 × 3 = 1×3 = 3 = 1 12 4 6×2 2 6 6 3 To divide an integer by a fraction, or a fraction by an integer, think of the integer as a fraction with a denominator of 1. Q: 3 ÷ 8 = ? 4 A: Rewrite the integer 8 as the fraction 8 . Then flip this second 1 fraction and multiply: 3 ÷ 8= 3 ÷ 8 = 3 × 1 = 3 32 8 4 4 1 4 Improper fraction — a fraction with a numerator that is bigger than the denominator. A positive improper fraction will have a value greater than 1. Ex: 23 is an improper fraction, because the numerator 23 is greater 5 then the denominator 5.

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Step 2.1 Lesson

Mixed number — a number with an integer part and a fraction part that is less than 1. Improper fractions can be expressed as mixed numbers. Ex: The improper fraction 23 can also be expressed as the mixed 5 3 number 4 . 5 To convert an improper fraction to a mixed number, divide the denominator into the numerator to get an integer quotient with a remainder. The quotient is the integer part of the mixed number, and the remainder becomes the new numerator, which you put over the original denominator. Q: Express 100 as a mixed number. 3 A: Divide 3 into 100, which yields 33 with a remainder of 1. The integer part of the answer, then, is 33, and the fraction part is the remainder 1 over the original denominator 3: 100 = 33 1 3 3 To convert a mixed number to an improper fraction, multiply the integer part by the denominator of the fraction part, then add the numerator. The result is the new numerator, which you put over the original denominator. Q: Express 21 3 as an improper fraction. 7 A: Multiply the integer part 21 by the denominator 7, then add the numerator 3, yielding 150 for the new numerator. Put that over the original denominator: 21 3 = 150 7 7 Reciprocals — two numbers whose product is 1. Ex: 3 and 4 are reciprocals because 3 × 4 = 1. 4 3 4 3 Finding the reciprocal of a fraction is easy—just flip it—that is, switch the numerator and denominator. Q: What is the reciprocal of 2 ? 5 A: Flip it. The reciprocal is 5 . 2 The reciprocal of a positive number is positive, and the reciprocal of a negative number is negative. Q: What is the reciprocal of – 3 ? 8 A: Flip the fraction and keep the minus sign. The reciprocal is – 8 . 3 To find the reciprocal of another type of number, first reexpress it as a fraction.

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Math Review

Q: What is the reciprocal of 13 1 ? 3 A: First turn the mixed number into a fraction. Multiply 13 and 3, and then add 1, giving you 40 for the new numerator. Put that over the original denominator 3 and you get 40 . Now, to get the 3 reciprocal, flip it. The answer is 3 . 40 Comparing fractions — When you have two fractions with a common denominator, it’s easy to see which fraction is greater — it’s the one with the larger numerator. Q: Which is greater: 7 or 8 ? 25 25 A: The fractions have the same denominator, so the greater one is the one with the larger numerator: 8 . 25 One way to compare fractions that do not have a common denominator is to reexpress them so that they do. Q: Which is greater: 4 or 5 ? 7 8 A: Reexpress both fractions with a common denominator of 56: 4 = 32 7 56

and

5 = 35 8 56

The greater fraction is the one with the larger numerator: 35 is 56 greater than 32 , and so 5 is greater than 4 . 56 8 7 Sometimes it’s easier to compare fractions by reexpressing them with a common numerator. In such case, the one with the smaller denominator will be the greater fraction. Q: Which is greater: 5 or 10 ? 16 33 A: In this case it’s a lot easier to use the common-numerator approach than the common-denominator approach. Double the numerator and denominator of the first fraction: 5 = 10 16 32 Now the fractions have the same numerator, so the greater one is the one with the smaller denominator: 10 is greater than 10 , and 32 33 so 5 is greater than 10 . 16 33 Another way to compare fractions is to convert them both to decimals. Q: Which is greater: 16 or 13 ? 25 20 A: Convert both fractions to decimals: 16 = 0.64 and 25

13 = 0.65 20

It is especially easy to convert a fraction to a decimal when you use a calculator. But of course that is not possible on the GMAT.

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Step 2.1 Lesson

Sometimes when you convert a fraction to a decimal by dividing the bottom into the top, you get a decimal that goes on forever. This kind of endless decimal is a repeating decimal — a decimal with one digit or sequence of digits that repeats indefinitely. Q: Convert 7 to a decimal. 15 A: When you divide the numerator 7 by the denominator 15, you get: 0.4666666666... 15 7.0000000000...

)

Q: Convert 15 to a decimal. 7 A: When you divide the numerator 15 by the denominator 7, you get: 2.1428571428... 7 15.0000000000...

)

In the first example above, it’s a single digit that repeats. To write that more simply, put a bar over the repeating digit: 0.4666666666... = 0.46 In the second example, it’s a the sequence of digits 142857 that repeats. To write that more simply, put a bar over the repeating sequence: 2.1428571428... = 2.142857 To find a particular digit in a repeating decimal, note the number of digits in the sequence that repeats. If there are 2 digits in that sequence, then every 2nd digit is the same. If there are 3 digits in that sequence, then every 3rd digit is the same. And so on. Q: What is the 49th digit after the decimal point in the decimal equivalent of 5 ? 27 A: The decimal equivalent is 0.185185185.... There are 3 digits in the sequence that repeats, so every 3rd digit is the same: the 3rd, 6th, 9th, 12th, 15th etc. digits are all 5. Thus the 48th digit is also a 5, and therefore the 49th digit is a 1.

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Math Review

PRACTICE QUESTIONS 11-20 (FRACTIONS) 11. All of the following are equal EXCEPT: (A)

4 5

(B)

8 10

(C) 16 25

(D) 32 40

(E) 40 50

(C) 1 4

(D) 1 3

(E) 1 2

(D) 12

(E) 14 2 5

12. 1 + 2 × 3 – 4 = 2 3 4 5 (A) 0

(B) 1 5

13. What is the product of 2 2 and 4 1 ? 3 2 (A) 7 1 6

(B) 8 1 3

(C) 10 3 5

14. What is the sum of the reciprocals of 1 1 and 1 2 ? 9 3 (A)

9 25

(B) 27 50

(C) 1 23 50

(D) 1 1 2

(E) 2 7 9

(D) 6 9

(E) 9 14

15. Which of the following is greatest? (A) 2 3

(B) 3 4

(C) 5 7

16. Which of the following has the greatest reciprocal? (A) – 5 4

(B) – 4 5

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(C) 4 5

(D) 6 5

(E) 5 6

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Step 2.1 Lesson

17. What is the 99th digit after the decimal point in the decimal equivalent of 1 ? 11 (A) (B) (C) (D) (E)

0 1 3 6 9

18. A recipe requires 2 1 cups of flour, 2 3 cups of sugar, and 1 1 cups of milk 2 4 3 to make one cake. Victor has 15 cups of flour, 16 cups of sugar, and 8 cups of milk. What is the greatest number of cakes Victor can make using this (A) (B) (C) (D) (E)

recipe? 5 6 7 8 9

19. Martha biked 18 2 miles in 2 hours and 40 minutes. What was her 3 average rate of speed in miles per hour? (A) 7 (B) 7 2 3 (C) 8 1 3 (D) 9 (E) 9 1 3 20. Exactly 3 of the people in the room are under the age of 21, and exactly 7 5 of the people in the room are over the age of 65. If the total number 13 of people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21? (A) (B) (C) (D) (E)

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21 35 39 60 65

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Math Review

3. PERCENTS Most percent problems can be solved by plugging into one basic formula: Percent × Whole = Part This formula describes the relationship among three quantities. Given any two of them, you can find the third. Whether you’re looking for the Percent, the Whole, or the Part, use the same formula. Q: What is 80% of 25? A: You know the Percent (80%) and the Whole (25), and you’re looking for the Part: Percent × Whole = Part 0.80 × 25 = Part Part = 20 Q: 21 is 75% of what number? A: You know the Percent (75%) and the Part (21), and you’re looking for the Whole: Percent × Whole = Part 0.75 × Whole = 21 21 = 28 Whole = 0.75 Q: 30 is what percent of 24? A: You know the Part (30) and the Whole (24), and you’re looking for the Percent: Percent × Whole = Part Percent × 24 = 30 30 = 1.25 = 125% Percent = 24 In the last example, the Part was bigger than the Whole. That’s why the Percent was greater than 100%. If the Part can be bigger than the Whole, how are you supposed to be able to tell which is the Part and which is the Whole? You can tell by watching for these little key words: “of” and “is”/“are.” The Whole is almost always associated with the word “of,” and the Part is almost always associated with the verb “is”/“are.” Q: What is 80% of 25? A: The word “what” comes just before the word “is,” and so it’s the Part. The 25 comes just after the word “of,” and so it’s the Whole. Q: 21 is 75% of what number? A: The 21 comes just before the word “is,” and so it’s the Part. “What number” comes just after the word “of,” and so it’s the Whole. Q: 30 is what percent of 24? A: The 30 comes just before the word “is,” and so it’s the Part. The 24 comes just after the word “of,” and so it’s the Whole.

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Total PrepKit for the GMAT®

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To solve a percent word problem, use the key words and your understanding of the sense of the problem to identify the Percent, the Whole, and the Part. Plug the two numbers you know into the formula and calculate the number you’re looking for. Q: In a baseball game, the starting pitcher lasted 5 innings and threw 65 pitches, 39 of which were strikes. What percent of her pitches were strikes? A: The total number of pitches (65) is the whole. The number of strikes (39) is the part. You’re looking for the percent: Percent × Whole = Part Percent × 65 = 39 Percent =

39 = 0.6 = 60% 65

Q: On his history final, John answered 84 percent of the questions correctly. If he answered 63 questions correctly, what was the total number of questions on the test? A: The number of correct answers (63) is the Part. The Percent is 84, and you’re looking for the Whole: Percent × Whole = Part 84% × Whole = 63 63 Whole = = 75 0.84 To calculate the percent increase or decrease, divide the amount of change by the original amount and multiply by 100%. Percent increase =

Amount of increase × 100% Original amount

Percent decrease =

Amount of decrease × 100% Original amount

Q: Last month, the Dow Jones average of American stocks went up from 9,875 to 10,033. What was the percent increase in the Dow Jones average last month? A: The amount of increase is 10,033 – 9,875 = 158 points. The original amount is 9,875. Plug those two numbers into the formula: Amount of increase

× 100% Original amount 158 = × 100% 9875 = 0.016 × 100% = 1.6%

Percent increase =

Q: From 1990 to 2000, the population of Middletown decreased from 73,824 to 64,596. What was the percent decrease in the population of Middletown from 1990 to 2000?

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Math Review

A: The amount of decrease is 73,824 – 64,596 = 9,228. The original amount is 73,824: Amount of decrease

× 100% Original amount 9228 = × 100% = 12.5% 73824

Percent decrease =

To calculate the result of a percent increase or decrease when you’re given the original amount, find that percent of the original amount and add it or subtract it. Q: The regular price for a box seat is $30. On Monday nights the price is reduced by 20 percent. What is the price of a box seat on Monday nights? A: First find 20% of $30: 20% of $30 = 0.2 × $30 = $6 The amount of decrease is $6. Subtract that from the regular price to get the discounted price: Discounted price = $30 – $6 = $24 It’s a bit more complicated to calculate the original amount when given the percent increase or decrease and the new amount. You cannot just multiply the percent by the new amount. The thing to do instead is to add the percent increase to 100% (or subtract the percent decrease from 100%), then divide that into the new amount. Q: This year, the regular price for a box seat is $30, which is 20 percent more than last year. What was the price of a box seat last year? A: You cannot just figure out what’s 20% less than $30, as we did in the previous example. Here you must first add 20% to 100%, which gives you 120%, and then divide that into $30: Old price =

New price $30 = = $25 120% 1.2

Be careful with combined percent increases and decreases. If a quantity increases first by x percent, and then the new quantity increases by y percent, you cannot simply say that the combined percent increase is the sum x + y. You cannot add percents in this case because they are percents of different bases. Here, for example, is a case in which 20 and 20 do not add up to 40. Q: In the first week of a clearance sale, the original price P of chair was reduced by 20 percent to price Q. In the second week price Q was reduced by another 20 percent to final price R. Final price R is what percent less than original price P? A: Reducing by 20% is the same as multiplying by 0.8. Q is 20% less than P, so: Q = 0.8P Then, R is 20% less than Q, so: R = 0.8Q = 0.8(0.8P) = 0.64P So R is 64% of P. In other words, R is 36% less than P. © The MBA Center

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PRACTICE QUESTIONS 21-30 (PERCENTS) 21. If 51 of the 85 marbles in a bag are green, what percent of the marbles are green? (A) (B) (C) (D) (E)

57% 60% 63% 65% 67%

22. 18 is 24 percent of what number? (A) (B) (C) (D) (E)

73 74 75 76 77

23. If 7 of the student body is male, what percent of the student body is 16 female? (A) (B) (C) (D) (E)

37.5% 43.75% 56.25% 62.5% 68.25%

24. In addition to the price of the meal, Janet paid sales tax equal to 8.5 percent of the price of the meal, and a tip equal to 15 percent of the price of the meal. If she paid $2.04 in sales tax, how much was the tip? (A) (B) (C) (D) (E)

$3.06 $3.36 $3.42 $3.60 $4.08

25. If the price of a painting rises from $5,000 to $100,000, what is the percent increase? (A) (B) (C) (D) (E)

58

95% 190% 950% 1,900% 9,500%

© The MBA Center

Math Review

26. A promotion gave Martin a 32 percent increase in his hourly wage. If his hourly wage after the promotion was $9.90, what was it before the promotion? (A) (B) (C) (D) (E)

$7.50 $7.60 $7.72 $8.00 $8.18

27. The price of a share of stock increased by 20 percent in one year. The following year the price increased by 30 percent. By what percent did the price increase over the two-year period? (A) (B) (C) (D) (E)

44% 45% 50% 55% 56%

28. The population of Centerville increased by exactly 20 percent between the years 1990 and 2000. If the population in the year 2000 was 15,600, what was the population in 1990? (A) (B) (C) (D) (E)

12,000 12,480 13,000 14,580 18,720

29. From 1990 to 1995, the population of Smallville increased by 50 percent, and from 1995 to 2000, the population increased by 200 percent to 13,284. The population in 2000 was how much greater than the population in 1990? (A) 2,952 (B) 4,428 (C) 7,971 (D) 8,856 (E) 10,332 30. In the first half of the 20th century, the population of a particular country increased by 200 percent. In the second half of the century, the population increased by 300 percent. What was the percent increase for the 20th century as a whole? (A) 500% (B) 600% (C) 800% (D) 1,100% (E) 1,200%

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Step 2.1 Lesson

4. AVERAGE, MEDIAN,

AND

MODE

Average (arithmetic mean) — the sum of a set of numbers divided by the number of numbers in the set Average (arithmetic mean) = Sum of the numbers Number of numbers Q: What is the average (arithmetic mean) of 2, 5, 8, 19, and 56? A: The sum of the numbers is 2 + 5 + 8 + 19 + 56 = 90. There are 5 numbers in the list, so you divide the sum by 5: Average = 2 + 5 + 8 + 19 + 56 = 90 = 18 5 5 Averaging averages — You can average the averages of two groups only if you know that the two groups are the same size. Q: A science test was administered to 40 students: 20 boys and 20 girls. The boys’ average (arithmetic mean) score was 86 and the girls’ average score was 92. What was the average score for all 40 students? A: The two groups are the same size, so you can just average the averages: Average = 86 + 92 = 178 = 89 2 2 Do not average the averages if you do not know the relative sizes of the groups. Q: A Spanish test was administered to a group of students. The boys’ average (arithmetic mean) score was 84 and the girls’ average score was 78. What was the average score for all the students? A: You do not have enough information. You can not assume that the number of boys is the same as the number of girls, and so you can not just average the averages. Weighted average — If you have two groups of different sizes, but you know the actual or relative sizes, then you can find a weighted average. To find the weighted average, multiply each average by the appropriate weighting factor before adding, and then divide by the sum of the weighting factors. If you are given actual numbers, use them as the weighting factors. Q: An English test was administered to 20 boys and 10 girls. The boys’ average (arithmetic mean) score was 84 and the girls’ average score was 78. What was the average score for all 30 students? A: Multiply the boys’ average by 20 and the girls’ average by 10, add the products, and divide the sum by 30: Average = 20(84) + 10(78) = 1680 + 780 = 2460 = 82 30 30 2

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Math Review

Using the average to find the sum — If you know the average of a list of numbers and you know how many numbers are in the list, you can use the following variation of the average formula to find the sum: Sum of the numbers = (Average) × (Number of numbers) Q: Julia paid an average (arithmetic mean) of $42 a night for 7 nights of hotel stays. What was the total amount she paid for the 7 nights of hotel stays? A: Multiply the average paid per night by the number of nights to get the total amount paid: Sum of the numbers = $42 × 7 = $294 This variation of the average formula is also useful when you’re looking for a missing number in an average. Just remember, whenever you know the average and you know how many numbers there are, then you also know what the sum is. Q: Martin’s average (arithmetic mean) score on 4 economics tests last semester was 95. If he scored 91, 97, and 100 on the first 3 tests, what was his score on the 4th test? A: Multiply the average score by the number of tests to get the sum of the test scores: Sum of the numbers = 95 × 4 = 380 The first 3 scores add up to 91 + 97 + 100 = 288, and so the 4th score was 380 – 288 = 92. Consecutive integers — integers that follow one another in order Ex: 4, 5, 6, 7, 8, 9, 10, and 11 are consecutive integers. Ex: 24, 26, 28, 30, and 32 are consecutive even integers. Ex: –5, –3, –1, 1, and 3 are consecutive odd integers. Ex: –10, –5, 0, 5, 10, 15, 20, and 25 are consecutive multiples of 5. In all of the above examples, the numbers are evenly spaced. In other words, the difference between one number and the next is constant. Consecutive numbers are often evenly spaced, but not always. Look at the following examples. Ex: 2, 3, 5, 7, 11, 13, 17, and 19 are consecutive prime numbers. Ex: 2, 4, 8, 16, and 32 are consecutive powers of 2. Average of evenly-spaced numbers — When the numbers in a list are evenly spaced, it is easy to find their average (arithmetic mean). It’s the number in the middle. Q: What is the average (arithmetic mean) of 13, 14, 15, 16, 17, 18, and 19? A: The numbers are evenly spaced, and so the average is the number in the middle: 16. If the number of numbers is even, then the average is halfway between the two numbers in the middle. Q: What is the average (arithmetic mean) of 22, 24, 26, 28, 30, 32, 34, and 36? A: The numbers are evenly spaced, but this time there is an even number (8) of them and so the average is halfway between the two numbers in the middle, 28 and 30. The average is 29. © The MBA Center

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Total PrepKit for the GMAT®

Step 2.1 Lesson

How to find the middle number — When a list of evenly spaced numbers is relatively short, it’s easy enough just to see the number that’s in the middle. For a longer list, the way to find the number in the middle is to find the average of the first and last numbers in the list. Q: What is the average (arithmetic mean) of all the odd numbers from 15 through 49 inclusive? A: The average of the whole set of numbers is the same as the average of the first and last numbers: Average = First + Last = 15 + 49 = 54 = 27 2 2 2 Finding the sum of evenly spaced numbers — Because it is easy to find the average of a set of evenly spaced numbers, it is also easy to find their sum. Remember, the sum is equal to the average multiplied by the number of numbers. Q: What is the sum of all the positive integers up to and including 99? A: First find the average by averaging the first and last: Average = First + Last = 1 + 99 = 100 = 50 2 2 2 There are 99 integers in the list, so to find the sum, multiply the average by 99: Sum = Average × Number = 50 × 99 = 4,950 To count the number of consecutive integers — subtract the smallest from the largest and then add 1. Q: There are how many positive 3-digit integers? A: The smallest of the positive 3-digit integers is 100, and the largest is 999. To count them, subtract (999 – 100 = 899) and add 1 (899 + 1 = 900). The answer is 900. Median — the middle number. To find the median, first arrange the numbers in order from least to greatest and then find the number that’s right in the middle. Q: Find the median: 12, 734, 52, –74, 345, 1, 8, –90, 23 A: Arrange the numbers by size: –90, –74, 1, 8, 12, 23, 52, 345, 734 Now the number in the middle is 12, and so the median is 12. If there’s an even number of numbers in the set, then there is no one number in the middle. In that case, find the pair of numbers in the middle and take their average (arithmetic mean). Q: Find the median: 45, 3, 67, 2, 498, 5, 3, 10 A: Arrange the numbers by size: 2, 3, 3, 5, 10, 45, 67, 498 This time there are 8 numbers in the set, so there is no number exactly in the middle. The middle pair of numbers is 5 and 10. The average of those numbers is 7.5, and so the median is 7.5. Mode — the number that appears most frequently. Q: Find the mode: 1, 1, 2, 3, 4, 4, 7, 7, 8, 8, 8, 8, 9, 10, 10 A: The number 8 appears four times, more often than any other number, and so the mode is 8.

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Math Review

If two numbers appear with equal frequency, then there are two modes. Q: Find the mode: 24, 24, 24, 25, 27, 27, 27, 28, 29, 29, 30 A: The numbers 24 and 27 both appear three times, more often than any other number, and so there are two modes: 24 and 27. If no number appears more often than once, then there is no mode. Q: Find the mode: 1, 3, 5, 7, 13, 63, 198, 873 A: No number appears more than once, and so there is no mode. Range — the positive difference between the largest and smallest values in a set of numbers. Q: Find the range: 31, 43, 25, –17, 19, 63, 18, –3 A: The largest number is 63 and the smallest is –17, and so the range is 63 – (–17) = 80. Standard deviation — a quantitative description of the dispersion, or spread, of a set of numbers. To find the standard deviation: 1. Calculate the average (arithmetic mean). 2. Calculate the differences between the average and each number in the set. 3. Square these differences. 4. Calculate the average of the squares. 5. Take the square root of that average. Q: What is the standard deviation of the set {1, 3, 3, 5}? A: You can tell by inspection that the average (arithmetic mean) is 3. The differences from the average are –2, 0, 0, and 2. The squares of the differences are 4, 0, 0, and 4. The average of those squares is 2, and the square root of that average is the square root of 2. So the standard deviation is approximately 1.4. On the GMAT, you are not likely to be asked to calculate the standard deviation for a large set of numbers. But you should have some feeling for what standard deviation means. Q: Set A = {11, 12, 13, 14, 15}. Set B = {9, 11, 13, 15, 17}. Which set has the greater standard deviation? A: You should be able to tell, without actually calculating, that Set B will have the greater standard deviation. That is because the elements in Set B are more widely dispersed — the differences between and the average are greater. (In fact, the standard deviation for Set A is the square root of 2 (about 1.4), and the standard deviation for Set B is 2 times the square root of 2 (about 2.8). Q: Set C = {11, 12, 13, 14, 15}. Set D = {81, 82, 83, 84, 85}. Which set has the greater standard deviation? A: You should be able to tell, without actually calculating, that these two sets have the same standard deviation. They have the same dispersions about their respective averages. (In fact, the standard deviation for each set is the square root of 2 (about 1.4).

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Step 2.1 Lesson

PRACTICE QUESTIONS 31-40 (AVERAGE, MEDIAN,

AND

MODE)

Questions 31-34 refer to the following sets: Set A = {0, 0, 12} Set B = {0, 0, 0, 15} Set C = {0, 1, 7, 7} Set D = {1, 4, 4, 6} Set E = {1, 4, 5, 5} 31. Which set has the greatest average (arithmetic mean)? (A) Set A (B) Set B (C) Set C (D) Set D (E) Set E 32. Which set has the greatest median? (A) Set A (B) Set B (C) Set C (D) Set D (E) Set E 33. Which set has the greatest mode? (A) Set A (B) Set B (C) Set C (D) Set D (E) Set E 34. Which set has the greatest standard deviation? (A) Set A (B) Set B (C) Set C (D) Set D (E) Set E

{0, 0, 6, 6, 6, 9, 10, 10, 12, 12} 35. What is the product of the median and the mode of the above set of numbers? (A) (B) (C) (D) (E)

64

13.5 26 32.5 45 54

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Math Review

36. After the first four tests of the semester, Claudia’s average (arithmetic mean) score is 76. What score does Claudia need on the fifth test to bring her average up to 80? (A) (B) (C) (D) (E)

84 87 90 93 96

37. A chemistry test was administered to 21 boys and 24 girls. The boys’ average (arithmetic mean) score was 60 and the girls’ average score was 90. What was the average score for all 45 students? (A) (B) (C) (D) (E)

74 75 76 77 78

38. What is the average (arithmetic mean) of all the even numbers from 186 through 540 inclusive? (A) (B) (C) (D) (E)

363 364 365 366 367

39. What is the sum of all the positive integers up to and including 50? (A) (B) (C) (D) (E)

1,250 1,275 2,050 2,450 2,500

40. The average (arithmetic mean) of three integers a, b, and c is exactly twice the median. If a < b < c, and a = 0, what is the value of c ? b (A) (B) (C) (D) (E)

2 3 4 5 cannot be determined from the information given

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Step 2.1 Lesson

5. EXPONENTS AND SQUARE ROOTS Exponents An exponent indicates how many times that number appears as a factor in a product. Q: 25 = ? A: The exponent 5 indicates that 2 appears as a factor 5 times: 25 = 2 × 2 × 2 × 2 × 2 = 32 In the expression 25, the 2 is called the base and the whole expression is called a power. It can be read “2 to a power of 5,” or “2 to the 5th power,” or most simply “2 to the 5th.” An exponent of 2 is most often read “squared,” and an exponent of 3 is most often read “cubed.” Ex: 52 is read “5 squared” and equals 5 × 5, or 25. Ex: 63 is read “6 cubed” and equals 6 × 6 × 6, or 216. Parentheses are used to show that a negative number is being raised to a power. Ex: (–3)2 equals (–3) × (–3), or 9. Ex: (–3)3 equals (–3) × (–3) × (–3), or –27. Notice that a negative number raised to an even power is positive, and that a negative number raised to an odd power is negative. Notice also that if there are no parentheses, you are to apply the exponent before the minus sign. Q: –42 = ? A: Square the 4 to get 16, then add the minus sign: –42 = –16 When a fraction or decimal between 0 and 1 is squared or cubed or raised to a higher power, the result is smaller than the original number. 3

 1 1 1 1 1 Ex:   = × × = 2 2 2 8  2 Ex: (0.9)2 = 0.9 × 0.9 = 0.81 The Rules Of Exponents To multiply powers with the same base, keep the base and add the exponents. Ex:

319 × 312 = 319 + 12 = 331

To divide powers with the same base, keep the base and subtract the exponents. Ex:

5 24 5

6

= 5 24 − 6 = 518

To raise a power to a power, multiply the exponents. Ex:

2

(610) = 610 × 2 = 620

To multiply powers with the same exponent, keep the exponent and multiply the bases. Ex:

66

59 × 49 = (5 × 4)9 = 209

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Math Review

Square Roots The number A is a square root of B if A squared equals B. Q: What are the square roots of 9? A: 3 squared equals 9, so 3 is a square root of 9. –3 squared also equals 9, so –3 is also a square root of 9. Every positive number has two square roots, one positive and one negative. On the other hand, as far as the GMAT is concerned, negative numbers have no square roots. The symbol

is used to represent the nonnegative square root.

Q: 9 = ? A: The nonnegative square root of 9 is 3, and so

9 = 3.

You should be able to recognize numbers up to 144 that have integer square roots. These numbers are called perfect squares. 1 = 12

16 = 42

49 = 72

100 = 102

4 = 22

25 = 52

64 = 82

121 = 112

9 = 32

36 = 62

81 = 92

144 = 122

If an integer is not a perfect square, then its square root is an irrational number — that is, a number that cannot be expressed precisely as a fraction or decimal. An irrational number is a real number — it has a value and a place on the number line. Two very important irrational numbers are and

2

3 . You should have some sense of the value of these numbers: 2 ≈ 1.414 3 ≈ 1.732

The Rules Of Square Roots The product of square roots is equal to the square root of the product. Ex: 2 × 3 = 2×3 = 6 The quotient of square roots is equal to the square root of the quotient. 10 10 Ex: = = 2 5 5 The power of square roots is equal to the square root of the power. 3 Ex:  2  = 2 3 = 8   You cannot simplify the sum of square roots if they have different numbers inside the radical. Ex: 2 + 3 cannot be written any more simply. To add square roots with the same number inside the radical, use what’s called a coefficient — a number written in front of the radical to express how many square roots have been added. Ex:

6+ 6+ 6 =3 6

Ex: 2 6 + 3 6 = 5 6 © The MBA Center

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Step 2.1 Lesson

To simplify a square root, factor out the perfect squares inside the radical, unsquare them, and put the result in front. Q: Simplify: 300 A: Factor out a perfect square of 100 and reexpress 300 as 100 × 3: 300 = 100 × 3 Now you can break this square root into two and unsquare the perfect square: 100 × 3 = 100 × 3 = 10 3 If there is already a number in front of the radical, multiply. Q: Simplify: 2 18 A: You can factor out a perfect square of 9 and reexpress 18 as 9 × 2: 2 18 = 2 9 × 2 = 2 × 9 × 2 = 2 × 3 × 2 = 6 2 Rationalizing the denominator — To simplify an expression that has a square root in the denominator, multiply both the numerator and denominator by that same square root. This will give you an integer instead of a square root on the bottom. This process is called rationalizing the denominator. Q: Simplify: 2 5 5 2 A: Multiply both the numerator and denominator by 2 5

2 5× 2

2 10 = 10

10 5

PRACTICE QUESTIONS 41-50 (EXPONENTS

AND

5 2

=

5 2× 2

=

2:

SQUARE ROOTS)

41. –104 = ? (A) –10,000 (B) –1,000 (C) –40 (D) 1,000 (E) 10,000 42. 510 × 510 = ? (A) (B) (C) (D) (E)

100 520 5100 2520 25100

43. 27 × 25 × 312 = ? (A) (B) (C) (D) (E)

68

612 624 1212 1224 12420

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Math Review

44. All of the following are equal EXCEPT: (A) (B) (C) (D) (E)

220 219 + 219 410 45 + 45 165

45. 35 + 35 + 35 = ? (A) 93

(B) 94

(C) 95

(D) 96

(E) 915

46. 2 5 ( 3 2 + 2 2 ) = ? (A) 5 10 (B) 10 10 (C) 10 5 (D) 20 5 (E) 30 47.

(−4)

4

=?

(A) –16

(B) –4

(C) 16

(D) 64

(E) 128

48. All of the following are equal EXCEPT: (A)

1

(B)

2

49.

2 3 +3 2 2

1 2

(C)

2 4

(D)

3 6

(E)

6 12

=?

(A) 2 + 2 3 (B)

2+ 6 (C) 2 + 3 6 (D) 3 + 2 3 (E) 3 + 6 50.

50 + 200 = ? (A) 2 15 (B)

5 5

(C)

5 10 (D) 10 5 (E) 15 2

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Step 2.1 Lesson

6. EQUATIONS To solve an equation with one variable and no exponents, the basic rule is this: do whatever you must to both sides to get the variable all by itself on one side, or, in other words, to isolate the variable. You can add the same thing to both sides, subtract the same thing from both sides, multiply both sides by the same thing, or divide both sides by the same thing. As long as you do exactly the same thing to both sides, you will maintain the equality. Q: Solve: –3x + 5 = 11 A: To start to isolate x, first subtract 5 from both sides: −3 x + 5 = 11 −3 x + 5 − 5 = 11 − 5 −3 x = 6 Now, to isolate x, divide both sides by –3: −3 x 6 = −3 −3 x = −2 How do you know what operations to perform in what order? Usually you’ll just know from experience. But here is a systematic procedure: 1. Eliminate all denominators by multiplying both sides of the equation by the LCM of all denominators. 2. Eliminate all parentheses. 3. Move all terms that contain the variable to one side and all terms that do not contain the variable to the other side. 4. Combine all terms that contain the variable into a single term. 5. Divide both sides by the coefficient of the variable.

(

)

Q: Solve: 2 x − 5 = 1 x + 5 4 3 A: First eliminate the denominators. The LCM of 3 and 4 is 12, so multiply both sides by 12: 12 ×





1 x − 5) = 12 ×  x + 5 ( 3  4 8( x − 5) = 3 x + 60 2

Then eliminate the parentheses by distributing the 8: 8 x − 40 = 3 x + 60 Now move every term with an x to the left (by subtracting 3x from both sides) and every term without an x to the right (by adding 40 to both sides): 8 x − 3 x = 60 + 40 5 x = 100 Now all you have left to do to isolate x is to divide both sides by 5: 5x

100 = 5 5 x = 20

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Math Review

Solving “In Terms Of” If an equation has more than one variable, you cannot normally find a numerical root, but you can still solve the equation. To “solve” means to isolate the variable. Q: Solve for x: x + 10 = y A: To isolate the x, subtract 10 from both sides: x + 10 = y x + 10 − 10 = y − 10 x = y − 10 The equation is solved for x. The solution is said to give x in terms of y. When solving for one variable in terms of another, the 5-step equationsolving procedure outlined above becomes especially useful. Q: Solve for n: v =

np r + nt

A: First, eliminate the denominator by multiplying both sides by r + nt: np v= r + nt np r + nt v r + nt = r + nt v r + nt = np

( (

) )

(

)

Then distribute to eliminate the parentheses: rv + ntv = np Now move every term with an n to one side and every term without n to the other. Subtract np from both sides and subtract rv from both sides: rv + ntv − np − rv = np − np − rv ntv − np = −rv Next, rewrite the left side as one term with n. To do that, you “factor” n out:

(tv − p)n = −rv

Lastly, divide both sides by the “coefficient” of n:

(tv − p)n =

−rv tv − p tv − p −rv n= tv − p

You now have a form with n isolated. That’s the solution. It gives n in terms of p, r, t, and v. Solving A Pair Of Equations If you have two distinct equations with two unknowns, you can solve for the roots of the equations. First, pick a variable and isolate it in one of the equations. Then substitute the equivalent expression for that variable in the other equation, eliminating that variable from the equation and giving you one equation with one variable, which you can solve by the usual means.

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2x + 3y = 18 Q: Solve for x and y:  3x − 5y = 8 A: You can start with either equation and either variable. Let’s start with the first equation and solve for x. Subtract 3y from both sides, and then divide both sides by 2: 2 x + 3y = 18 2 x = 18 − 3y x = 9−

3y 2

Now you know that is the same as x. Take that new expression for x and substitute it for x in the other equation: 3 x − 5y = 8  3y  3  9 −  − 5y = 8 2  Now you have one equation with one variable. To solve for y, first distribute the 3 and multiply both sides by 2: 9y − 5y = 8 2 54 − 9y − 10 y = 16 54 − 19y = 16 27 −

Then subtract 54 from both sides and divide both sides by –19: −19y = −38 y=2 Now that you know that y = 2, plug 2 in for y in either of the original equations to find x: 2 x + 3y = 18

()

2 x + 3 2 = 18 2 x + 6 = 18 2 x = 12 x=6 And so the solution is x = 6 and y = 2. Note that you can find numerical roots of a pair of equations only if they are distinct equations. 2a − 6b − 1 = 3 Q: Solve for a and b:  5a − 3 = 15b + 7 A: Solve the first equation for a: 2a − 6 b − 1 = 3 2a = 6 b + 4 a = 3b + 2 Now substitute 3b + 2 for a in the other equation:

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Math Review

(

5a − 3 = 15 b + 7

)

5 3 b + 2 − 3 = 15 b + 7 Look at what happens when you try to solve for b: 15 b + 10 − 3 = 15 b + 7 15 b + 7 = 15 b + 7 Any number will work for b. There are infinitely many solutions. That’s because what looked like two equations to start with were in fact just the same equation in two different forms. The second equation is just another way of writing the first equation. You do not have two distinct equations, and so you are not able to find numerical solutions. A popular alternative method for solving a pair of equations is to “add” the equations. Your goal is the same: you want to get rid of one variable so you can solve for one variable at a time. To do that, you will normally need to reexpress one or both equations so that a variable has coefficients that will cancel when you add. 7x − 6y = −4 Q: Solve for x and y:  4x + 3y = 17 A: If you multiply both sides of the second equation by 2, you get 8x + 6y = 34. Now the coefficients of y in the two equations are opposites and the y terms will cancel when you add the two equations: 7 x − 6y = −4 8 x + 6y = 34 15 x

= 30

Divide both sides by 15 and you find that x = 2. Plug that in for x in one of the original equations and you’ll find that y = 3. Solving Inequalities To solve an inequality means to isolate the variable on one side. The process is much the same as the process for solving an equation. Q: 5x – 13 > 3x – 5 A: To begin to isolate x, first subtract 3x from both sides and add 13 to both sides: 5 x − 13 > 3 x − 5 5 x − 13 − 3 x + 13 > 3 x − 5 − 3 x + 13 2x > 8 Then divide both sides by 2 get the solution: x > 4. The only thing different about solving an inequality is that when you multiply or divide both sides by a negative number, you must flip the sign. Q: −7x + 15 ≤ 8 A: To begin to isolate x, first subtract 15 from both sides: −7 x + 15 ≤ 8 −7 x + 15 − 15 ≤ 8 − 15 −7 x ≤ −7 All that’s left to do now is to divide both sides by –7. When you do that, you must flip the sign, that is, change ≤ to ≥. The solution is x ≥ 1. © The MBA Center

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Step 2.1 Lesson

Factoring Polynomials When simplified, polynomials have no parentheses. There are times, however, when you want parentheses. The process of reexpressing a polynomial with parentheses, i.e., as a product, is called factoring. Ex: To factor the polynomial 3x2 + 7x + 2 means to reexpress it as (3x + 1)(x + 2). To factor a polynomial, try to figure out what simpler monomials or polynomials could be multiplied to produce the polynomial you are trying to factor. Q: Factor: x2 – 10x A: This polynomial is relatively easy to factor. You can see that the two terms each have a factor of x, so you can just “factor out” the x: x2 – 10x = x(x – 10) Q: Factor: 2x2 – x – 3 A: If this polynomial is factorable, then it will probably factor into two binomials, one beginning with 2x and the other beginning with x: 2x2 – x – 3 = (2x )(x ) The second part of each factor will be a number, and the product of those numbers will be –3. Thus they could be +1 and –3, or –1 and +3: Those are the only pairs of integers that have a product of –3. But in this case the order is important. It makes a difference which one goes in the first factor with the 2x and which one goes in the second factor with the x. Pick a pair and try it. Say, +1 and –3: (2x + 1)(x – 3) = 2x2 – 5x – 3 The first and third terms are the right ones, but the middle term is wrong. Now try the same numbers in the other order. Put the –3 in the first factor and the +1 in the second factor: (2x – 3)(x + 1) = 2x2 – x – 3 Remember that some polynomials are not factorable. Q: Factor: x2 + 3x – 5 A: If this polynomial is factorable, then it will probably factor into two binomials, each beginning with x: x2 + 3x – 5 = (x )(x ) The second part of each factor will be a number, and the product of those numbers will be –5. Thus they could be –1 and +5, or +1 and –5. Those are the only possibilities. Pick a pair and try it. Say, –1 and +5: (x – 1)(x + 5) = x2 + 4x – 5 That pair did not work, so try the other possibility, +1 and –5: (x + 1)(x – 5) = x2 – 4x – 5 That pair did not work either, and there are no other possibilities, so this polynomial is not factorable.

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Math Review

Factor Patterns With practice and experience, you will become adept at factoring. You will begin to recognize patterns. There are three factor patterns in particular you should know: 1. Common monomial factor 2. Difference of squares 3. Square of a binomial Whenever you are trying to factor a polynomial, the first thing to look for is a common monomial factor — that is, a monomial that can be factored out of every term in the polynomial. Q: Factor: 2x3 + 6x2 + 10x A: In this polynomial, every term has a factor of 2x. That means you can “factor it out.” To do so, write 2x in front of an open parenthesis: 2x3 + 6x2 + 10x = 2x( ) Now, inside the parentheses, write term by term what’s left after you divide by 2x: 2x3 + 6x2 + 10x = 2x(x2 + 3x + 5) A second factor pattern you should be able to spot is what is called the difference of squares. This is one of the easiest patterns to recognize. It consists of two monomials squared separated by a minus sign. A polynomial in the form a2 – b2 factors to (a – b)(a + b). So to factor the difference of squares, “unsquare” them both and make two binomials out of the results — one with a minus sign and one with a plus sign. Q: Factor: 9x2 – 16 A: This is an example of a difference of squares: in front of the minus sign you have 9x2, which is the square of 3x, and after the minus sign you have 16, which is the square of 4. Unsquare the first square and you get 3x. Unsquare the second square and you get 4. Put those results into two binomials, one with a minus sign and the other with a plus sign: 9x2 – 16 = (3x – 4)(3x + 4) A third factor pattern you should be able to spot is the square of a binomial. This pattern consists of three terms — a first term that’s a square, a third term that’s a square, and a middle term that’s equal to twice the product of the square roots of the first and third terms. This pattern is probably easier to visualize symbolically: a2 + 2ab + b2 = (a + b)2 a2 – 2ab + b2 = (a – b)2 Q: Factor: y2 – 8y + 16 A: The first term is the square of y, the third term is the square of –4, and the middle term is twice the product of y and –4. So this is the square of the binomial y – 4: y2 – 8y + 16 = (y – 4)2

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Step 2.1 Lesson

Solving Quadratic Equations By Factoring A quadratic equation is an equation in which the unknown is squared. Quadratic equations can have as many as two roots. To solve a quadratic equation by factoring, first rearrange the equation so that it is in the form “polynomial = 0.” Then factor the polynomial. When the polynomial is factored, you have a product that’s equal to 0, which means that one of the factors must be 0. Q: Solve: x2 + 12 = 7x A: First rearrange the equation into “polynomial = 0” form: x2 – 7x + 12 = 0 Now factor the polynomial: (x – 3)(x – 4) = 0 In this form, the equation tells you that the product of x – 3 and x – 4 is 0. That means that either x – 3 = 0 or x – 4 = 0. x − 3 = 0 OR x − 4 = 0 x = 3 OR x = 4 So the two roots are 3 and 4. Q: Solve: 2x2 + 7x = –3 A: First rearrange the equation into “polynomial = 0” form: 2x2 + 7x + 3 = 0 Now factor the polynomial: (2x + 1)(x + 3) = 0 In this form, the equation tells you that the product of 2x + 1 and x + 3 is 0. That means that either 2x + 1 = 0 or x + 3 = 0: 2 x + 1 = 0 OR x + 3 = 0 1 x=− OR x = −3 2 So the two roots are −

1 and –3. 2

If when you put the equation into “polynomial = 0” form the polynomial is the square of a binomial, then there will be only one root. Q: Solve: x2 + 10x = –25 A: First rearrange the equation into “polynomial = 0” form: x2 + 10x + 25 = 0 Now factor the polynomial: (x + 5)2 = 0 In this form, the equation tells you that the square of x + 5 is 0. That means that x + 5 = 0. So the only root is –5.

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Math Review

Quadratic Formula You can always solve a quadratic equation with what is called the quadratic formula. Once you have the equation in “polynomial = 0” form, think of it this way: ax 2 + bx + c = 0 If the coefficient of the x2 term is a, the coefficient of the x term is b, and the number term is c, then the solution to the equation is: x=

− b ± b 2 − 4ac 2a

This formula is especially useful when the polynomial is not factorable. Q: Solve: x2 + 2x = 9 A: First rearrange the equation into “polynomial = 0” form: x2 + 2x – 9 = 0 Now plug a = 1, b = 2, and c = –9 into the quadratic formula:

( )( )

2 − b ± b 2 − 4ac −2 ± 2 − 4 1 −9 x= = = −1 ± 10 2a 21

()

But the quadratic formula can also be handy when the polynomial is factorable, but factoring seems like too much trouble. Q: Solve: 12x2 + 20 = 31x A: First rearrange the equation into “polynomial = 0” form: 12x2 – 31x + 20 = 0 Now plug a = 12, b = –31, and c = 20 into the quadratic formula: − b ± b 2 − 4ac 31 ± = x= 2a

© The MBA Center

(−31) − 4(12)(20 ) = 31 ± 1 = 4 24 3 2(12) 2

OR

5 4

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Step 2.1 Lesson

PRACTICE QUESTIONS 51-60 (EQUATIONS) 51. Solve for x: (A) (B) (C) (D) (E)

(

)

1 1 x + 5 = x +1 2 3

–1 –3 –5 –7 –9

(

52. Solve for x: 5 x + 2y = −3 4y − x − 2 (A) (B) (C) (D) (E)

)

–7y + 3 –3y – 3 –3y + 7 3y – 7 7y + 3

3x + 2y = −1 53. Solve for x:  4 x + 3y = 1 (A) –7 (B) –5 (C) 0 (D) 5 (E) 7 7 x + 4y = 19 54. Solve for x + y:  4 x + 7 y = 3 (A) – 5 3 (B) 2 11 3 (D) 16 3 (E) 16 (C)

55. Solve for x: x2 – 2x = 24 (A) (B) (C) (D) (E)

78

–4 or 8 –4 or 6 –3 or 8 3 or –8 4 or 6

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Math Review

56. Solve for x: (A) (B) (C) (D) (E)

x 2 + x = 2  2 x − 4 = 0

–2 only 1 only 2 only –2 or 2 There is no real solution.

57. If 2 – 1 = 1 + 2 , then x = x x 1 3 (B) 1 2 (C) 1 (A)

(D) 2 (E) 3 58. If x ≠ 3, then 3x(x – 3) – x + 3 = x–3 (A) (B) (C) (D) (E)

x+1 x–3 3x + 1 3x – 1 3x + 3

59. If (x + 3)2 = 144, which of the following could be the value of x? (A) 15 (B) 12 (C) –9 (D) –12 (E) –15 60. If the equation x2 + kx + 1 = 0 has exactly 1 real solution, which of the following could be the value of k? (A) (B) (C) (D) (E)

–4 –3 –2 –1 0

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7. QUADRILATERALS Rectangle — a quadrilateral with four right angles. Opposite sides of a rectangle are parallel and equal in length. The diagonals of a rectangle are equal, and they bisect each other. [Bisect means to divide into two equal pieces.] The two dimensions of a rectangle are generally called the length and width. [There is no consensus on which is the length and which is the width. For some people, the length is the longer dimension and the width is the shorter dimension. For other people, the length is the vertical dimension and the width is the horizontal dimension. On the GMAT, it doesn’t matter.]

L

K

The perimeter of a rectangle is length plus width plus length plus width, or, in other words, twice the length plus twice the width. If the length is l and the width is w, then the formula is: Perimeter of a rectangle = 2l + 2w

4 J

9

M

Figure 1

Q: What is the perimeter of a rectangle JKLM in Figure 1? A: Plug 4 and 9 in for l and w in the formula: Perimeter = 2l + 2w = 2(4) + 2(9) = 26 The area of a rectangle is length times width: Area of a rectangle = l w

Q

R

3 P

Q: What is the area of rectangle PQRS in Figure 2? A: Plug 3 and 8 in for l and w in the formula: Area = lw = 3 s 8 = 24

8 Figure 2

S

Square — rectangle with four equal sides. As with any rectangle, the diagonals of a square are equal and bisect each other. The diagonals of a square are also perpendicular. Because a square is a rectangle, the perimeter of a square is twice the length plus twice the width. But because the length and width are equal, you can write the formula more simply. If the length of one side is s, then: Perimeter of a square = 4s Because a square is a rectangle, the area of a square is length times width. But, again, because the length and width are equal, you can write the formula more simply: Area of a square = s2 Q: If a square has perimeter 20, what is the area? A: The perimeter of a square is 4 times the length of one side, and so the length of one side is one-fourth the perimeter. One-fourth of 20 is 5. If the length of a side is 5, then the area is 5 squared, or 25. Parallelogram — a quadrilateral with two pairs of parallel sides. Opposite sides of a parallelogram are equal. Opposite angles are equal, and consecutive angles are supplementary. Diagonals bisect each other.

80

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Math Review

The perimeter of a parallelogram is equal to the sum of the lengths of the four sides. If you know the lengths of any two consecutive sides, then you know all four lengths and you can calculate the perimeter. You cannot calculate the area of a parallelogram if all you know is the length of the sides. To find the area you need what are called the base and the height. Any side can serve as the base. The height then is defined as the perpendicular distance between the base and the opposite side. (Figure 3)

h

When you know the base b and the height h, then you can use the formula:

b

Area of a parallelogram = bh

Figure 3

Q: What is the area of the parallelogram in Figure 4? A: The base is 6 and the height is 4: Area = bh = 6 s4 = 24

5

4 6

Be aware that all squares are rectangles and that all rectangles are parallelograms, but that not all parallelograms are rectangles and not all rectangles are squares. When a GMAT math question says “rectangle,” the figure referred to might be a square.

Figure 4

Here is a summary of the characteristics and formulas for squares, rectangles, and parallelograms: SQUARE

RECTANGLE

PARALLELOGRAM

sides:

All equal.

angles:

All right.

All right.

Opposite angles are equal.

diagonals:

Equal and perpendicular bisectors.

Equal bisectors.

Bisectors.

perimeter:

P = 4s

P = 2l + 2w

Sum of the sides.

area:

A = s2

A = lw

A = bh

Opposite sides are Opposite sides are equal. equal.

Trapezoid — a quadrilateral with one pair of parallel sides and one pair of nonparallel sides. To find the area of a trapezoid, call the two parallel sides the bases b1 and b2 and the perpendicular distance between them the height h. Then: Area of a trapezoid = b1  b 2 h 2

8

Think of it as the height times the average of the bases. Q: What is the area of the trapezoid in Figure 5? A: The average of the bases is 9, and the height is 5, so the area is 9 s 5 = 45.

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5 10 Figure 5

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PRACTICE QUESTIONS 61-70 (QUADRILATERALS) 61. Figure 6 is which of the following? I. quadrilateral II. rectangle III. parallelogram (A) (B) (C) (D) (E)

Figure 6

I only II only I and II only I and III only I, II, and III

62. If the area of the rectangle in Figure 7 is 21, what is the perimeter? 3

(A) (B) (C) (D) (E)

Figure 7

63. If rectangles A and B in Figure 8 have the same perimeter, what is the area of rectangle B?

8 6

B

A

5

(A) (B) (C) (D) (E)

Figure 8

Q

R

P

S Figure 9

5

24 26 30 36 42

64. The quadrilateral in Figure 9 is a parallelogram. If the degree measure of angle P is 2x – 25, and the degree measure of angle Q is 3x + 15, what is the value of x? (A) 38 (B) 51 (C) 64 (D) 76 (E) 131 65. If the perimeter of the trapezoid in Figure 10 is 22, what is the area?

5 8 Figure 10

82

10 10.5 14.5 20 21

(A) (B) (C) (D) (E)

20 22 26 32 40

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Math Review

Questions 66-70 refer to quadrilaterals A, B, C, D, and E in Figure 11. 5

66. How many of the quadrilaterals in Figure 11 are rectangles? (A) (B) (C) (D) (E)

1 2 3 4 5

5

A

5

5 5

67. How many of the quadrilaterals in Figure 11 are parallelograms? (A) (B) (C) (D) (E)

5

1 2 3 4 5

5 6 4

C

A B C D E

6 D

4

88°

69. Which of the quadrilaterals in Figure 11 has the least area? A B C D E

4

6

4

(A) (B) (C) (D) (E)

5

88°

68. Which of the quadrilaterals in Figure 11 has the greatest area? (A) (B) (C) (D) (E)

B

6 8 3

E

3

8 70. Which of the quadrilaterals in Figure 11 has the greatest perimeter? (A) (B) (C) (D) (E)

Figure 11

A B C D E

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Step 2.1 Lesson

8. TRIANGLES Triangle — polygon with three sides. In one sense the triangle is the simplest of polygons: it has the fewest sides. But in many ways the triangle is the most complex. There are many facts and formulas for triangles, and there are several special triangles with their own special facts and formulas. One simple trait common to all triangles is that the three interior angles add up to 180 degrees. So whenever you know the measures of two angles, you can easily find the measure of the third.

86°

Q: What is the value of x in Figure 12? A: The two given angles add up to 86 + 34 = 120 degrees. That leaves 180 - 120 = 60 degrees for the other angle, and so x = 60.

x°

34°

If you extend one side of a triangle, you create what is called an exterior angle. Because an exterior angle is supplementary to the adjacent interior angle, and because the measure of that interior angle is equal to 180° minus the other two interior angles, it follows that an exterior angle is equal to the sum of those other two interior angles. (Those angles — the interior angles other than the adjacent one — are called the remote interior angles.)

Figure 12

78° 32°

Q: What is the value of y in Figure 13? A: The angle marked y° is an exterior angle. The remote interior angles are marked 32° and 78°, and so y = 32 + 78 = 110.

y°

Figure 13

If you extend all three sides of a triangle, the three resulting exterior angles will add up to 360°.

t°

Q: What is the value of s + t + u in Figure 14? A: The angles marked s°, t°, and u° are exterior angles at the three vertices, and so s + t + u = 360.

u° s°

Area Of A Triangle To find the area of a triangle you need the base and the height. Any side can serve as the base. The height then is defined as the perpendicular distance between the base and the opposite vertex. When you know the base b and the height h, then you can use the formula:

Figure 14

Area of a triangle = 1 bh 2

B

A

C

D Figure 15

If all you know is the length of two sides of a triangle, you cannot find the area — unless those two sides happen to be perpendicular.

F 2 E

12 Figure 16

84

Q: In Figure 15, AC = 10 and BD = 3, what is the area of triangle ABC? A: AC and BD are perpendicular, so you can use them as the base and height: Area = 1 bh = 1 (10)(3) = 15 2 2

G

Q: In Figure 16, what is the area of triangle EFG? A: EF and EG are perpendicular, so you can use them as the base and height: Area = 1 bh = 1 (2)(12) = 12 2 2 © The MBA Center

Math Review

Any side of a triangle can potentially be used as the base. It does not have to be the side on the bottom. Look for a side for which you are given a height.

H

Q: In Figure 17, what is the area of triangle HJK? 16

A: You should use HJ as the base, because that's the only side for which you are given a height. HJ and IK are perpendicular, so you can use them as the base and height. Note that HJ is equal to the sum of HI and IJ: Area = 1 bh = 1 (16 + 5)(12) = 126 2 2 Side-Angle Relationships

20 I 5 J

12 13

K

Figure 17

The longest side of a triangle will always be found opposite the biggest angle. Likewise, the shortest side will be found opposite the smallest angle. Thus, if you know the relative measures of the three angles, then you also know the relative lengths of the three sides. Or, if you know the relative lengths of the sides, then you also know the relative measures of the angles. Q: In triangle FGH, the measure of angle F is 53°, and the measure of angle G is 62°. Arrange the sides in order from longest to shortest. A: When you know the measures of two angles of a triangle, you can determine the measure of the third. The two given angles add up to 53 + 62 = 115 degrees. That leaves 180 – 115 = 65 degrees for measure of angle H. The biggest angle is H, and so the side opposite that, FG, is the longest. The smallest angle is F, and so the side opposite that, GH is the shortest. The order of the sides from longest to shortest, then, is FG, FH, GH. If two sides of a triangle have the same length, it follows that the angles opposite the equal sides are equal. Likewise, if two angles have the same measure, it follows that the sides opposite the equal angles are equal. Furthermore, if all three sides of a triangle are equal, it follows that the angles are all equal, and likewise, if all three angles are equal, then all three sides are equal. Q: In triangle LMN, the length of LM is 10, the length of MN is 10, and the length of LN is 12. Arrange the angles in order from biggest to smallest. A: LN is the longest side, and so the angle opposite that, M, is the biggest. The other two sides are equal in length, so the angles opposite them, L and N, are equal. Triangle Inequality Theorem — The length of one side of a triangle is greater than the positive difference between the other two side lengths and less than the sum. Thus, if you know the lengths of two sides of a triangle, then you know the lower and upper limits for the length of the third side. Q: In triangle ABC, the length of AB is 3 and the length of BC is 7. What is the range of possible values for the length of AC ? A: AC must be greater than the positive difference between the other two sides, which is 7 – 3 = 4. And AC must be less than the sum of the other two sides, which is 7 + 3 = 10. Thus 4 < AC < 10.

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Special Triangles Isosceles Triangle — a triangle with two equal sides. The equal sides of an isosceles triangle are called the legs. Short hatch marks are often used to indicate equal sides. As we have seen, if two sides of a triangle are the same length, then the angles opposite them are equal. The equal angles of an isosceles triangle are called the base angles (even if they're not at the bottom). The other angle is called the vertex angle.

T

70o

S

When you know that a particular pair of sides are equal, you can use one angle measure to find the other two.

U

Figure 18

8 70o

55o

55o Figure 19

Q: In triangle STU in Figure 18, ST = TU. If the measure of angle S is 70°, what are the measures of angles T and U? A: Angles S and U are the base angles and so they are equal. Thus angle U measures 70°. They add up to 140°, which leaves 180 – 140 = 40 degrees for the measure of angle T. Be careful. If all you know is that you have an isosceles triangle, you cannot necessarily use one angle to find the measures of the others. You need to know whether the given angle is a base angle or the vertex angle. Q: If the measure of one angle of an isosceles triangle is 70°, what are the measures of the other two angles? A: You cannot answer this question because, without a diagram or some more information, you do not know whether the 70° angle is a base angle or the vertex angle. If it is a base angle, then the triangle would look like triangle STU above and the other two angles would be 70° and 40°. But it is also possible that the 70° angle is the vertex angle, in which case the other two angles would each be 55° and the triangle would look like Figure 19. Equilateral triangle — a triangle with three equal sides. If all the sides are equal, it follows that all the angles are equal. Furthermore, if the three angles are equal and add up to 180°, then each angle of an equilateral triangle measures one-third of 180°, or 60°. (Figure 20)

60o

60o

60o Figure 20

Right triangle — a triangle with a right angle (that is, a 90° angle). If one angle measures 90°, it follows that the other two angles are acute and add up to 90°. In a right triangle, the 90° angle is always the biggest angle, and so the side opposite the 90° will always be the longest side. The longest side is called the hypotenuse. The other two sides, the sides that are perpendicular, are called the legs. Pythagorean Theorem The lengths of the sides of a right triangle are related. This relationship is summarized in the Pythagorean theorem, which says that the sum of the squares of the legs is equal to the square of the hypotenuse. Algebraically speaking, if the lengths of the legs are a and b and the length of the hypotenuse is c, then:

a2 + b2 = c2

86

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Math Review

In Figure 21, for example, the legs have lengths 8 and 15, and the hypotenuse has length 17. The squares of the legs are 82 = 64 and 152 = 225. The sum of the squares of the legs is 64 + 225 = 289, which is indeed equal to the square of the hypotenuse: 172 = 289.

17

8

You can use the Pythagorean theorem to find the length of the hypotenuse when you know the lengths of the legs, or to find the length of a leg when you are given the lengths of the other leg and the hypotenuse. Q: The legs of the right triangle in Figure 22 have lengths 7 and 24. What is the length of the hypotenuse? A: The squares of the legs are 72 = 49 and 242 = 576. The sum of the squares of the legs is 49 + 576 = 625. That’s the square of the hypotenuse, so to find the hypotenuse, take the square root: hypotenuse =

15 Figure 21

7 24

625 = 25

Figure 22

Q: One of the legs of the right triangle in Figure 23 has length 10 and the hypotenuse has length 15. What is the length of the other leg? A: The square of the given leg is 102 = 100 and the square of the hypotenuse is 152 = 225. The difference is 225 – 100 = 125. That’s the square of the other leg, so to find the leg, take the square root: leg = 125 The square root of 125 is not an integer, though it can be simplified: 125  25 5  5 5

10

15

Figure 23

To express the length precisely, just leave it in this form. (It is approximately 11.18.) Be careful. You can use the Pythagorean theorem to find the third side of a right triangle only if you know whether the given sides are both legs or a leg and hypotenuse. Q: The lengths of two sides of a right triangle are 5 and 4. What is the length of the third side? A: You cannot answer this question unless you know whether the given side lengths of 5 and 4 are the two legs or a leg and hypotenuse. If they are the two legs, then: hypotenuse =

5 2  4 2  25  16  41

If they are a leg and hypotenuse, then: leg =

5 2 4 2  25 16  9  3

Pythagorean triple — A set of three integers that satisfy the Pythagorean theorem. The simplest and most frequently encountered Pythagorean threesome is 3-4-5 . Whenever you see a right triangle with legs 3 and 4, you should realize immediately, without actually using the Pythagorean theorem, that the hypotenuse is 5. And whenever you see a right triangle with hypotenuse 5 and leg 3 or 4, you should realize immediately what the other leg is. Q: The legs of the right triangle in Figure 24 have lengths 3 and 4. What is the length of the hypotenuse? A: There's no need to use the Pythagorean theorem. You should realize right away that the hypotenuse is 5. © The MBA Center

3

4 Figure 24

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3

5 Figure 25

6

8 Figure 26 24

30 Figure 27

Step 2.1 Lesson

Q: One leg of the right triangle in Figure 25 has length 3 and the hypotenuse has length 5. What is the length of the other leg? A: There's no need to use the Pythagorean theorem. You should realize right away that the other leg is 4. The set {3, 4, 5} is not the only set of three integers that fits the Pythagorean theorem. So too will any set of three integers in the ratio 3:4:5, such as {6, 8, 10}, {9, 12, 15}, {30, 40, 50}, and {54, 72, 90}. Q: The legs of the right triangle in Figure 26 have lengths 6 and 8. What is the length of the hypotenuse? A: There's no need to use the Pythagorean theorem. You should realize right away that the hypotenuse is 10. Q: One leg of the right triangle in Figure 27 has length 24 and the hypotenuse has length 30. What is the length of the other leg? A: The ratio of the given leg to the hypotenuse is 4:5, so this is a multiple of the 3-4-5 triangle. Each side is multiplied by 6, and the side you’re looking for is 3 × 6 = 18. Be careful. A right triangle with two sides in a 3-to-4 or 3-to-5 or 4-to-5 ratio is not necessarily a multiple of the 3-4-5 triangle. Q: The legs of a right triangle have lengths 12 and 15. What is the length of the hypotenuse? A: The legs are in ratio of 4:5. This is not a multiple of a 3-4-5 triangle, because in such a triangle it must be a leg and the hypotenuse that are in a ratio of 4:5. To find the length of the hypotenuse in this case, you must use the Pythagorean theorem: hypotenuse = 12 2 + 15 2 = 144 + 225 = 369 = 3 41 Q: Two sides of a right triangle have lengths 30 and 40. What is the length of the third side? A: There is not enough information to answer this question. You are not told whether the two sides are the two legs or a leg and hypotenuse. It makes a difference. If they are the two legs, then this is a multiple of the 3-4-5 triangle and the third side is 50. But if they are a leg and hypotenuse, then you will have to use the Pythagorean theorem: leg = 40 2 − 30 2 = 1600 + 900 = 700 = 10 7 Besides the 3-4-5 and its multiples, there are many other Pythagorean triples. A very popular one on the GMAT is the 5-12-13.

5 12 Figure 28 24

26 Figure 29

88

Q: The legs of the right triangle in Figure 28 have lengths 5 and 12. What is the length of the hypotenuse? A: There's no need to use the Pythagorean theorem. You should realize right away that the hypotenuse is 13. Multiples of the 5-12-13 are Pythagorean triples as well. Q: One leg of the right triangle in Figure 29 has length 24 and the hypotenuse has length 26. What is the length of the other leg? A: The ratio of the given leg to the hypotenuse is 12:13, so this is a multiple of the 5-12-13 triangle. The given sides are twice 12 and 13, respectively, and so the missing side is twice 5, or 10. © The MBA Center

Math Review

45-45-90 Triangle All isosceles right triangles have the same side proportions. When the legs are both 1, the hypotenuse is 2 . When the legs are both 2, the hypotenuse is 2 2 . When the legs are both 3, the hypotenuse is 3 2 . In other words, whatever the length of a leg, just multiply that by 2 to get the hypotenuse. Q: In Figure 30, what is the length of the hypotenuse? A: Because the legs are both 5, this is a right isosceles triangle. Just multiply the leg length by 2 to get the hypotenuse: 5 2 . To turn a leg length into the hypotenuse, you multiply by

2 . So to turn

the hypotenuse into a leg, you do the opposite — divide by

2.

5

5 Figure 30

Q: In Figure 31, what are the lengths of the legs? A: The hatch marks indicate that the legs are equal, and so this is a 6

right isosceles triangle. To turn the given hypotenuse length of 6 into a leg length, divide by 2 : leg =

6 2



6 2 2 2



6 2 3 2 2 Figure 31

30-60-90 Triangle All 30-60-90 triangles have the same side proportions. When the shorter leg (opposite the 30° angle) is 1, then the longer leg (opposite the 60° angle) is 3 and the hypotenuse is 2. So when the shorter leg is 2, then the longer leg is 2 3 and the hypotenuse is 4. And when the shorter leg is 10, then the longer leg is 10 3 and the hypotenuse is 20. Q: In Figure 32, what are the lengths of the longer leg and hypotenuse? A: The shorter leg is 5, so the longer leg is

3 times that, or 5 3. The

60o 5 30o

hypotenuse is twice the shorter leg, or 10.

Figure 32

If what you are given is the hypotenuse, then divide by 2 to get the shorter leg, and then multiply the shorter leg by

3 to get the longer leg. And if

what you are given is the longer leg, then divide by

3 to get the shorter

leg, and then multiply the shorter leg by 2 to get the hypotenuse. Q: In Figure 33, what are the lengths of the shorter leg and the hypotenuse? A: The longer leg is 9. Divide that by shorter leg =

60o

3 to get the shorter leg:

9

9 3

3

3 3

9 3 3

3 3

Multiply the short leg by 2 to get the hypotenuse:

30o 9 Figure 33

hypotenuse 2 s 3 3  6 3 © The MBA Center

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PRACTICE QUESTIONS 71-80 (TRIANGLES) 71. If the measure of one angle of an isosceles triangle is 96°, what is the degree measure of the smallest angle? (A) (B) (C) (D) (E)

42° 48° 64° 84° Cannot be determined from the information given.

72. If the measure of one angle of an isosceles triangle is 40°, what is the degree measure of the biggest angle? (A) 70° (B) 80° (C) 100° (D) 140° (E) Cannot be determined from the information given. 73. If the lengths of the two legs of a right triangle are 10 and 24, what is the length of the hypotenuse? (A) (B) (C) (D) (E)

25 26 30 34 Cannot be determined from the information given.

74. If the lengths of two sides of a right triangle are 9 and 12, what is the length of the third side? (A) (B) (C) (D) (E)

12 15 18 21 Cannot be determined from the information given.

75. If the lengths of two sides of an isosceles triangle are 3 and 7, which of the following could be the perimeter of the triangle? I. 13 II. 15 III. 17 (A) (B) (C) (D) (E)

90

I only III only I and III only II and III only I, II, and III

© The MBA Center

Math Review

76. What is the value of x in Figure 34?

2x°

(A) 26 (B) 39 (C) 51 (D) 78 (E) 102

(x + 78)°

x°

Figure 34

77. What is the area of the triangle in Figure 35? 10

(A) 25 (B) 50 (C) 75 (D) 90 (E) 100

45° Figure 35

78. If the length of one leg of a right triangle is 6, and if the perimeter is 18, what is the area of the triangle? (A) (B) (C) (D) (E)

12.5 13.5 21 25 27

79. In Figure 36, AD = 20 and DC = 36. If the area of triangle ABC is 420, what is the perimeter of triangle ABC? (A) 120 (B) 132 (C) 144 (D) 156 (E) 168

B

A

20

D

36

C

Figure 36

80. What is the area of the triangle in Figure 37? (A) 9 + 9 2 (B) 9 + 9 3 (C) 9 2 + 9 3

6

105°

45° Figure 37

(D) 18 + 18 2 (E) 18 + 18 3

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Step 2.1 Lesson

9. CIRCLES D C E F

A chord that passes through the center of a circle is called a diameter. The same word is also used to mean the distance across the circle. The diameter of a circle is equal to twice the radius. R

11 S

P

F 121o D 119o

G Figure 40

Q: In Figure 39, Q, R, and S are points on circle P. If PR = 11 what is the length of diameter QS? A: The radius is 11, so the diameter is twice that, or 22. An angle formed by two radii, with the center as the vertex, is called a central angle. The central angles of a circle add up to 360°.

Figure 39

E

A circle will often be designated by the name of the point in the middle, which is called the center. The distance from the center to any point on the circle is called the radius (plural: radii). All radii of a circle are the same length. A line segment with endpoints on a circle is called a chord of the circle. In the circle in Figure 38, CD and EF are chords.

Figure 38

Q

Circle — set of all the points in a plane that are the same given distance away from a particular point.

Q: In Figure 40, E, F, and G are points on circle D. If the measure of angle EDF is 121° and the measure of angle FDG is 119°, what is the degree measure of angle EDG? A: The three central angles add up to 360 degrees. The two given angles add up to 121 + 119 = 240 degrees, and so angle EDG measures 360 – 240 = 120 degrees. Circumference — the distance around a circle. All circles are similar and so all circles have the same ratio of circumference to diameter. This ratio is an irrational number approximately equal to 3.14. This number is called pi, a Greek letter, written P. If you know the diameter of a circle, you can get the circumference C by multiplying by P:

C = Pd Since the diameter is also twice the radius, the formula can also be written like this:

C = 2Pr Circumference is a measure of length. It is expressed in linear units: inches, meters, miles, etc. It is conventional to write numbers in front of P and letters after it. Thus, when the diameter is expressed as d, it goes after (Pd), but when you put a number in for d, it goes in front (12P). Q: If the circumference of circle P is 12, what is the radius? A: Plug C = 12 into the formula and solve for r: 12  2 Pr r

92

6 P

© The MBA Center

Math Review

Length Of An Arc The part of the circumference of a circle extending from one given point to another is called arc. For any two points on a circle, there are two arcs. Unless the two points are directly opposite each other (that is, endpoints of a diameter), one arc will be shorter than the other. The shorter arc, the one that goes less than halfway around the circle, is called the minor arc. The longer arc, the one that goes more than halfway around the circle, is called the major arc. In Figure 41, the part of the circumference of the circle below that goes from A to C through B can be called arc ABC or minor arc AC.

A

An arc has two different measures: the degree measure and the length. The degree measure is a description of the arc’s curvature and is simply the measure of the central angle formed by its endpoints and the center of the circle.

Figure 41

Q: In circle O in Figure 42 what is the degree measure of minor arc DE? A: Central angle DOE measures 54°, and so the degree measure of minor arc DE is also 54°. The length of an arc is a fraction of the circle’s circumference. To find the length of an arc, you need to know not just the measure of the central angle, but also something about the size of the circle, such as radius or diameter or circumference. To calculate the length of an arc, first divide the degree measure of the central angle by 360. That will tell you what fraction of the circumference is on the arc. Then find the circumference and multiply it by the fraction.

B

C

D 10 54° O

E

Figure 42

Q: In circle O in Figure 42, what is the length of minor arc DE? A: First divide the degree measure of the central angle by 360: 54 3 = 360 20 Then find the circumference. Plug r = 10 into the formula: C = 2π(10) = 20π Now multiply the fraction by the circumference: 3 length of arc DE = ( 20 π ) = 3 π 20 The process of finding the length of arc when you know the radius r and the degree measure of the central angle a can be summarized in one formula: length of arc =

a ⋅ 2 πr 360

Area Of A Circle The formula for the area A of a circle of radius r is:

A = πr2 Area is expressed in square units: square inches, square feet, square meters, etc.

5 O

Q: What is the area of circle O in Figure 43? A: Plug r = 5 into the formula: A = π(52) = 25π

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Figure 43

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The formulas for circumference and area look somewhat similar. To avoid confusing them, remember that area is a measure of square units and therefore has the r squared. You need the radius to find the area. To find the area when you're given the diameter, first divide the diameter by 2 and then proceed with the above formula. Q: What is the area of a circle of diameter 6? A: First divide the diameter by 2 to get r = 3, then plug that into the formula: A = π(32) = 9π To find the area when you're given the circumference, use the circumference formula to find the radius. Q: What is the area of a circle of circumference 20π? A: First use the circumference formula to find r: 20 π = 2 πr r = 10 Then plug r = 10 into the area formula: A = π(102) = 100π Area Of A Sector A closed figure formed by two radii and an arc is called a sector. You can think of a sector as a fraction of the interior of a circle. You can find the area of a sector if you know the measure of the interior angle and something about the size of the circle, such as the radius. Use the angle measure to determine what fraction of the circle is contained within the sector. P

O

45° 4

Q

Q: What is the area of the shaded portion of circle O in Figure 44? A: The radius is 4, and so the area of the whole circle is 16π. The central angle measures 45°. Put that over 360° to see what fraction of the circle is contained within the sector: 45 360

Figure 44

=

1 8

Thus the area of the sector is 1 of the area of the circle: 8 area of sector =

1 8

( 16 π ) = 2 π

If the degree measure of the central angle is a and the radius is r, then the formula is: area of sector =

a 360

⋅ πr 2

Q: What is the area of the sector formed by a 20° central angle in a circle of radius 6? A: Plug a = 20 and r = 6 into the formula: area of sector =

94

( )

20 π 6 2 = 2π 360

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Math Review

PRACTICE QUESTIONS 81-90 (CIRCLES) 81. What is the circumference of a circle of area 16π? (A) 4π (B) 8π (C) 16π (D) 32π (E) 64π

82. What is the area of a circle of circumference 16π? (A) 4π (B) 8π (C) 16π (D) 32π (E) 64π A 83. What is the length of minor arc AB in Figure 45? (A) (B) (C) (D) (E)

π 2π 3π 4π 5π

5 O

108° B

Figure 45 84. What is the area of the shaded region in Figure 46? (A) 52π (B) 60π (C) 65π (D) 72π (E) 144π

130° 12 O

Figure 46 85. In Figure 47, the angles marked x° and y° are central angles. If the ratio of x to y is 4 to 5, what is the value of x? (A) (B) (C) (D) (E)

130 140 150 160 170

x° y°

Figure 47

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A

B

86. In Figure 48, if ABCD is a square of area 10, what is the area of the circle? (A) 5π (B) 10π (C) 25π (D) 50π (E) 100π

C

D

Step 2.1 Lesson

Figure 48 87. What is the area of the shaded region in the Figure 49? 6

(A) (B) (C) (D) (E)

70° O

28π 29π 30π 31π 32π

Figure 49 A B

5 O

C

88. In circle O in Figure 50, if the length of arc ABC is 2π, what is the area of the shaded region? (A) 4π (B) 5π (C) 8π (D) 10π (E) 12π

Figure 50 89. In Figure 51, O is the center of both circles. If OD = DE = 3, what is the area of the shaded region? D

O

E

(A) (B) (C) (D) (E)

9π 12π 18π 24π 27π

Figure 51 A

O

x°

90. In Figure 52, if the length of minor arc AB is 10, and the length of major arc AB is 35, what is the value of x? B

(A) (B) (C) (D) (E)

75 80 85 90 95

Figure 52

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Math Review

10. PHINEAS’ FAVORITE WORD PROBLEMS Phineas is big on word problems. Certain types of word problems come up on the GMAT over and over again. Here are some of Phineas’ favorites. Rate Problem With A Change In Units A rate is a ratio of quantities with different units. Solving a rate problem generally involves setting up a proportion. Phineas likes to complicate rate problems by switching one of the units between the given information and the question. The easiest way to do a problem like this is first to find the solution in terms of the original units, and then to convert. Q: A machine makes copies at a rate of 2.5 copies per second. How many minutes will it take the machine to make 3,000 copies? A: First set up a proportion to find the answer in seconds. 2.5 copies in 1 second equals 3,000 copies in how many seconds? 2.5 copies 3000 copies = 1 second x seconds 2.5 x = 3000 x = 1200 To convert seconds to minutes, multiply by (1 min/60 sec). ( 1200 seconds ) ×

1 minute = 20 minutes 60 seconds

Phineas can make matters doubly complicated by switching both units: Q: At a filling station in France, Adrian paid 171 francs for 25 liters of gasoline. At the conversion rates of 7.2 francs per 1 US dollar, and 3.8 liters per 1 US gallon, what was the price of the gasoline in dollars per gallon? A: You could start by dividing 171 francs by 25 liters to get the rate in francs per liter, and then convert the francs to dollars and the liters to gallons. Or you could convert first and then divide. Both methods will work. But perhaps the most direct method is to multiply francs over liters by dollars over francs by liters over gallons. If you set it up properly, the units you’re not interested in (francs and liters) will cancel and your answer will be in dollars per gallon: 171 francs 25 liters

×

1 dollar 7.2 francs

×

3.8 liters 1 gallon

= 3.61 dollars per gallon

Notice that Phineas kindly gave you the francs-per-dollar and liters-pergallon conversion rates. Fortunately Phineas does not expect you to know a lot of conversion rates. You do not need to remember anything like how many ounces in a pound, inches in a foot, yards in a mile, centimeters in an inch, liters in a gallon, or grams in a pound. You do not even need to know how many centimeters in a meter or grams in a kilogram. If you ever need one of these conversion rates to solve a problem, Phineas will give it to you. That’s because none of these units are universal. Phineas does not expect Americans to know all about meters, liters, and grams. Nor does he expect non-Americans to know all about inches, feet, ounces, pounds, pints, and gallons. © The MBA Center

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So don’t waste any of your precious GMAT preparation time memorizing conversion rates. The only units for which Phineas expects you know the conversion rates are units of time: seconds, minutes, hours, days, weeks, months, and years. Combined Rate Another way Phineas likes to complicate rate problems is by asking you to combine them. Q: Dale can stuff 100 envelopes in 12 minutes, and Chris can stuff 100 envelopes in 8 minutes. Working together, how many minutes will it take them to stuff 1,000 envelopes? A: To combine the rates, add them: 100 100 200 300 500 + = + = 12 8 24 24 24 That fraction can be simplified, but it’s easy to use in the next step as is. Now that you have the combined rate, you can set up a proportion and solve: 500 1000 = 24 x x = 48 Working together they can stuff 1,000 envelopes in 48 minutes. The infamous “two-trains-approaching” type word problem is really just a matter of combining rates. Q: A train departs Altoona at 6:00 a.m. and proceeds at a steady rate of 75 miles per hour towards Bakersville. Another train departs Bakersville at the same time and proceeds along the same track towards Altoona at a steady rate of 125 miles per hour. If the track is 650 miles long, at what time will the trains meet? A: When the trains meet, each mile of track will have been traversed by one or the other. Between them they will have traveled the entire distance, at a rate equal to the sum of the individual speeds: 650 miles 650 miles = = 3.25 hours ( 75 + 125 ) miles per hour 200 miles per hour That means the trains will meet 3 and a quarter hours after 6:00 a.m., or at 9:15 a.m. Working Together When the problem concerns the amount of time it takes two individuals alone to accomplish some task, and the amount of time it takes them working together to accomplish the task, use this formula:

t t + =1 a b In this formula, a represents the time in takes one person alone, b represents the time it takes the other person alone, and t represents the amount of time it takes them working together. If you are given values for two of the quantities a, b, and t, you can solve for the third.

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Q: Working alone, Maria can paint a room in 8 hours. Maria’s assistant can paint the same room in 24 hours. How much time would it take Maria and her assistant, working together, to paint the room? A: Here a = 8 and b = 24. Plug them into the formula and solve for t: t t  1 8 24 3t t  1 24 24 4t 1 24 4t  24 t 6 When three individuals are working together, the formula becomes:

t t t   1 a b c Q: Machine A can produce 1,000 widgets in 5 hours. Machine B can produce 1,000 widgets in 10 hours. If machines A, B, and C working independently and simultaneously can produce 1,000 widgets in 3 hours, how many hours would it take machine C alone to produce 1,000 widgets? A: Here a = 5, b = 10, and t = 3. Plug them into the formula and solve for c: 3 3 3   1 5 10 c 9 3  1 10 c 3 1  c 10 c  30 Here’s a variation on this problem type in which you are not given any particular values: Q: John, working alone, can do a certain job in half the time it takes Peter working alone. John and Peter, working together, can do the job 2 hours faster than John working alone. How many hours would it take John, working alone, to do the job? A: Use the same formula. You’re looking for a, the time it takes John alone. Express the other times in terms of a. The time it takes Peter alone is 2a, and the time it take them together is a – 2: a 2 a 2  a 2a 2a 4 a 2  2a 2a 3a 6 2a 3a 6 a © The MBA Center

1 1 1  2a 6

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Average Rate The general formula is: Total A Total B In the case of average speed, the formula is: Average A per B 

Average speed 

Total distance Total time

Q: Mary drove 660 miles to visit her grandmother. It took her 5 hours to drive the first 360 miles, and it took her 6 hours to drive the last 300 miles. What was her average rate of speed, in miles per hour, for the entire trip? A: The total distance traveled is 660 miles. The total time is 5 + 6 = 11 hours. So: Total distance Average speed  Total time 660 miles   60 miles per hour 11 hours Watch out for questions that ask for average rate or average speed. Sometimes the temptation will be just to average the individual rates or speeds, but that approach almost never gets you the correct answer. In the following question, for example, it might seem logical to some people that the average speed for the round trip will be the average of the two one-way speeds. Q: Thelma ran from her front door to the mailbox at a rate of 15 kilometers per hour, and walked back by the same path at a rate of 5 kilometers per hour. What was her average rate of speed, in kilometers per hour, for the round trip? A: To find average speed, you need the total distance and the total time. Here, you’re not given any distances. Let’s call the one-way distance from the door to the mailbox d kilometers. Then the total distance for the round trip is 2d. And what about the total time? What you need to do is find the two one-way times in terms of d. Going from the door to the mailbox she goes d kilometers at 15 kilometers per hour. The first time, then, is: d kilometers d  hours 15 kilometers per hour 15 Returning from the mailbox to the door, she goes d kilometers at 5 kilometers per hour. The second time, then, is: d kilometers d  hours 5 kilometers per hour 5 And so the total number of hours is: d d d 3d 4d +  +  15 5 15 15 15 Now you have expressions for the total distance and the total time. When you plug them into the formula and divide, the d’s drop out and you get a numerical answer: Total distance 2d kilometers   7.5 kilometers per hour Total time 4d hours 15

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Mixture Problems Another classic word problem type that Phineas loves is the mixture problem. The situation described will be something like this: a certain amount A, of which a certain fraction or percent is something, is combined with a certain amount B, of which a certain fraction or quantity is something, to yield a mixture, of which a certain fraction or percent is something. The basic set-up is this: (fractionA)(A) + (fractionB)(B) = (fractionA+B)(A + B) Or: (percentA)(A) + (percentB)(B) = (percentA+B)(A + B) Each formula relates five quantities: A, B, and the three fractions or percents. Given any four of these quantities, you can solve for the fifth. Q: If 5 liters of a solution that is 60 percent alcohol is added to 20 liters of a solution that is 40 percent alcohol, what percent of the resulting solution is alcohol? A: Here you are given percentA = 60, A = 5, percentB = 40, and B = 20. You are asked to solve for fractionA+B so call that x: (0.60)(5) + (0.40)(20) = (x)(5 + 20) Solve this equation and you’ll find that x = 0.44, and so the percent alcohol in the resulting solution is 44. Phineas also likes the variation of this problem type in which a combination of quantities with different unit prices yields a mixture with a new unit price. The set-up is this: (priceA)(A) + (priceB)(B) = (priceA+B)(A + B) Q: Peanuts sell for $0.90 a pound, and cashews sell for $3.25 a pound. How many pounds of cashews must be added to 6 pounds of peanuts to make a mixture that will sell for $1.84 a pound? A: Here you are given priceA = 0.90, A = 6, priceB = 3.25, and priceA+B = 1.84. You are asked to solve for B, so call that x: (0.90)(6) + (3.25)(x) = (1.84)(6 + x) Solve this equation and you’ll find that x = 4.

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PRACTICE QUESTIONS 91-100 (PHINEAS’ FAVORITE WORD PROBLEMS) 91. If one person is born every 15 seconds in country X, approximately how many people are born in 1 year? (A) 1,600,000 (B) 2,100,000 (C) 3,200,000 (D) 21,000,000 (E) 32,000,000 92. Machine A can produce 100 widgets in 40 minutes. Machine B can produce 100 widgets in 30 minutes. How many hours will it take the two machines working together to produce 7,000 widgets? (A) 8 (B) 10 (C) 16 (D) 20 (E) 24 93. Two runners start at the same time from the same point on an oval track. Runner A runs clockwise around the track at a rate of 25 feet per second, and runner B runs counterclockwise at a rate of 15 feet per second. The total distance around the track is 1000 feet. When they meet, runner A will have run how many feet more than runner B? (A) 100 (B) 150 (C) 200 (D) 250 (E) 300 94. Hose A can fill a pool in 10 hours. Hose B can fill the pool in 15 hours. How many hours will it take the two hoses working simultaneously to fill the pool? (A) 5 (B) 6 (C) 7.5 (D) 12.5 (E) 25 95. Alice can snap a pound of beans in 6 minutes. Bert can snap a pound of beans in 4 minutes. Carmen can snap a pound of bean in 3 minutes. How long will it take the three of them working together to snap a pound of beans? (A) 1 minute (B) 1 minute, 20 seconds (C) 1 minute, 33 seconds (D) 1 minute, 40 seconds (E) 2 minutes

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96. Robert ran for 1 hour at 15.0 kilometers per hour, and then he walked for 8 hours at 6.0 kilometers per hour. What was his average rate of speed in kilometers per hour for the whole trip? (A) 7.0 (B) 7.5 (C) 8.0 (D) 9.0 (E) 10.5 97. Lydia drove half of the distance from A to B at 120 kilometers per hour, and the other half of the distance at 80 kilometers per hour. What was her average rate of speed, in kilometers per hour, for the whole trip? (A) 96 (B) 98 (C) 100 (D) 102 (E) 104 98. An opera house has 2,200 seats, some in the orchestra and the rest in the balcony. Orchestra seats cost $50 each, and balcony seats cost $30 each. When every seat is sold, the total receipts are $82,000. How many orchestra seats are there? (A) 750 (B) 800 (C) 850 (D) 900 (E) 950 99. Professor Adams has a total of 54 students in two classes, A and B. Exactly one fifth of the students in class A are seniors, and exactly one half of the students in class B are seniors. If exactly one third of all of his students are seniors, how many seniors are in class A? (A) 6 (B) 8 (C) 10 (D) 12 (E) 16 100. Elizabeth put a total of $5,000 into two investments one year ago. One investment earned 8 percent interest and the other investment earned 12 percent interest. If the combined interest earned was $462, how much was invested at 8 percent? (A) $1,550 (B) $1,875 (C) $2,250 (D) $3,125 (E) $3,450

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ANSWER KEY TO PRACTICE QUESTIONS

104

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

C C E B A A A C A E

51. 52. 53. 54. 55. 56. 57. 58. 59. 60.

E A B B B A E D E C

11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

C B D D B C A A A C

61. 62. 63. 64. 65. 66. 67. 68. 69. 70.

E D E A C C E A D E

21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

B C C D D A E C E D

71. 72. 73. 74. 75. 76. 77. 78. 79. 80.

A E B E B B A B A B

31. 32. 33. 34. 35. 36. 37. 38. 39. 40.

A E C B D E C A B D

81. 82. 83. 84. 85. 86. 87. 88. 89. 90.

B E C A D A B B E B

41. 42. 43. 44. 45. 46. 47. 48. 49. 50.

A B A D A B C C E E

91. 92. 93. 94. 95. 96. 97. 98. 99. 100.

B D D B B A A B A E

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Step 3 Problem Solving

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GENERAL OUTLINE

Almost two-thirds of the questions in the Quantitative Section of the GMAT CAT are Problem Solving questions, so your final score for the section will depend to a large extent on your ability to solve Problem Solving questions quickly and accurately. This lesson introduces Problem Solving questions, provides a systematic method for solving them, and gives several specific strategies designed to help you save time and eliminate wrong answers.

THE

FOLLOWING TOPICS WILL BE COVERED IN THIS LESSON:

The Problem Solving Directions The Challenge Of These Questions The Wrong Answer Factory The MBA Center Approach To Problem Solving Questions Specific MBA Center Strategies For Problem Solving Questions

KEY TERMS The Wrong Answer Factory. The Wrong Answer Factory is the name we have given to the people who create wrong answers designed to attract the unwary test taker. Inserting Numbers. Inserting numbers is a strategy that allows the test taker to plug numbers into the problem in order to simplify calculations. Backsolving. Backsolving is a technique, especially helpful for difficult word problems, that consists of inserting the answer choices back into the problem in order to determine the correct answer. Process of Error Identification. Process of Error Identification is a strategy by which you eliminate wrong answers to get to the right answer.

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Problem Solving

READY… Problem Solving questions are combined with Data Sufficiency questions in the Quantitative Section of the GMAT CAT. Although the ultimate decision is up to the computer, you should expect that approximately 23 of the 37 questions in the Quantitative Section will be Problem Solving questions. Problem Solving questions are simply math questions in a multiplechoice format. A Problem Solving question consists of a math problem in question form followed by five answer choices, only one of which is correct. The wrong answer choices are designed to tempt test takers who either make common mistakes or don’t understand the problem. How the test makers produce wrong answer and how you can avoid them are both discussed later in this lesson.

THE DIRECTIONS The directions for the Problem Solving questions are similar to the following: GMAT CAT – Section 3 : Quantitative End

When finished reading directions click on the icon below

Directions: Solve the following problems and indicate the best answer from the choices given. Numbers: All numbers used are real numbers. Figures: Figures accompanying problems are intended to provide information useful in solving the problem. Except when otherwise specifically stated, figures are drawn as accurately as possible. All figures lie in a plane unless otherwise stated. Straight lines may appear jagged on the computer screen.

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THE DIRECTIONS MEAN

The directions first state that you should select the “best” answer. What this means, of course, is that you should choose the correct answer. These are math problems, so there should be only one correct answer. If you find that more than one answer is possible, it is likely that you have misunderstood the problem. The directions also indicate that all numbers used are real numbers. This simply means that all of the numbers used in the test have a place on the number line. None of the numbers are imaginary or complex numbers. Finally, the directions state that, unless © The MBA Center

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otherwise indicated, figures are meant to provide useful information and are drawn as accurately as possible. This means that diagrams are generally drawn to scale, so you can use the diagrams to help you guess at the answers if you get stuck. Here is a typical Problem Solving question: Score Value: 530

01:15 Note: On the actual GMAT CAT the answer choices will not be lettered as they are in this diagram. Instead, each answer choice will correspond to an oval on the screen. To indicate your answer, you simply use the mouse to click on the appropriate oval.

GMAT CAT– Section 3 : Quantitative

1 of 37

If the area of a square is 80, then what is the area of the largest circle that could fit within the square? (A) (B) (C) (D) (E)

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10P 20P 25P 40P 80P

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The correct answer to this question is (B) or 20P. Answers (A) and (D) are meant to lure test takers who make simple multiplication errors and choices (C) and (E) are designed to trick test takers who don’t understand the problem. Authors Note: On the GMAT CAT, the answer choices will be preceded by hollow ovals. You indicate your choice by clicking on the appropriate oval using the mouse. In this chapter and in the rest of this book, however, the answer choices will be designated by the letters A, B, C, D, and E for ease of reference.

WHAT PROBLEM SOLVING QUESTIONS TEST Problem Solving questions test your mastery of basic mathematical concepts and your ability to solve complex problems accurately, and above all, to do it quickly. The difficulty with solving Problem Solving questions is generally not in calculating an answer, but sorting through the information given and quickly finding the best approach to determine the correct answer. Because you must arrive at a solution, Problem Solving questions also test your ability to work with numbers carefully and accurately.

THE CHALLENGE The principal challenge of the Quantitative Section of the GMAT is time. If you were given an unlimited amount of time, you could probably answer most of the questions in this section. Unfortunately, time is very limited. Most test takers find it difficult to finish all 37 questions in the Quantitative Section before time has expired. Time is a particular problem with respect to Problem Solving questions because you not only have to determine how to solve the problems, but you must also do the math necessary to arrive at a solution. For this reason the MBA Center method stresses both mastery of the necessary mathematics and employment of the time-saving strategies in this lesson.

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Problem Solving

AIM… THE RANGE OF DIFFICULTY OF PROBLEM SOLVING QUESTIONS On the GMAT CAT, Problem Solving questions are chosen from a very large database of questions categorized by content and difficulty. The difficulty level of a question is based on how previous test takers have responded to it. The CAT tries to determine your level of ability and give you questions that are appropriate. In theory, you will eventually reach a level of difficulty where you will get roughly half of the questions right and roughly half wrong. Below are three questions representing three different levels of difficulty:

AN

EASY QUESTION

01:13

Score Value: 350

GMAT CAT– Section 3 : Quantitative

2 of 37

If x – 5 = 15, then what is the value of 2x ? (A) 20 (B) 40 (C) 100 (D) 200 (E) 400

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MEDIUM QUESTION

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Score Value: 500

GMAT CAT– Section 3 : Quantitative

3 of 37

If x and y are prime numbers, and the average (arithmetic mean) of x and y is 14, then x could be which of the following? (A) 2 (B) 3 (C) 7 (D) 11 (E) 13

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DIFFICULT QUESTION Score Value: 680

GMAT CAT– Section 3 : Quantitative

4 of 37

Series T is a sequence of numbers where each term after the first term is x greater than the term that precedes it. If the sum of the first and last terms of series T is 14, then what is the sum of the first three terms of series T and the last three terms of series T? (A) (B) (C) (D) (E)

–7 7 14 42 84

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! ! ! ! !

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01:09

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PHINEAS AND THE WRONG ANSWER FACTORY For every Problem Solving question there are five answer choices, only one of which is correct. The other four answers are wrong, but there’s more to it than that. After writing a question and determining the correct answer, the test writer (whom we’ve nicknamed Phineas) sets about to devise incorrect answers that will attract test takers who have made a common mistake, who only partially understand the problem, or who haven’t any idea what the question is asking. This is really what makes Problem Solving questions difficult. Take a look at the previous example of a difficult question with a different set of answers. Revisited GMAT CAT– Section 3 : Quantitative

4 of 37

Series T is a sequence of numbers where each term after the first term is x greater than the term that precedes it. If the sum of the first and last terms of series T is 14, then what is the sum of the first three terms of series T and the last three terms of series T? ! ! ! ! !

(A) (B) (C) (D) (E)

➩

01:09

Score Value: 680

Catch-22 John F. Kennedy July 14, 1789 42 London

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Not quite a 680-level question now, is it? So you can see that the wrong answers are very important in making Problem Solving questions difficult.

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Problem Solving

HOW PHINEAS DEVISES WRONG ANSWERS Learning how Phineas creates wrong answers will help you to eliminate incorrect answer choices and improve your chances on the Problem Solving questions. In general, there are three different types of wrong answers: those designed to trick people who have made a common mistake (adding two numbers instead of subtracting, for example); those designed to tempt people who only partially understand the problem; and those designed to fool people who have no idea how to solve the problem. The following example illustrates how Phineas devises the wrong answers for the Problem Solving questions: Score Value: 500

GMAT CAT– Section 3 : Quantitative

5 of 37

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01:07

Jack bought a packet of pens in a store. If Patti went to another store and bought 10 percent more pens than Jack and paid 10 percent more per pen than Jack, what percent more did Patti spend on pens than Jack? (A) (B) (C) (D) (E)

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21%

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! ! ! ! !

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Phineas starts with the correct answer, in this case 21, but his work is far from finished. He still must think of four plausible wrong answer choices. Now, Phineas devises incorrect answers designed to attract test takers who make common mistakes or who don’t understand the problem. From years of experience designing and administering the GMAT, Phineas knows that the most common mistakes are: Simple arithmetic mistakes (adding instead of subtracting, for example) ● Omitting a step of a multiple-step problem ● Confusing units of measure or time (forgetting to convert from hours to minutes, for example) ●

In addition, many test takers who don’t understand a problem are attracted by answer choices that repeat numbers that appear in the problem or answer choices that “look” different from the other answer choices (the only answer choice with an exponent, for example). These are generally wrong.

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LET’S TAKE A LOOK AT PHINEAS’ FINAL PRODUCT: Reprise

Score Value: 500

GMAT CAT– Section 3 : Quantitative

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Jack bought a packet of pens in a store. If Patti went to another store and bought 10 percent more pens than Jack bought and paid 10 percent more for each pen than did Jack, what percent more did Patti spend on pens than Jack? (A) (B) (C) (D) (E)

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Answer choice (A) simply repeats the number 10, which appears in the question. This kind of answer choice is very popular among test takers who have no idea what to do. Answer choice (B) is 10 percent more than 10 percent, an overly simplistic solution to a medium to difficult problem. Answer choice (C) is structurally different from the rest. It is the only one with a decimal. This answer, like the first answer choice attracts test takers who don’t understand the problem. Answer choice (D) simply adds the two 10’s in the question, a onestep solution to a multi-step question.

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Problem Solving

THE MBA CENTER METHOD FOR PROBLEM SOLVING QUESTIONS The MBA Center Method for Problem Solving questions emphasizes a systematic and organized approach for each and every question. The method is designed to help you solve the Problem Solving questions quickly and accurately, without wasting time and without making careless errors. You should practice using this method when you work through the examples in this lesson and when you do the Problem Solving practice exercises in this book. Step 1: Read and understand the question. In order to answer a Problem Solving question you must first understand what information you are given and exactly what the question asks you to find. Take the time necessary to read carefully through the problem in order to ensure that you don’t make a careless mistake or fall into one of Phineas’ traps. Above all, make sure you understand exactly what the question asks you to find. Take a look at the following example: Score Value: 550

A GMAT CAT– Section 3 : Quantitative

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In 1955, 300 of a company’s 750 employees were women. In 1987, the company had 900 employees, 430 of whom were women. The number of female employees increased by what percent from 1955 to 1987?

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GMAT CAT– Section 3 : Quantitative

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In 1955, 300 of a company’s 750 employees were women. In 1987, the company had 900 employees, 430 of whom were women. The number of female employees in 1987 was what percent of the number of female employees in 1955?

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Notice the difference between the two questions. The first asks for the percent increase and the second asks for the percent of. Two very different questions. Note also that the number of male employees is irrelevant in both questions. If you misunderstood the question — for example, if you thought the second example was asking for the percent increase — Phineas will have a wrong answer waiting for you. Step 2: Determine the best way to solve the question. Generally, there is more than one way to solve a Problem Solving question. The method you should use is the one that will get you to the correct answer in the least amount of time. You can always solve Problem Solving questions by simply working through them mathematically, but there are often quicker, easier ways to arrive at the correct answer. In this lesson you will learn strategies designed to help you save time on Problem Solving questions. When you read Problem Solving questions, try to determine early on which time-saving strategies and shortcuts you can use. Step 3: Decide how much time to spend on the question. Time is precious on the GMAT CAT, so you can’t afford to spend too much time pondering any one question. If you’ve been through steps one and two of the MBA Center Method and you’re stuck, you have to determine how much time and effort to put in before you guess. Remember, the early questions are a lot more valuable than the later questions, so you should try to avoid guessing until later in the section. But if you get a problem that you really don’t think you will be able to solve, you shouldn’t waste time staring at the question. If you think you are going to have to guess on a problem, you should try to eliminate as many answers as you can and guess quickly rather than wasting a lot of time and energy trying to solve the problem. Take a look back at Time Management on the CAT in the previous lesson to get an idea of how much time you should spend on the questions in the various stages of the section. Step 4: If you’re stumped, guess. Summary of the MBA Center Method for Problem Solving Read and understand the question. Determine the best way to solve the question. Decide how much time to spend on the question.

Remember that the CAT determines your level of ability and gives you questions that are appropriate, so you will find that most of the questions on the CAT are difficult for you. Therefore, you are going to have to guess on some of the questions. That’s unavoidable. But you can improve your chances of guessing correctly by eliminating wrong answer choices. In this lesson you will learn how to use the Process of Error Identification to narrow down the answer choices. You should practice using this strategy in order to improve your chances of guessing the correct answer.

If stumped, guess.

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Problem Solving

FIRE! In this section of the lesson we are going to show you how to apply specific techniques to solve the problems more easily and more accurately.

INSERTING NUMBERS Many Problem Solving questions require you to work with algebraic expressions (a formula or equation with variables such as x and y). Some questions give you an algebraic expression directly while some, particularly word problems, require you to set up an algebraic expression on your own. Often, the best way to solve these problems is to substitute numbers for the variables in the problem. Here is how the strategy of inserting numbers works: Identify the unknowns or variables in the problem. Sometimes the problem will explicitly state what the variables are (a carpet has dimensions x by y, for example). Often, particularly in word problems, you will have to spot the variables yourself (a farmer sells 2 of 5 his goods, for example). The first step in using this strategy is determining what the variables are.

Make life easy for yourself. Pick low, easy numbers to insert in the problem.

Determine the equations you need to solve the problem. Again, you are sometimes given the equations in the problem itself or in the answer choices. These are easy to spot. In word problems, however, you are often required to set up the equations yourself. Look for words that express a mathematical relationship such as “doubled” or “increased by x percent” to help you set up equations contained in the problem. Pick numbers to stand in for the variables. Pick numbers that will make calculations simple. Generally, you should pick low integers in order to make your work easy. In percent increase/decrease problems, pick numbers that will give you 100 as a starting value. For problems involving fractions, pick numbers that are multiples of the denominators of the fractions so that the calculations will work out to integers. Insert the numbers and solve the equations. Insert the numbers you picked above and solve the equations. For many problems, this will lead you directly to the correct answer choice. For some questions, particularly number property questions (“Which of the following is a prime number?” for example) and questions with variables in the answer choices, more than one answer choice may work using the numbers you picked. If this happens, eliminate the answer choices you can and pick a fresh set of numbers. The correct answer choice will work for any set of numbers picked.

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Step 3.1 Lesson

Here’s an example of a Problem Solving question and how you can use the strategy of inserting numbers to solve it. Score Value: 560

GMAT CAT– Section 3 : Quantitative

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A jar contains a number of beads and a second jar contains three times as many beads as the first. If 60 percent of the beads in the first jar are red and 20 percent of the beads in the second jar are red, then what percent of the total beads in both jars are red? (A) (B) (C) (D) (E)

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First, you must determine what the unknowns or variables are in the problem. In this case, you know the percentage of red beads in both jars, but you don’t know just how many beads there are in either jar. These are your unknowns. Now you need to pick a total number of beads for each of the jars. You know that all of the information necessary to determine the answer is somewhere in the problem. Because the total number of beads is never mentioned, you know that the total number of beads in the jars can’t make a difference. That means that you can pick any numbers that will make your calculations easy. Since this is a percent problem, you want to pick numbers that will give you 100 as a starting point. Pick 25 for the first jar. The question tells you there are three times as many beads in the second jar as the first, so the total number of beads in the second jar has to be 75. If there are 25 beads in the first jar and 75 beads in the second jar, then the total number of beads in both jars is 100, which is just what we wanted. You’re now ready to solve the problem. If there are 25 beads in the first jar, and 60% of them are red, then the number of red beads in the first jar is 60% of 25, or 0.6 × 25 = 15. Likewise, there are 75 beads in the second jar, 20% of which are red, so the number of red beads in the second jar is 0.2 × 75 = 15. If there are 15 red beads in the first jar and 15 red beads in the second jar, then the total number of red beads in both jars is 30. Remember, you’re asked to determine what percent of the total beads in both jars are red. You know that the total number of beads in both jars is 100. The question then is this: 30 is what percent of 100? That’s easy. It’s 30%, which is the correct answer.

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Problem Solving

The types of questions that can usually be solved by inserting numbers: Percent increase/decrease problems without values in the question Score Value: 590

GMAT CAT– Section 3 : Quantitative

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If the time it takes a company to build a dam is determined by the

On percent problems, pick numbers that give you 100 as a starting value.

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2 formula d nw , where d is the depth of the dam in meters, w is the

width in meters, and n is the number of employees involved, and the plans for a certain dam are changed so that the depth increases by 20 percent, the width decreases by 30 percent, and the number of employees increases by 40 percent, what will be the percent change in the time required to build the dam? (A) (B) (C) (D) (E)

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40% 28% 15% 30% 88%

decrease decrease increase increase increase

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Score Value: 600

GMAT CAT– Section 3 : Quantitative

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Last year, a certain store made a 10 percent profit on all sales. This year, sales are 20 percent higher than last year, but the store’s profits are only 5 percent of sales. This year’s profits are what percent of last year’s profits? (A) 60% (B) 80% (C) 100% (D) 120% (E) 140%

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Problems involving fractions without totals: Score Value: 620

GMAT CAT– Section 3 : Quantitative

If a vendor sells

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2 1 5 of his goods in the morning and 3 of the

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remaining goods in the afternoon, what fraction of his goods did he sell in the morning and afternoon combined? ! (A) 3 8 ! (B) 2 5 ! (C) 3 5 ! (D) 2 3 ! (E) 11 15

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Score Value: 570

GMAT CAT– Section 3 : Quantitative

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A certain drug is used to fight a deadly microbe. It is known that

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when the drug is given to a patient it kills 1 of the microbes in the

3

first 24 hours. During each successive 8-hour period, the drug kills

1 of the microbes present at the beginning of that period. After 2 2 days, what fraction of the microbes initially present will remain? ! (A) 1 48

! (D) 1 8

! (B) 1 24

! (E) 1 6

! (C) 1 12

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Problem Solving

Questions involving number properties: (odd or even, prime or not prime, integer or not integer, etc.) Score Value: 630

GMAT CAT– Section 3 : Quantitative

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If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true?

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I. a + b + c is an even integer. II. ab is an even integer. a+ b =c III. 2 (A) (B) (C) (D) (E)

I only II only I and II only II and III only I, II, and III

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Score Value: 640

GMAT CAT– Section 3 : Quantitative

13 of 37

If x and y are distinct prime numbers, then which of the following is a prime number?

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! (A) xy ! (B) 3xy2 x2– y2 ! (C) x – y – y ! (D)

2x2– 2y2 – 2x x–y

2 2 ! (E) x – y + 3y – x x–y

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Questions with variables in the answer choices: Score Value: 650

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GMAT CAT– Section 3 : Quantitative

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If n identical pipes can fill an x-gallon pool in t hours, then at the same rate how long will it take one such pipe to fill a y-gallon pool? (A) ty xn (B) nty x (C) n xyt (D) y xnt (E) xy nt

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Score Value: 460

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GMAT CAT– Section 3 : Quantitative

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B INSERTING NUMBERS OUTLINE Identify the unknowns or variables in the problem Determine the equations you need to solve the problem Pick numbers to stand in for the variables Insert the numbers and solve the equations Questions that can usually be solved by inserting numbers: Percent increase/decrease problems without values in the question Problems involving fractions without totals Questions involving number properties (odd or even, prime or not prime, integer or not integer, etc.) Questions with variables in the answer choices

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A

C D

Square ABCD above is partially within a circle with center A. Each of sides AB and AD of the square is a radius of the circle. If the area of square ABCD is x, then what is the area of the circle?

(A)

x2 3P

2 (D) P x

(B)

x 4P

(E)

x 3 4P

(C) P x

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Problem Solving

BACKSOLVING Backsolving is similar to inserting numbers, but instead of picking numbers yourself you simply use the answer choices given to you. Remember that there is only one correct answer among the answer choices and it is the only answer that will agree with the information in the problem. Therefore, you can plug each answer choice into the equation or equations in the problem. The one that works is the correct answer. Backsolving is particularly helpful when you get stuck on a difficult or complex problem. Generally, you should only attempt to backsolve problems with integers as answer choices. Here’s how backsolving works: Start with the middle answer choice (generally). Because the answer choices are arranged in order from least to greatest or greatest to least, you should generally start with the middle answer choice. That way, if the answer choice is too large or too small, you will have eliminated the answer choice you picked and the two above or below it. However, if it appears that using the middle answer choice will make calculations difficult, pick a different answer choice. Work through the problem using the answer choice you picked. Substitute the answer choice into the equation or equations in the problem. If all of the equations work, then you’ve found the correct answer. If any of the equations do not work out using the answer choice you picked, then you should eliminate it and pick another answer choice. If necessary, check the next answer choice. If you backsolve an answer choice and it doesn’t work, you can eliminate it. If the answer choice is too large, you can eliminate both of the answer choices that are larger than it. Likewise, if the answer choice is too small, you can eliminate both of the answer choices that are smaller than it. Now you can pick from the two remaining answer choices and try again. Here’s an example of a Problem Solving question and how you can use the strategy of backsolving to solve it. Score Value: 530

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GMAT CAT– Section 3 : Quantitative

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Four friends live together in an apartment and split the monthly rent equally. When one of the friends moves out, the remaining three split the rent equally and each pays $50 per month more than before. How much is the total monthly rent for the apartment? (A) $240 (B) $360 (C) $480 (D) $600 (E) $800

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Start with the middle answer choice, in this case $480, and work through the problem. If the total rent for the apartment is $480, then each of the four friends initially pays $120 per month (480 ÷ 4 = 120). The question then tells you that after one of the friends leaves, each of the remaining three pays $50 more than before. If each person was paying $120 before, they would now be paying $170 each per month (120 + 50 = 170), but if that’s true then the total monthly rent would be $510 (170 × 3 = 510), which is higher than $480, so we know that the total monthly rent has to be higher than $480. Eliminate the middle answer choice and the two that are lower than it. Now we move to the next highest answer choice, in this case $600, and work through the problem the same way. If the total rent for the apartment is $600, then each of the four friends initially pays $150 per month (600 ÷ 4 = 150). The question then tells you that after one of the friends leaves, each of the remaining three pays $50 more than before. If each person was paying $150 before, they would now be paying $200 each per month (150 + 50 = 200). If each person pays $200 per month, then the total monthly rent is $600 (200 × 3 = 600), which is correct. So $600 is the best answer. The types of questions that can usually be backsolved: Word problems with integers as answer choices: Score Value: 580

GMAT CAT– Section 3 : Quantitative

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A salesman is paid $5.00 per hour for every hour he works in the office and $8.00 for every hour he spends on the road. If the salesman earned $360 during a certain week, and if he worked twice as many hours in the office as he spent on the road, then how many hours did the salesman work in the office during the week?

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(A) 20 (B) 40 (C) 50 (D) 60 (E) 70

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Problem Solving

Score Value: 590

GMAT CAT– Section 3 : Quantitative

18 of 37

A car dealer had a sale in order to sell off excess stock. Before the sale, the dealer had three times as many cars as he had trucks. During the sale, he sold 100 cars and 25 trucks. If after the sale the dealer has twice as many cars as he has trucks, then how many cars did the dealer have prior to the sale? (A) 60 (B) 90 (C) 120 (D) 150 (E) 180

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Score Value: 620

GMAT CAT– Section 3 : Quantitative

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The ratio of flowering to nonflowering plants on an acre of land is 3 to 2. After 140 nonflowering plants are removed from the property, the new ratio of flowering to nonflowering plants is 4 to 1. How many plants were there on the acre of land before the 140 nonflowering plants were removed? (A) 224 (B) 252 (C) 280 (D) 560 (E) 700

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Step 3.1 Lesson

Problems with complex algebraic expressions and integers as answer choices: Score Value: 650

GMAT CAT– Section 3 : Quantitative

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If (x – 1)(x – 2)(x – 3)(x – 4) = 24, then x could be which of the following? ! ! ! ! !

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(A) 4 (B) 5 (C) 6 (D) 7 (E) 8

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Score Value: 580

GMAT CAT– Section 3 : Quantitative

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If (x – 1)(y – 2) + (x – 3)(y – 4) + (x – 5)(y – 6) = 8, and x + y = 9, then x could be which of the following? ! ! ! ! !

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(A) 0 (B) 1 (C) 2 (D) 3 (E) 7

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BACKSOLVING OUTLINE Start with the middle answer choice (generally) ● Work through the problem using the answer choice you picked ● If necessary, check the next answer choice ●

Questions that can usually be backsolved: ● Word problems with integer answer choices ● Problems with complex algebraic expressions and integers as answer choices

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Problem Solving

PROCESS OF ERROR IDENTIFICATION Remember that for each question there is only one right answer and the other four are incorrect, so there are really two paths to the correct answer choice: 1) You can solve the problem or 2) you can eliminate all of the wrong answers, leaving only the best answer. Even if you are able to eliminate only two or three answer choices, your chances of getting the question right increase tremendously. You should therefore practice using the Process of Error Identification to zero in on the right answer. This strategy works especially well when a question has you completely stumped. Here’s how The Process of Error Identification works: Try to get a general idea what the question is asking. In order to identify and eliminate answer choices that don’t make sense in the context of the question, you must first understand what the question asks you to find. Many times wrong answer choices are designed to fool the test taker who doesn’t read the question carefully enough. Take a look at the following example: Score Value: 590

A GMAT CAT– Section 3 : Quantitative F

Regular hexagon ABCDEF is inscribed in a circle with area 9π. What is the perimeter of hexagon ABCDEF?

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B

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Score Value: 590

GMAT CAT– Section 3 : Quantitative

22 of 37

Regular hexagon ABCDEF is inscribed in a circle with area 9π. What is the area of hexagon ABCDEF?

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Did you notice the difference between the two questions? The first asks for the perimeter of the hexagon and the second asks for the area. Two very different questions. Eliminate answer choices that seem unreasonable. Remember that the answer choices are designed to attract test takers who have made a common mistake (adding instead of subtracting, for example) or who have misunderstood the problem. Many times you will be able to see that several of these answer choices are unreasonable if you simply take a step back and look at the problem using your common sense. Try these examples: Score Value: 560

GMAT CAT– Section 3 : Quantitative

F

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Regular hexagon ABCDEF is inscribed in a circle with area 16π. What is the area of hexagon ABCDEF? ! (A) 4

! (D) 24

! (B) 6 3

! (E) 48 2

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First, note what the question asks you to find. In this case it is the area of the hexagon inscribed in the circle. If you look at the figure, you can see that the hexagon is smaller than the circle, but not that much smaller. π is about 3.14, so you can estimate that the area of the circle is about 48. Now, you can safely eliminate any answer choice that is larger than 48 or significantly smaller than 48.

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Problem Solving

Score Value: 610

GMAT CAT– Section 3 : Quantitative

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David can sail m miles in 13 hours. At that constant rate, how many hours will it take David to sail n miles?

! (A)

mn 13

! (C)

13m n

! (B)

13 mn

! (D)

13n m

! (E)

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In this question you are asked to determine how long it will take David to sail n miles. You should first notice that as n increases the amount of time it will take David to sail n miles has to increase as well. For example, it would certainly take David longer to sail 1,000 miles than it would to sail 10 miles. So you can eliminate any answer choices where n appears in the denominator of the fraction. Remember that as the denominator of a fraction increases the value of the fraction decreases. Therefore, answer choices (B), (C) and (E) are gone. If you guess at this point, you have a fifty-fifty shot. Now you should note that as m increases, David is sailing faster. For example, if David sails 1,000 miles in 13 hours he is certainly moving faster than if he sails only 10 miles in 13 hours. You know that the faster David sails, the less time it will take him to sail n miles, so you can eliminate any answer choice where m appears in the numerator of the fraction. Therefore, you can eliminate answer choices (A), (C), and (E). Since you’ve already eliminated answer 13n choice (B), the only answer choice remaining (D), or , which is m the correct answer.

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Score Value: 610

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If John had three times the amount money he has now, he would have exactly the amount necessary to purchase three compact discs at $9.95 each and two tapes at $7.92 each. How much money does John have? ! ! ! ! !

(A) $12.32 (B) $13.55 (C) $15.23 (D) $16.81 (E) $17.79

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Now try the Process of Error Identification on the following problem:

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Try working with only the last digits. In this example you know that the last digit of the total price of the discs is 5 and the last digit of the total price of the tapes is 4. If you add the two together, you know that the last digit of the total cost of the discs and the tapes is 9. Because we know that John has one third the amount necessary to purchase the discs and the tapes, we know that the last digit of the amount he actually has must end in a 3.

Step 3.1 Lesson

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Problem Solving

SUMMARY Problem Solving questions are simply math questions in a multiplechoice format. They are designed to test your mastery of basic math concepts and your ability to reason quantitatively. The main challenge of the Quantitative Section is time. The time you are allowed is very limited and must be managed well in order to make sure you can answer all the questions before time expires. The MBA Center Method employs specific strategies designed to help you save time when answering Problem Solving and Data Sufficiency questions. For every question there is only one correct answer. The wrong answers are designed by Phineas to attract test takers who make common mistakes or who don’t completely understand the question. Understanding how Phineas devises wrong answers will help you to avoid traps. The MBA Center Method for Problem Solving questions emphasizes a systematic and effective approach for every question. The method is designed to help you solve the Problem Solving questions quickly and accurately, without wasting time and without making careless errors. The MBA Center strategies of inserting numbers, backsolving, and eliminating incorrect answer choices are time-saving strategies that will enable you to answer many Problem Solving questions quickly and correctly.

PROBLEM SOLVING LESSON ANSWER KEY 1. 2. 3. 4. 5. 6.a

B B D D E 43 1 % 3 6.b 143 1 % 3 7. 8. 9. 10. 11. 12. 13.

B B A C C B C

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14. B 15. C 16. D 17. B 18. D 19. D 20. B 21. D 22.a 18 22.b

27 3 2

23. D 24. D 25. C

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Problem Solving

HOMEWORK/PRACTICE TEST PROBLEM SOLVING ANSWER GRID

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Step 3.2 Homework

Problem Solving – Homework End

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TIME – 25 MINUTES 16 QUESTIONS Directions: Solve the following problems and indicate the best answer from the choices given. Numbers: All numbers used are real numbers. Figures: Figures accompanying problems are intended to provide information useful in solving the problem. Except when otherwise specifically stated, figures are drawn as accurately as possible. All figures lie in a plane unless otherwise indicated. Straight lines may appear jagged on the computer screen.

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1 – 1 2 3 1. = 1 4 (A)

1 24

(B)

7. If the perimeter of a rectangle is 32 feet and its area is 60 square feet, what is the length, in feet, of each of the longer sides? 5 12

(C)

2 3

(D)

4 5

(E)

10 3

2. Working at the same constant rate, 4 proofreaders can proofread 180 pages per hour. How many pages could 15 proofreaders, all working at this same rate, proofread in 2 hours?

(A) 5 (B) 6 (C) 10 (D) 12 (E) 15

8. What is the least positive integer divisible by each of the integers 9 through 12, inclusive? (A) 1,980 (B) 3,960 (C) 5,940 (D) 10,890 (E) 11,880

(A) 216 (B) 1,350 (C) 1,800 (D) 2,160 (E) 5,400

3. A company’s profits for 1996 equaled 7 percent of its revenues. If its profits in 1996 were 27 million dollars, approximately what were the company’s revenues, in millions of dollars, in 1996 ? (A) 1.89 (B) 3.86 (C) 18.9 (D) 38.6 (E) 386

4. How many minutes does it take to read 40 pages reading at the constant rate of 100 pages per hour? (A) 5 (B) 20 (C) 15 2 3

(D) 24

9. How many integers between 150 and 200, inclusive, can be evenly divided by both 3 and 5 ? (A) 3 (B) 4 (C) 5 (D) 12 (E) 27

10. For all numbers p and q, the operation ! is defined by p ! q = p2(q – 3). If 2 ! x = –20, what is the value of x ? (A) –10 (B) –8 (C) –7 (D) –5 (E) –2

(E) 40

5. A video store charges its members a base fee of $24 per year plus $3 for each 2-day video rental. If a member was charged $42 for membership and 2-day video rental fees for 1990, then at the same rate how many 2-day videos did the customer rent in 1991 if his charges for 1991 were double his 1990 charges? (A) 6 (B) 12 (C) 14 (D) 20 (E) 28

6. A company manufactures 78 faulty devices out of every 100,000 devices it manufactures. If it manufactured a total of 3 million devices last year, how many of them were faulty?

11. In a sequence of 10 increasing consecutive integers, the sum of the last five integers is 230. What is the sum of the first 5 integers in the sequence? (A) 225 (B) 220 (C) 215 (D) 210 (E) 205 12. The fixed operating costs to a team owner of holding a live football match total $80,000. In addition, there is an average cost to the owner of $6 per spectator who attends the match. If each spectator pays $14 for a ticket, how many spectators must attend for the owner to make a profit of $160,000 ? (A) 10,000 (B) 20,000 (C) 30,000 (D) 40,000 (E) 50,000

(A) 234 (B) 260 (C) 2,340 (D) 2,600 (E) 23,400

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13. If 1 < a < b < c

16. A company hires a consultant to help with the development of a new product line. The consultant is able to choose from two methods of payment, either a flat fee of $800 plus 6 percent of the revenues from the new product, or a flat fee of $200 plus 10 percent of the revenues from the new product. For what amount of revenue would the consultant’s salary be the same under either payment methods?

1 1 1 c then which of the following must be true?

1 and if x = a

and y = 1 1 b

and z =

(A) z < y < x (B) x < y < z (C) x < z < y (A) $3,750 (B) $6,250 (C) $15,000 (D) y < z < x (E) z < x < y (D) $18,500 (E) $25,000

w

l

14. The rectangular window represented in the figure above, of dimensions w centimeters by l centimeters, is surrounded by a frame 4 centimeters wide. Which of the following represents the area of the frame, in square centimeters? (A) 8w + 8l + 128 (B) 8w + 8l + 64 (C) 8w + 8l +16

(D) 4w + 4l + 16

(E) 4w + 4l + 4

15. If (x + 1)2 = 900, then x – 4 could be equal to which of the following? (A) 27 (B) 26 (C) –33 (D) –34 (E) –35

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PROBLEM SOLVING HOMEWORK/PRACTICE TEST ANSWER KEY 1. C 2. B 3. E 4. D 5. D 6. C 7. C 8. A 9. B 10. E 11. E 12. C 13. E 14. B 15. E 16. C

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EXPLANATIONS TO PROBLEM SOLVING HOMEWORK/PRACTICE TEST 1. (C) First you should find a common denominator, in this case 12. You can then multiply both the top and the bottom by 12. Thus: # 1 1& 12% " ( $ 2 3' (6 " 4) 2 = = or ( C) 3 # 1& 3 12 % ( $4'

2. (B) This is essentially a ratio question. Eliminate (A) because it's just too small. To solve, find out how many pages one proofreader does in one hour: 180 = 45. 4 Multiply this rate by 15 proofreaders to get 675. Then multiply by 2 because they work for 2 hours. Thus 1,350, or (B), is the answer.

3. (E) This is a great question to backsolve. Rephrase the question this way: 27 million dollars is 7% of which answer choice? Notice also that the numbers in the choices are pretty far apart. This means you can estimate. Instead of 7%, try 10%. Try (C). 10% of 18.9 million, is 1.89 million. You want 27 million, so (C) is too small. So, then, are (A) and (B). Eliminate them. Try (D). 10% of 38.6 million is 3.86 million. Still too small. Try (E). 10% of 386 million is 38.6 million. Close enough to 27 million. Go with (E). To actually solve the question, you could have set up an equation: 7% x = 27,000,000 Then divide 27,000,000 by .07 and you get approximately 386 million. Note though, that when the choices are far apart (here for example, you have 3.86, 386, and 386 million) the challenge is to get the right number of decimal places, not the exact figure.

4. (D) This is a ratio question. Be careful of minutes and hours. 100 pages: 60 minutes = 40 pages: x minutes.

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In other words: 100 = 40 60 x Remember, always look to reduce on the GMAT before multiplying out. Here, 100 = 10 = 5 60 6 3 Now we have 5 = 40 . 3 x When you cross-multiply, you get 5x = 120. So x = 24, or (D).

5. (D) The math in this question is not hard, but it is somewhat tricky. First, the charges were doubled in 1991. In 1990 the charges were $42, so in '91 the charges must be $84. The question is how many 2-day rentals the customer was charged for. So we have to subtract the $24 member fee. Now we have $60. Since each 2-day rental was $3, we divide 60 by 3 and get 20. Be careful not to fall for the trap of just doubling the number of 2-day rentals from 1990.

6. (C) Again, keep an eye on the answer choices. Notice that the choices are quite spread out. This indicates that it is important to get the right number of digits. You can set the problem up as a ratio: 78 x = 100,000 3,000,000 Then you isolate x and get 3,000,000(78) = x 100,000 x = 2,340 7. (C) This is another great problem to solve by backsolving. As usual, begin with (C). Assume the length is 10. Since the area according to the problem is 60, the width must be 6. Now check that a rectangle with length 10 and width 6 actually has perimeter 32. This is correct, as 10 + 10 + 6 + 6 = 32, so (C) is the right answer.

8. (A) This looks like a really tough problem with really big numbers, but hold on. Relax. Remember that the GMAT is not testing you to see if you are a human calculator. To find a least common multiple, take the prime factors of each number. For 9, the prime factors are 3 and 3. For 10, 5 and 2. © The MBA Center

Problem Solving

For 11, just 11. For 12, 2, 2, and 3. Now, just remember not to count the prime factors that come up for more than 1 number. For example, 10 has a prime factor of 2, but so does 12. You only count the 2's from the 12. Now you multiply out all the prime factors without the repeats: 3 x 3 x 5 x 2 x 11 x 2 = 1,980. Another method to solve this problem is to backsolve. Start with (C) and divide each number into 5940. They all go evenly. (C) could be the right answer at this point. (D) and (E) are definitely wrong, since we're looking for the least positive integer. Then try (A) and (B), both of which also work. (A) is the smallest so it must be the answer.

9. (B) Numbers that can be divided by both 3 and 5 must be divisible by 15. 150 is divisible by 15 (and thus 3 and 5). That is the first one. Then every 15 there is another: 165, 180, 195, making a total of 4. Inclusive means you include the two numbers given, 150 and 200.

Another option is to actually figure out what the numbers are and then compute the sum. Since five consecutive numbers add up to 230, the average of the 5 numbers is 230/5, or 46. The last 5 numbers, then are 44, 45, 46, 47, 48. The first 5 are 39, 40, 41, 42, 43, and these numbers add up to 205.

12. (C) This is probably easiest to solve by backsolving. As usual, start with C. Suppose there are 30,000 spectators. Multiply by 14 to get $420,000. Then subtract the $80,000 fixed cost and you get $340,000. Then subtract the cost of $6 for each spectator, $180,000. You now have left $160,000. This is the expected value, so C is the right answer.

13. (E) This is a good problem to do by subbing. Pick easy numbers for a, b, and c, such as 2, 3, and 4. 1 1 Now x = a or 2

Lastly z =

Then y =

1 1 or or 3. 1 1 b 3

1 1 # 1& % ( $c '

10. (E) A weird symbol question. Don't be intimidated by the symbols, because the definition is given to you. p ! q = p2(q – 3). Now, since you are asked about 2 ! x, you just substitute 2 for p and x for q. The result is 22(x – 3) = –20 4(x – 3) = –20 4x – 12 = –20 4x = –8 x = –2

This is the same as 1 , or with our numbers, 1 . 4 c

11. (E) You know that the integers are consecutive. This makes our work much easier, but don't get tricked! Saying that the sum is just 5 less is too easy; instead, think about the fact that the 1st integer is 5 less than the 6th, the 2nd is 5 less than the 7th, the 3rd is 5 less than the 8th, etc. In other words, each number on the list of the first 5 is 5 less than a corresponding number on the list of the last 5. The total, then is 25 less than the list of the last 5, making the sum 205.

14. (B) To find the area of the frame, you can find the area of the big rectangle and subtract the area of the smaller rectangle, leaving only the frame. The length of the big rectangle is l + 4 + 4, or l + 8. The width of the big rectangle is w + 4 + 4, or w + 8. The area of the big rectangle, then, is (l + 8)(w + 8) = lw + 8w + 8l + 64. Now subtract the area of the smaller rectangle, lw, and you have left 8w + 8l + 64, or B. Note that a common error on this problem is to consider the length of the big rectangle l + 4, instead of l + 8. You have to count the 4 centimeters on both sides of the frame.

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Then put them in order:

1 1 , , 3, or z < x < y. 4 2

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15. (E) Remember that with squares, you have to consider a negative and a positive possibility. Since (x + 1) 2 = 900, (x + 1) = +30 or –30. If x + 1 = 30, x = 29 and x – 4 = 25, but this is not in the answer choices. Therefore try (x + 1) = –30. Then x = –31. Then x – 4 = –35. You could also backsolve, testing each answer choice against the equation.

16. (C) This problem could also be solved either algebraically or by backsolving. To do it algebraically: 800 + 0.06x = 200 + 0.10x 600 = 0.04x 15,000 = x

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Step 4 Problem Solving Workshop

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Step 4 Workshops

Problem Solving – Workshop End

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TIME – 60 MINUTES 32 QUESTIONS Directions: Solve the following problems and indicate the best answer from the choices given. Numbers: All numbers used are real numbers. Figures: Figures accompanying problems are intended to provide information useful in solving the problem. Except when otherwise specifically stated, figures are drawn as accurately as possible. All figures lie in a plane unless otherwise stated. Straight lines may appear jagged on the computer screen.

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EASY

5. If 3 – x3 = 2 + x2 , what is the value of x ? (A) –1

1. A new car costs $5,250 if the buyer pays cash. On an installment plan, the buyer pays 10 percent down and 12 monthly payments of $450 each. How much greater would the expense be paying with the installment plan than paying cash? (A) (B) (C) (D) (E)

2 3

(C) 1 (D) 3 2 (E)

$150 $225 $600 $675 $750

5

6. Which of the following is equivalent to the two inequalities x + 5 > 12 and x – 4 < 9 ?

2. There are 8 married couples at a dinner party. If 5 individuals leave, what is the greatest number of married couples that can remain? (A) (B) (C) (D) (E)

(B)

6 5 4 3 2

(A) (B) (C) (D) (E)

7 7 5 5 5

< < < < <

13 17 17 13 7

C

7. What is the area of the circular region with center C shown above?

60 150 260 300 600

4. Brian read 108 pages of a novel on Tuesday. On Wednesday he read the remaining 192 pages, reading at the same average rate he read on Tuesday. If his reading on Wednesday took 3 hours longer than his reading on Tuesday, what is his average reading rate, in pages per hour? (A) (B) (C) (D) (E)

< < < < <

(6,8)

3. A publishing company publishes three types of books—fiction, biography, and history—in the ratio 2:5:8, respectively. If the company publishes an average of 40 fiction books per month, how many books does it publish per month? (A) (B) (C) (D) (E)

x x x x x

(A) 20 (B) 36 (C) 64 (D) 100 (E) 198

28 36 42 64 100

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Step 4 Workshops A

8. If (4x – 1) 2 = 0, then x =

B 60°

(A) x = – 1 2 (B) x = – 1 4

O

12. If the circle above with center O has an area of 16), then what is the perimeter of ABCO?

(C) x = 0 (D) x = 1 4 (E) x = 1 2

4 (A) 8 + 3 8 (B) 16 + 3

9. If a > b, c > d, e > f, and f > c, then which of the following must be true? I. II. III.

C

(C) 16 + 4 (D) 16 + 8 (E) 32 + 8

a>e e>d e>c

(A) I only (B) II only (C) III only (D) I and III (E) II and III 10. A store decides to decrease the price of all its items by 15 percent. After 30 days in order to sell more items the store again decreases the price of its items by an additional 15 percent. What was the total decrease compared to the original price? (A) (B) (C) (D) (E)

15% 27.75% 30% 70% 85%

11. A company had profits in 1992 equal to 11 percent of its revenues. If the profits amounted to 22 million dollars, approximately what were the company’s revenues, in millions of dollars, in 1992? (A) (B) (C) (D) (E)

100 122 150 200 220

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MEDIUM

17. Of the following, the closest approximation to

13. Forty percent of the pets in a certain apartment building are dogs. Of the pets which are not dogs, 24 are cats and 18 are birds. If cats, dogs, and birds are the only types of pets in the building, how many pets are in the building? (A) (B) (C) (D) (E)

70 90 110 130 150

14. If (8 + 4 ) (a + 3) = 0, and a * –3, then a = a (A) –8 (B) –2 (C) – 1 2 (D) 1 2

(20 - 90)(201) is: 10 - 45 (A) (B) (C) (D) (E)

18. A car dealer has a large inventory of cars of which 25 percent are red, 15 percent are blue, 30 percent are black and the remainder are other colors. For each color of car, 70 percent are equipped with automatic transmission and of these, 20 percent have air-conditioning. What is the probability that a car chosen at random will not be black and will have both automatic transmission and air-conditioning? (A) (B) (C) (D) (E)

(E) 2

20 40 60 80 100

9.8% 14% 30% 70% 90.2%

15. The average (arithmetic mean) of the five numbers x, 91, 120, 134, and 220 is what per cent of the sum of the five numbers? (A) (B) (C) (D) (E)

20% 22% 25% 30% It cannot be determined from the information given.

2 4

I. x is a multiple of 3 II. x is a multiple of 4 III. x is a multiple of 5

(B)

2 2

(A) (B) (C) (D) (E)

(D)

I only II only I and II only I and III only I, II, and III

B

D

C

19. For the figure above, what is the ratio of the area of the larger square to the area of the smaller square? (A)

16. If x is the product of three consecutive positive integers, which of the following must be true?

A

(C) 1

(E)

2 2

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20. If x and y are prime numbers, then the product of x and y could be any of the following EXCEPT (A) (B) (C) (D) (E)

an odd integer an even integer a divisor of 45 equal to 36 less than 5

21. The value of x for which x2 + 6 = 5x and x2 + 12 = 7x is, (A) (B) (C) (D) (E)

–3 –2 2 3 4

O

23. If circle O above has area x, what is the length of its radius in terms of x ? (A) x x (B)

22. A chemist starts with a solution that is 10 percent alcohol. After the chemist adds a certain amount of pure alcohol, the resulting solution is 25 percent alcohol. By what percent was the volume increased?

(C)

x

x (D) 2 (E)

x

(A) 15% (B) 20% (C) 50% (D)120% (E) 150%

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DIFFICULT

24. A swimming pool is in the shape of a rectangular solid, and its width is 25 meters, its length is 50 meters and its depth is 4 meters. If the pool is half full, approximately how much water, in cubic meters, is needed to make it 7 full? 8 (A) 312 (B) 625 (C) 1,875 (D)2,188 (E) 2,500

27. If N = 1000x + 100y + 10z, where x, y, and z are different positive integers less than 4, the remainder when N is divided by 9 is (A) (B) (C) (D) (E)

2 4 6 8 9

28. If x and y are positive integers such that 1 > 1 1 2 x + 3 > 9 and 2 < y < 20, then which of 3 the following CANNOT be true?

25. In a certain high school, the ratio of teachers to students is 5 to 108. If 12 new students entered the school, the ratio would change to 5 to 112. How many teachers does the high school have? (A) (B) (C) (D) (E)

(A) (B) (C) (D) (E)

x+y=3 x+y=4 x–y=3 x–y=4 x2 + y2 = 25

5 10 15 20 25 a°

26. A store sold a total of 416 toy robots during an 8-day sale and a total of 275 toy trains during an 11day sale. The average (arithmetic mean) number of toy robots sold per day during the 8-day sale was what percent greater than the average number of toy trains sold per day during the 11-day sale? (A) (B) (C) (D) (E)

28 47 67 108 127

b°

a 29. In the figure above, if a+b = 3 , then a = 4 (A) (B) (C) (D) (E)

45 75 105 115 135

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30. At a certain store, 1 of the sodas sold in one 8 week were Pepsis and 1 of the remaining sodas sold 3 were Coca Colas. If x of the sodas sold were Coca Colas, how many were Pepsis? 3 (A) 8 x (B) 3 x 7 (C) 7 x 16 7 (D) 8 x

32. A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 35 percent, what is the discount rate on mysteries? (A) (B) (C) (D) (E)

9 10 13 22 25

(E) x

31. If a, b, and c are positive integers and 3a = 3b + 3c, which of the following must be true? I. a = b II. b < c III. a > c (A) (B) (C) (D) (E)

I only II only III only I and III II and III

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Step 4 Workshops

PROBLEM SOLVING WORKSHOP ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.

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D B D A E A D D E B D A A C A A A A E D D B B C C D C D E B C E

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Step 5 Data Sufficiency

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Step 5.1 Lesson

GENERAL OUTLINE

Approximately one-third of the questions in the Quantitative Section of the GMAT CAT are Data Sufficiency questions. These questions test your ability to think quantitatively, distinguish between relevant and irrelevant data, and determine whether or not you have sufficient information to answer a given question. This lesson introduces Data Sufficiency questions and provides a systematic method for solving them.

THE

FOLLOWING TOPICS WILL BE COVERED IN THIS LESSON:

Introduction To Data Sufficiency The Two Types Of Data Sufficiency Questions The MBA Center Approach To Data Sufficiency Questions MBA Center Strategies For Data Sufficiency Questions Common Data Sufficiency Traps

KEY

TERMS

Question: The heart of every data sufficiency problem is the initial question. You must determine whether, based on the information provided in the statements, you have information sufficient to answer the initial question. Statement: Each Data Sufficiency problem includes two numbered statements which provide information related to the initial question. The information in the statements is sufficient only if it allows you to answer the initial question. Determine-the-Quantity Question: This type of Data Sufficiency question asks you to determine the value of a quantity. The information in the statements is sufficient to answer the question only if it allows you to determine one discrete value for the quantity. Yes-or-No Question: As the name implies, this type of question requires either a yes or a no answer. The information in the statements is sufficient only if it allows you to answer the question definitely yes or definitely no.

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Data Sufficiency

READY… Data Sufficiency problems are combined with Problem Solving questions in the Quantitative Section of the GMAT CAT. You should expect that approximately 14 of the 37 questions in the Quantitative Section will be Data Sufficiency problems. Like Problem Solving questions, Data Sufficiency problems test your mastery of basic math concepts and your ability to reason quantitatively. In addition, Data Sufficiency problems test your ability to distinguish between relevant and irrelevant data and determine whether you have enough information to answer a given question. In general, Data Sufficiency problems require fewer calculations than Problem Solving questions. Therefore, the ability to work with numbers and perform calculations is less important for Data Sufficiency problems than it is for Problem Solving questions. Data Sufficiency covers the same math topics as Problem Solving: 1. 2. 3. 4.

Arithmetic Algebra Geometry Word Problems

Data Sufficiency problems consist of a question followed by two statements. You must determine whether the information provided in the statements, either individually or combined, is sufficient to answer the question. Here is a typical Data Sufficiency question: 01:15

Score Value: 500

GMAT CAT – Section 3 : Quantitative

1 of 37

What is the area of a rectangular lawn? (1) 75 percent of the lawn is mowed. (2) A rectangular region, 10 meters by 12 meters, is mowed, and the rest of the lawn is unmowed. (A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient. (B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient. (C) Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient. (D) Each of statements (1) and (2) is sufficient to answer the question. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.

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This question does not require you to determine the area of the lawn. Rather you must determine whether the information given to you in the statements, alone or combined, is sufficient to determine the area.

Sufficient is sufficient If you determine the area of the lawn, you’ve spent too much time on the question. You only need to determine whether you have enough information to calculate the area of the lawn.

Statement (1) is clearly not sufficient to answer the question. Knowing that 75% of the lawn is mowed is not sufficient to determine the size of the entire lawn because you don’t know the area of the mowed region. Likewise, statement (2) is not sufficient to determine the size of the lawn. If you know that a 10-by-12 (or 120 square meters) region of the lawn is mowed, you know that the area of the lawn is greater than 120 square meters, but you can’t determine the total area of the lawn. If you combine statements (1) and (2) you can determine the area of the lawn, so the third answer choice is correct. Statement (1) tells you that a region representing 75% of the area of the lawn is mowed and statement (2) gives you the area (10 by 12, or 120 square meters) of that region. If you let x equal the total area of the lawn, then you can determine the area of the lawn from the equation 75% (or .75) x x = 160. So the total area of the lawn is 160 square meters. Authors Note: On the GMAT CAT, the answer choices will be preceded by hollow ovals. You indicate your choice by clicking on the appropriate oval using the mouse. In this chapter and in the rest of this book, however, the answer choices will be designated by the letters A, B, C, D, and E for ease of reference.

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Data Sufficiency

THE DIRECTIONS The directions for the Data Sufficiency questions are similar to the following:

End

➩

GMAT CAT – Section 3 : Quantitative

Directions: Each data sufficiency problem consists of a question followed by two statements containing data related to the question. You must determine whether the information provided in the statements, either individually or combined, is sufficient to answer the question given. Using the information in the statements, plus your knowledge of mathematics and commonly known facts (such as the number of seconds in a minute), you must indicate whether

Directions

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(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient (B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient (C) Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient (D) Each of statements (1) and (2) is sufficient to answer the question (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question Numbers: All numbers used are real numbers. Figures: Figures accompanying data sufficiency problems will accurately reflect the information provided in the question, but will not necessarily reflect the additional information given in statements (1) and (2). All figures lie in a plane unless otherwise stated. Straight lines may appear jagged on the computer screen. In data sufficiency questions that ask for a value (what is the value of x?, for example), the information provided in the statements is sufficient only if it allows you to determine exactly one numerical value.

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WHAT THE DIRECTIONS MEAN The directions first describe the form of the Data Sufficiency questions: a question (which is often accompanied by information or data) followed by two statements. Note that the directions do not indicate that you need to answer the question. You don’t. You are only required to determine whether the statements are sufficient to answer the question. The directions also indicate that you must use your knowledge of mathematics in order to determine if the information in the statements is sufficient. The math required by the Data Sufficiency questions is the same basic math required for the Problem Solving questions, all of which is covered in the Comprehensive Math Review in this manual. With respect to figures, the directions indicate that those accompanying Data Sufficiency questions will reflect information given in the question, but will not necessarily reflect the information given in the statements. This simply means that, to the extent information provided in one or both of the statements seems to disagree with a figure, you should use the information in the statement and disregard the figure. The Data Sufficiency Answer Choices Note that the Data Sufficiency answer choices are the same for every Data Sufficiency question. Memorize them now so that you will not have to waste time reading them on the actual test.

Finally, and perhaps most importantly, the directions indicate that when a problem asks for the value of a quantity (“What is the value of x?” for example), the information in the statements is sufficient only if it allows you to determine exactly one value for the quantity. For example, if one of the statements tells you that x2 = 25, this is not sufficient to determine the value of x because x could be 5 or –5.

THE RELATIONSHIP BETWEEN DATA SUFFICIENCY AND PROBLEM SOLVING QUESTIONS Data Sufficiency questions are similar to Problem Solving questions in several ways. Both types of questions test your mastery of basic math concepts and your ability to think quantitatively, and both require you to see the relationship between given data. Data Sufficiency questions are, however, different in that you do not need to calculate an answer. Rather, you must determine how information given in the statements is related to the question and whether it is sufficient to answer the question. Take a look at Example 1 in the form of a Problem Solving question. Revisited 01:15

Score Value: 500

GMAT CAT – Section 3 : Quantitative

1 of 37

If 75 percent of a rectangular lawn is mowed, and the part that is mowed is a rectangular region of 10 meters by 12 meters, then what is the area, in square meters, of the lawn? (A) (B) (C) (D) (E)

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Data Sufficiency

Note that you are provided with the same information as you were when this problem was presented as a Data Sufficiency question, but in this example you must actually calculate an answer. Another important difference between Problem Solving and Data Sufficiency questions is that you know that the information provided in Problem Solving questions is sufficient to determine the answer, but in Data Sufficiency questions it is possible that the information provided in both statements is not sufficient.

THE FORMAT — INFORMATION PROVIDED IN THE QUESTION In Data Sufficiency problems you are often provided with information in the question itself. You can assume any information provided in the question is true when you examine the statements. Take a look at the following examples: Score Value: 500 A GMAT CAT – Section 3 : Quantitative

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What is the value of x ?

(A) (B) (C)

x > 13

(2)

x < 19

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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GMAT CAT – Section 3 : Quantitative What is the value of the prime number x ?

(B) (C)

(1)

x > 13

(2)

x < 19

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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Score Value: 500

01:13

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Notice the difference? In Example 2(a) the information provided in the statements is not sufficient, even combined, to determine the value of x because x could be any value greater than 13 and less than 19. In Example 2(b) you are told in the question that x is a prime number. You can therefore assume this fact when you analyze the information provided in the statements. Statement (1) tells you that x is greater than 13, so you know that x is a prime number greater than 13. Likewise, statement (2) tells you that x is less than 19, so you know that x is a prime number less than 19. Alone, neither of the statements is sufficient to determine the value of x. But if you know that x is a prime number between 13 and 19, you can determine that x is in fact equal to 17. Therefore, combined, the information in the statements is sufficient to determine the value of x. Here are two additional examples of Data Sufficiency questions with information provided in the question: Score Value: 550

GMAT CAT – Section 3 : Quantitative

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What is the value of integer x ?

(A) (B) (C)

x2 < 13

(2)

x4 > 60

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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Score Value: 600

GMAT CAT – Section 3 : Quantitative

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01:09

What is the value of positive integer x ? x2 < 13

(2)

x4 > 60

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Data Sufficiency

THE TWO TYPES OF DATA SUFFICIENCY QUESTIONS There are two types of Data Sufficiency Questions: (1) questions that ask you to determine the value of a quantity and (2) yes-or-no questions. For questions that ask the value of a quantity, the information in the statements is sufficient only if you are able to determine one and only one value for that quantity. For yes-or-no questions the information in the statements is sufficient only if you are able to answer the questions definitely “yes” or definitely “no.” Take a look at the following examples: Score Value: 550

GMAT CAT – Section 3 : Quantitative

5 of 37

If x and y are positive integers, what is the value of x + y ?

(A) (B) (C)

x2 = y

(2)

x > 16

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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Or... Score Value: 550

GMAT CAT – Section 3 : Quantitative

6 of 37

If x and y are positive integers, is x + y less than 20 ? x2 = y

(2)

x > 16

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See the difference? Example 5 asks you to determine the value of x + y, so you need to determine one and only one value for x + y. Alone, statement (1) is not sufficient because x and y could be many different values (2 and 4, or 3 and 9, for example). Statement (2) is also not © The MBA Center

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sufficient because it doesn’t give a value for y and it only indicates that x is greater than 16. Combined, the statements are not sufficient. For example, x and y could be, respectively, 5 and 25, or 6 and 36, giving two different values for x + y.

Don’t forget that for yes-orno Data Sufficiency problems a “no”answer is just as good as a “yes” answer.

Example 6 is a yes-or-no question. You need only determine whether the answer to the question “is x + y less than 20?” is definitely “yes” or definitely “no.” Statement (1) is not sufficient because x+y could be less than 20, but it could also be greater than 20. For example, if x and y are 3 and 9, then x + y is less than 20, but if x and y are 5 and 25, then x + y is not less than 20. Statement (2) is also not sufficient because it doesn’t give a value for y and it only indicates that x is greater than 16. Combined, the statements are sufficient. If you know that x is greater than 16, then from statement (1) you know that y is greater than 256, so you know that x + y is greater than 20. This time you can answer the question positively “no” based on combined information. Look at these examples of yes-or-no and quantity Data Sufficiency questions. Score Value: 550

GMAT CAT – Section 3 : Quantitative

7 of 37

If x, y, and z are positive integers, what is the average (arithmetic mean) of x, y, and z ?

(B) (C)

(2)

y + z = 30

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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Score Value: 550

01:01

GMAT CAT – Section 3 : Quantitative

8 of 37

If x, y, and z are positive integers, is the average (arithmetic mean) of x, y, and z greater than 20 ? (1)

x + y = 20

(2)

y + z = 30

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x + y = 20

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Data Sufficiency

Score Value: 600

00:59

GMAT CAT – Section 3 : Quantitative

9 of 37

Triangle ABC is inscribed in a circle. What is the area of triangle ABC ?

(A) (B) (C)

C

B

(1)

Triangle ABC is an equilateral triangle.

(2)

The perimeter of triangle ABC is 9.

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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Score Value: 600

00:57

GMAT CAT – Section 3 : Quantitative

10 of 37

Triangle ABC is inscribed in a circle. Is the area of triangle ABC greater than 40 percent of the area of the circle?

(B) (C)

C

B

(1)

Triangle ABC is an equilateral triangle.

(2)

The perimeter of triangle ABC is 9.

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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THE CHALLENGE As with Problem Solving questions, the challenge with Data Sufficiency questions is time. In order to finish all 37 questions in the Quantitative Section you will need to move quickly and efficiently through all of the Data Sufficiency questions presented. Because you are not required to calculate answers, Data Sufficiency questions should require less time than Problem Solving questions. Even so, Data Sufficiency questions are often complex and generally require a fair amount of thought and a bit of intuition. For this reason the MBA Center method stresses a systematic approach to every Data Sufficiency question.

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Data Sufficiency

AIM… THE DIFFICULTY WITH DATA SUFFICIENCY The two principal mistakes test takers make on Data Sufficiency problems are (1) failing to see relationships between the statements and the question and (2) seeing relationships that don’t exist. From years of experience writing Data Sufficiency problems, Phineas knows the average test taker’s weaknesses and designs questions with traps and pitfalls that exploit those weaknesses. Here are some of the mistakes that average test takers make.

COMMON MISTAKE 1 — MISINTERPRETING DATA Score Value: 620

00:55

GMAT CAT – Section 3 : Quantitative

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What is the weight of a shipment of watermelons? (1) There are exactly 120 watermelons in the shipment. (2) Each watermelon weighs at least 3 pounds. (A) (B) (C) (D) (E)

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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The average test taker knows that statement (1) is not sufficient because there is no mention of the weight of the watermelons, and he knows that statement (2) is not sufficient because there is no mention of how many watermelons are in the shipment. Now, the average test taker might think, “if I multiply the quantity (120) by the minimum weight (3) I can determine the gross weight, so the answer must be (C).” This is wrong. To get the gross weight, you need to multiply the quantity by the average weight, which is not given to you in the problem.

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COMMON MISTAKE 2 — SEEING RELATIONSHIPS BETWEEN THE STATEMENTS AND THE QUESTION THAT DON’T EXIST Score Value: 580

GMAT CAT – Section 3 : Quantitative

12 of 37

If a machine produces 25 units per minute, how many units did it produce in time period T?

(A) (B) (C)

The machine was started at 6 a.m. and stopped at 11 a.m.

(2)

The machine operated for 5 hours.

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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The average test taker might think that the correct answer is (D) because both statement (1) and statement (2) provide the length of time period T and, since you know the rate at which the machine is producing units, determining the number of units produced in 5 hours seems a matter of simple arithmetic. This is wrong. Neither of the statements mentions time period T. Regarding statement (1) you can’t assume that the time period given is equal to time period T. This is also true with respect to statement (2).

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COMMON MISTAKE 3 — FAILING TO SEE RELATIONSHIPS THAT DO EXIST Score Value: 670

00:51

GMAT CAT – Section 3 : Quantitative

13 of 37

Is the odd integer x a prime number?

(A) (B) (C) (D) (E)

(1)

x + 2 is a prime number.

(2)

x – 3 is a prime number.

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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The average test taker will probably see that statement (1) is not sufficient on its own to answer the question. Moving on to statement (2), the average test taker will probably think that it too is not sufficient, failing to notice that if x is an odd integer then x – 3 must be an even integer. Statement (2) tells us that x – 3 is prime, so x – 3 must be equal to 2 because it is the only even prime number. If we know that x – 3 is equal to 2, then we know that x is equal to 5.

HOW TO ACE DATA SUFFICIENCY The three examples above illustrate the most common mistakes test takers make on Data Sufficiency problems. In order to help you avoid these traps we have developed a systematic three-step approach that you should use for every question.

THE MBA CENTER METHOD FOR DATA SUFFICIENCY QUESTIONS The MBA Center method for Data Sufficiency questions emphasizes a step-by-step approach to every question. If you work systematically through each statement, eliminating wrong answer choices as you go, you will save time, avoid common traps, and (if you end up having to guess) improve your chances of guessing the correct answer. Practice using this method when you work through the examples in this lesson and when you do the Data Sufficiency practice exercises in this book.

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Step 1: Read and understand the question before you move on to the statements. First read and understand the question. Before you move on to the statements ask yourself what information you need in order to answer the question. For example, if the question asks “What is the value of x?”, then you need an equation or expression that will allow you to determine a single value for x. But if the question asks “What is the value of x + y?” or “What is the average of x and y?”, then you need the values of both x and y or some equation or expression that will allow you to determine the sum of x and y. Take a look at the following examples of Data Sufficiency questions without statements. Try to determine what information would allow you to answer the questions.

GMAT CAT – Section 3 : Quantitative

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If x, y, and z are consecutive positive integers and x < y < z, what is the value of y ?

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GMAT CAT – Section 3 : Quantitative

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If x + 2y + 3z = 50, what is the value of x ?

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Step 2: Examine the statements separately, eliminating wrong answer choices. After you read the question and have some idea what information would be sufficient to answer it, move on to the statements. Pick the statement that looks easier and start with it. If that statement alone is sufficient to answer the question, you can eliminate answer choices (C) and (E). If the statement is insufficient, you can eliminate answer choices (A) or (B) (depending on which statement you started with), and (D). Next, move on to the other statement. It is important that you disregard all information from the previous statement. For example, if you started with statement (1) and determined that it was insufficient, make sure that you don’t unintentionally use information contained in statement (1) when you examine statement (2).

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Data Sufficiency

The following flow chart illustrates how you should eliminate wrong answer choices when you examine the statements. If you start with statement 1: STATEMENT 1 Sufficient

Insufficient

STATEMENT 2 Sufficient

Answer D

Insufficent

Answer A

Sufficient

Answer B

Insufficent

Eliminate B

Eliminate B, C, E

Eliminate A, D

Or if you start with statement 2: STATEMENT 2 Sufficient

Insufficient

STATEMENT 1 Sufficient

Answer D

Insufficent

Answer B

Sufficient

Answer A

Insufficent

Eliminate A

Eliminate A, C, E

Eliminate B, D

The above flow chart illustrates how you should eliminate incorrect answer choices as you examine the statements. If, for example, you know that statement (1) alone is sufficient, but you are unsure whether statement (2) alone is sufficient, you can eliminate answer choices (B), (C), and (E), which gives you a fifty percent chance of guessing the correct answer. Step 3: If necessary, consider the statements together.

Eliminating some wrong answer choices is better than eliminating none - it also improves your chances of guessing the correct answer.

You should only reach this step if you determine that each statement alone is insufficient. If either statement alone is sufficient to answer the question, you do not need to consider the statements together. At this point, the only possible answer choices are (C) and (E). Consider all of the information in the question and in the statements as one large problem and ask yourself if you have sufficient information to answer the question. Also, try to determine if information in one statement makes information in the other statement more useful. Take a look at the following example.

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Score Value: 650

00:41

GMAT CAT – Section 3 : Quantitative

16 of 37

(A) (B) (C)

xy = z –y

(2)

z=9

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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If x > 0 and y > 0, what is the value of x ?

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Note that the information contained in each of statements (1) and (2) is insufficient alone. But from statement (2) you know that z = 9, so you can substitute 9 for z in statement (1), which gives you the equation xy = 9-y, or, xy = 1y which allows you to determine that x = 1 . 9 9

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FIRE! DATA SUFFICIENCY STRATEGIES INSERTING NUMBERS Inserting numbers for unknowns or variables can be as useful for solving Data Sufficiency questions as it is for solving Problem Solving questions. Any number property Data Sufficiency question (is x prime?, is x an odd integer?, is x + y an even integer?, is x a multiple of 6?, for example) is a good candidate for inserting numbers. If substituting different numbers for the variables in a statement gives you two different answers to the question, then you know that the statement is not sufficient to answer the question. Try inserting numbers for variables in the following example. Score Value: 550

00:39

GMAT CAT – Section 3 : Quantitative

17 of 37

Is the positive integer x a multiple of 48 ?

(A) (B) (C) (D) (E)

(1)

x is a multiple of 16.

(2)

x is a multiple of 6.

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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Start with statement (1). You can pick the value 16 for x, which is a multiple of 16 but is not a multiple of 48. But you can also pick 48 as a value for x, which is a multiple of both 16 and 48. Because you are able to pick two values for x which satisfy statement (1) and give you two different answers to the question “is x a multiple of 48?” you know that statement (1) is not sufficient. Now move on to statement (2). It is also not sufficient because you can pick the values 6 or 48 for x, again giving you two different answers to the question “is x a multiple of 48?” Now you can combine the statements. The lowest number you can pick for x that is a multiple of both 16 and 6 is 48. If you continue to think of larger and larger values for x that are multiples of both 16 and 6, you will see that they are all multiples of 48, so statements (1) and (2) combined are sufficient to answer the question.

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Try inserting numbers in the following example. Score Value: 530

GMAT CAT – Section 3 : Quantitative

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Is the integer m odd?

(A) (B) (C)

m is a multiple of both 3 and 7.

(2)

m – 7 is an odd integer.

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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Try counting variables and equations. Remember that in order to solve for variables algebraically, you need as many equations as you have variables. For some Data Sufficiency questions you can simply count the number of variables you have and the number of equations you have in order to determine if there is information sufficient to answer the question. Take a look at the following example. Score Value: 550

GMAT CAT – Section 3 : Quantitative

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How many coins does Kelly have?

(A) (B) (C)

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John has twice as many coins as Kelly.

(2)

If Kelly had four times as many coins as she currently has, then she would have ten more coins than John.

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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Data Sufficiency

What are the equations contained in the statements? If you let j equal the number of coins John has and k equal the number of coins Kelly has, then statement (1) yields the equation j = 2k. So you have two variables, but only one equation. So statement (1) alone is not sufficient. Statement (2) yields the equation 4k = j + 10. Again, statement (2) gives you one equation and two variables, so it is not sufficient alone. If you combine statements (1) and (2), you have two equations and two variables, so you can solve for either variable. Try counting variables and equations in the following examples.

Make sure when you are counting equations that you actually have different equations. For example, if statement (1) gives you the equation x + 4y = 4 and statement (2) gives you the equation 2x – 8 = –8y, you can’t solve for either x or y because the equation in statement (2) is the same as the equation in statement (1), simply written in a different form.

Score Value: 600

GMAT CAT – Section 3 : Quantitative

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What is the length of side a ?

(A) (B) (C) (D) (E)

(1)

a2 + b2 = 25

(2)

b2 + c2 = 41

c

a

b

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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Score Value: 530

GMAT CAT – Section 3 : Quantitative

21 of 37

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00:31

If n + x = y, what is the value of x ? n – x = 20

(2)

y–x=n

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(1)

Sometimes you do not need to solve for each variable separately. For example, if a question asks you to determine the value of 3x + 4y, then knowing that 12x + 16y = 7 would be sufficient to answer the question.

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Step 5.1 Lesson

DATA SUFFICIENCY TRAPS In Problem Solving questions, Phineas tries to fool the unwary test taker with tempting wrong answer choices. Likewise, in Data Sufficiency there are traps you should be aware of. The following are some of the most common traps in Data Sufficiency questions.

SOMETIMES IT IS NECESSARY TO CALCULATE Even though Data Sufficiency questions do not usually require you to do any calculations, occasionally it is necessary to do so. Try the following example: Score Value: 600

GMAT CAT – Section 3 : Quantitative

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What is the value of x ?

(A) (B) (C)

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x2 + 25 = 10x

(2)

x2 – 8x = –15

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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Data Sufficiency

REDUNDANCY IN THE STATEMENTS Often one of the statements will provide you with all or some of the same information contained in the other statement. Phineas does this because an unwary test taker may become confused and assume that because one statement is sufficient, the other statement, which contains some of the same information, is also sufficient. Take a look at the following example. Score Value: 500

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Mike leaves Town A at 8:00 a.m. and drives at a constant speed to Town B. At what time will Mike arrive at Town B?

(A) (B) (C) (D) (E)

(1)

Mike passes Town C, which is midway between Town A and Town B, at 10:00 a.m.

(2)

Mike passes Town C two hours after leaving Town A.

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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Step 5.1 Lesson

ASSUMPTION TRAPS Many Data Sufficiency questions are written in such a way that the average test taker will assume information that isn’t provided. Here are some of the most common assumption traps on Data Sufficiency questions. Score Value: 550

GMAT CAT – Section 3 : Quantitative

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From January to February the number of full-time technicians at Company X increased by what percent?

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(1) In January, Company X had 200 employees, 25 percent of whom were full-time technicians. (2) In February, 28 percent of the employees at Company X were fulltime technicians. (A) (B) (C)

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(D) (E)

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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Data Sufficiency

COMMON MATH TRAPS Certain math traps appear frequently in Data Sufficiency questions. For example, if a statement indicates that x2 = 25, don’t forget that x could be either 5 or –5. Here is a list things you should remember in order to avoid some of the most common GMAT math traps: The square root of a number can be either positive or negative. A quadratic equation can have two, one, or zero solutions. An even power of a nonzero number is always positive. (If x is not equal to 0, and y is an even number, then xy is a positive number even if x is a negative number). An odd power of a nonzero number can be either positive or negative. If x is not equal to 0, and y is an odd number, then xy is a positive number if x is positive and a negative number if x is negative). The product of an integer (odd or even) and an even integer is always an even integer. The sum of any two odd numbers will always be even. The sum of any two even numbers will always be even. The sum of an even number and an odd number will always be odd. 2 is the smallest prime number and it is the only even prime number. Here are several examples of Data Sufficiency questions containing common math traps: Score Value: 550

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Is x2 > x3 ?

(A) (B) (C) (D) (E)

(1)

x xx

(2)

x2 < x4

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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Step 5.1 Lesson

Score Value: 550

GMAT CAT – Section 3 : Quantitative

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If a, b, and c are all positive integers, is abc an even number?

(A) (B) (C)

a + b is a prime number.

(2)

b + c is an even number.

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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GMAT CAT – Section 3 : Quantitative

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What is the value of x ?

(A) (B) (C)

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x2 + 14x + 49 = 0

(2)

x2 + 2x – 35 = 0

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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Data Sufficiency

Score Value: 550

GMAT CAT – Section 3 : Quantitative

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For all positive integers s and n, the function @ is defined by s@n = sn + 2s. If s@n is an even number, is n an odd number?

(A) (B) (C)

3s is an odd number.

(2)

s@5 is an odd number.

Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient Each of statements (1) and (2) is sufficient to answer the question Statements (1) and (2), alone or combined, are not sufficient to answer the question

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Step 5.1 Lesson

SUMMARY -Data Sufficiency questions represent one-third of all the questions in the Quantitative Section. -A Data Sufficiency question is composed of a question followed by two statements. -The Data Sufficiency answer choices are always the same. Memorize them so that you will not waste time reading them on the actual test. You must indicate whether: - Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked; - Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked; - Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient. - EACH statement ALONE is sufficient to answer the question asked; - Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

USE

THE

MBA CENTER 3-STEP APPROACH TO EACH QUESTION.

- Step 1: Read and understand the question before you move on to the statements. - Step 2: Examine each statement separately, using the Process of Error Identitfication to eliminate the wrong answer choices. - Step 3: If necessary, consider the two statements together. In addition to our general approach, the MBA Center has developed specific tips such as: - Guessing - Inserting numbers - Counting variables On difficult problems do not hesitate to use more advanced strategies like: - Identifying redundant statements - Recognizing assumption traps - Avoiding common math traps

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ANSWERS 1. 2.a 2.b 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

TO EXAMPLES

C E C E C E C E C C A E E B N/A N/A C C B C C E A A E A E A D

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HOMEWORK/PRACTICE TEST DATA SUFFICIENCY ANSWER GRID A !

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Step 5.2 Homework

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Data Sufficiency – Homework

TIME – 25 MINUTES 20 QUESTIONS Directions: Each data sufficiency problem consists of a question followed by two statements containing data related to the question. You must determine whether the information provided in the statements, either individually or combined, is sufficient to answer the question given. Using the information in the statements, plus your knowledge of mathematics and commonly known facts (such as the number of seconds in a minute), you must indicate whether

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(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not sufficient (B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient (C) Statements (1) and (2) COMBINED are sufficient to answer the question, but neither statement alone is sufficient (D) Each of statements (1) and (2) is sufficient to answer the question (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question Numbers: All numbers used are real numbers. Figures: Figures accompanying data sufficiency problems will accurately reflect the information provided in the question, but will not necessarily reflect the additional information given in statements (1) and (2). All figures lie in a plane unless otherwise stated. Straight lines may appear jagged on the computer screen. In data sufficiency questions that ask for a value (what is the value of x?, for example), the information provided in the statements is sufficient only if it allows you to determine exactly one numerical value.

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Example: How much money did Bill spend on movie tickets last week? (1) Bill bought 3 movie tickets last week. (2) Bill spent an average of $6 per movie ticket that he purchased last week. Explanation: Statement (1) indicates the number of movie tickets Bill purchased last week, but not the price of the tickets. It is therefore not sufficient to answer the question. Statement (2) alone indicates the average price Bill paid per movie ticket last week, but not the number of tickets purchased. Statement (2) is thus also not sufficient by itself to answer the question. Taken together, the two statements do provide enough information to answer the question. Therefore the answer is (C).

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Data Sufficiency

A B C D E

Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. EACH statement BY ITSELF is sufficient. Statement (1) and statement (2) COMBINED are not sufficient.

1. A stadium manager expected 13,200 spectators to attend a sporting event. If everyone who bought a ticket attended the event, how many full-price tickets were sold? (1) The number of full-price tickets sold was equal to 81 percent of the number of spectators expected by the stadium manager. (2) Of the 11,880 people who attended the event, 90 percent had bought full-price tickets. 2. Of the positive integers a, b, c, d, and e, which is the largest? (1) a + b = e (2) b + c = d 3. Is x2 an odd integer? (1) x is an odd integer. (2) x is a multiple of 3.

4. What is the value of 2mn ? (1) m + n = 8 (2) m – n = 8 5. An arts center rents out a music hall for performances, charging a base fee plus a commission that is equal to a fixed percentage of the revenues generated from ticket sales. How much did the arts center charge for Thursday’s concert? (1) The base fee for a concert in the music hall is $1,200. (2) The art center’s commission is 8 percent of the concert revenues.

6. What is the value of y ? (1) 8y + 16 = 0 (2) (y + 4)2 = y2 7. Rudolph and Nicholas each drove from Brimsburg to Durville along the same route. If Rudolph left Brimsburg at 8:00 a.m. and arrived in Durville at 12:15 p.m. the same day, at what time did Nicholas arrive in Durville? 1 (1) Nicholas left Brimsburg 2 hour earlier than Rudolph. (2) The route from Brimsburg to Durville that Rudolph and Nicholas took is 220 miles. 8. If 12 people are waiting for an elevator, of whom 8 want to go down, can the 8 who want to go down all enter the elevator without exceeding the maximum weight capacity of the elevator? (1) The maximum weight capacity of the elevator is 450 kilograms. (2) Ten of the people waiting for the elevator have an average weight of 54 kilograms.

z°

x°

y°

9. Is the the figure above an isosceles triangle? (1) z = 36 (2) x = 2z

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A B C D E

Step 5.2 Homework

Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. EACH statement BY ITSELF is sufficient. Statement (1) and statement (2) COMBINED are not sufficient.

10. Is ay = 6 – ax ? (1) 2a(x + y) = 12 (2) x = y = 4 and a = 0.75 11. What is the average (arithmetic mean) of a, b, and c ? (1) The average (arithmetic mean) of a and b is 24. (2) –c = a + b

12. What is the value of integer k ? (1) k is an integer. 2

15. If a certain photograph collection consists of some black-and-white photographs and some color photographs, how many color photographs are in the collection? (1) If 5 more photographs, all of them black-andwhite, were added to the collection, the ratio of color photographs to black-and-white photographs would then be 8 to 5. (2) There are 35 more color photographs than black-and-white photographs in the collection. 16. Is 3y greater than 50 ? (1) 3

y

1

=9

(2) k is prime.

(2)

13. Is x > y ?

17. What is the average (arithmetic mean) of x and y ?

(1) x2 > y2 (2) x – y > 0

(3 ) y

< 50

(1) x – y = 6 (2) The average (arithmetic mean) of x + 5 and y + 7 is 17.

14. In what year did Carson and Joan get married? 1 (1) Carson’s sister Loraine, who got married 2 2 years before Carson and Joan got married, got married in 1964.

18. What is the value of m + n ? (1) (m + n)2 = 25 (2) m and n are both positive integers.

(2) Carson and Joan’s 16th wedding anniversary was in 1982.

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Data Sufficiency

A B C D E

Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. EACH statement BY ITSELF is sufficient. Statement (1) and statement (2) COMBINED are not sufficient.

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IV

19. In the rectangular coordinate system shown above, point (p,q) lies in which quadrant? (1) pq < 0 (2) p + q < 0 20. Is abc < 24 ? (1) a < 2, b < 3, and c < 4 (2) ab = 4 and c2 = 15

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Step 5.2 Homework

DATA SUFFICIENCY HOMEWORK/PRACTICE TEST ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

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EXPLANATIONS TO DATA SUFFICIENCY HOMEWORK/PRACTICE TEST

1. (D) Statement (1) is sufficient because the problem states how many spectators the manager expected, so it is possible to compute 81% of this to find out how many had full-price tickets. Statement (2) is also sufficient because it is possible to compute 90% of 11,880 to get the answer.

2. (E) Statement (1) is not sufficient. Sub numbers as a test. For example a = 5, b = 10, and e = 15. The other variables, c and d could be anything. If they are both smaller than 15, for example 11 and 12, then e is the largest. If, however, c is 50 and d is 1,000,000, then d is the biggest. Statement (2) is not sufficient for the same reason. d could be the biggest, but the statement says nothing about a and e, so they could be very small or very big. Combined, the choices are still not sufficient. For example, it is possible that a = 5, b = 10, and e = 15 (from statement (1)), and b still is 10, c = 20, and d = 30. In this case d is the biggest. But if, for example, c = 1 and d = 11, e becomes the biggest.

3. (A) Before going to the statements, you might ask yourself when is x2 an odd integer? It turns out that whenever x is an odd number, x2 is odd, and whenever x is an even number, x2 is even. Statement (1) is sufficient. To verify this, try a few examples with simple odd numbers, such as 1, 3, 5, and 7. In each case, x2 is odd. The answer, then, based on statement (1), is “always yes,” so the statement is sufficient. Statement (2) is not sufficient. Try a few multiples of 3: 3, 6, 9, 12 etc. With 3, 32 = 9 which is odd, so the answer to the question is “yes.” With 6, 6 = 36, which is even, so the answer is “no.” With 1 “yes” and 1 “no” the answer is really “maybe,” which is the same as “not sufficient.” 2

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4. (C) Statement (1) is not sufficient. You could verify this by trying a few numbers. For example, 2 + 6 = 8. Then, when you go back to the question, 2(2)(6) = 24. Try another set of numbers. 4 + 4 = 8. 2(4)(4) = 32. Since in one case you get 24 and in another case you get 32, the statement is not sufficient. Statement (2) is also not sufficient. You could try 10 – 2 = 8. Then, when you go back to the question, 2(10)(2) = 40. Try a second example. 7,000,008 – 7,000,000 = 8. Now, when you go back to the question, 2(7,000,008)(7,000,000) does not equal 40. (No need to calculate here.) When you take the 2 statements together, you have 2 linear equations and 2 variables, meaning you can solve for each variable and then plug their values into the expression 2mn. You don't want to waste your time actually solving the equations.

5. (E) Before going to the statements, you might want to make a mental note that there are 3 pieces of missing information: 1) the base fee, 2) the revenues generated from ticket sales, and 3) the percentage of revenues from ticket sales that determines the commission. Statement (1) is not sufficient, as it provides only the base fee. You don't know the revenues from ticket sales or the percent of the revenues used to determine the commission. Statement (2) is also insufficient, as we don't know the base fee or the revenues generated from ticket sales. Together the statements are still not sufficient, as we know the base fee and the percent, but not the actual revenues from ticket sales.

6. (D) Statement (1) is sufficient because 1 linear equation with 1 unknown can always be solved. Statement (2) is also sufficient, though it is trickier to see why than in statement (1). An equation with a variable squared is sometimes sufficient to solve for the variable, and it is best to actually work it out. In this case:

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(y + 4)2 = y2 y2 + 8y + 16 = y2 8y + 16 = 0

Step 5.2 Homework

9. (C) Remember that isosceles means that 2 sides (and therefore 2 angles) are equal.

You can stop here, as you now have the same equation you had in statement (1). Again, the equation now is linear (meaning there are no exponents) and so it can be solved for 1 variable.

Statement (1) alone is not sufficient. The statement z = 36 doesn't indicate anything about x and y except that they add up to 144 (because 3 angles of a triangle must add up to 180°). x and y could be the same (they could each be 72), or they could be different.

7. (E) There is lots of missing information in this question. For example, how far apart are the towns? When did Nicholas leave? How fast did Nicholas go?

Statement (2) is also insufficient, as x or z remain variables. It's possible that x = 90, z = 45, and therefore y = 45 and the triangle is isosceles. It is also possible that x = 2, z = 1, and therefore y = 177 and the triangle is not isosceles.

Statement (1) is not sufficient, as we don't know how far apart the towns are or how fast Nicholas went. Statement (2) is not sufficient because we don't we don't know when Nicholas left or how fast he went. Together the statements are still not sufficient, as we know when Nicholas left and how far he went, but not how fast he went.

8. (E) This question is tricky, because there are a lot of unknowns. What is the maximum weight capacity of the elevator? How much do the people who are waiting weigh? And which 8 of the 12 people waiting will get in? And what did they eat for dinner last night? (Just kidding.) Statement (1) is not sufficient, because although the problem gives the capacity of the elevator, it does not give the weight of the people. Statement (2) is also not sufficient, the weight capacity of the elevator is not indicated. The statements together still don’t supply enough information. If the 8 people who actually get in each weigh 54 kg, their total weight is 432 kg which is safe (less than the capacity of 450 kg). But if, for example, 6 people get in who each weigh 54 kg, and the other 2 who get in were the 2 not referred to in statement (2), and they each weigh 200 kg (that is possible, albeit unlikely), the 8 would certainly exceed the capacity. With 2 different answers (1 yes and 1 no), the statements are not sufficient.

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Taken together, the statements are sufficient. We know that z = 36, x, which is double z, is then 72. And knowing 2 angles of a triangle you can always find the third. It is not necessary to continue, as whether the triangle is isosceles is irrelevant, it is only relevant to be able to determine if it is so. If you know all 3 angles, then certainly you can figure out whether the triangle is isosceles.

10. (D) Remember to look to simplify equations, as statements on the GMAT will often miraculously turn into exactly, or almost exactly, what is necessary to solve the problems. Statement (1) is sufficient. Simplify! 2a(x + y) = 12 a(x + y) = 6 ax + ay = 6 ay = 6 – ax Since this is exactly the equation in the question, the statement is sufficient to answer the question. Statement (2) is also sufficient. Statement (2) gives you a value for each variable. Since the values are given, it is possible to verify whether the equation works. As is it not necessary to determine whether the answer to the question is “yes” or “no,” it is not necessary to continue.

11. (B) Before going to the statements, you might want to just jot down the average formula: a + b + c = avg 3 Now go to statement (1). It is not sufficient because you don't know anything about c. c could be 2, or it could be 2,000,000,000. © The MBA Center

Data Sufficiency

Statement (2) is sufficient, though it might not be apparent at first glance. If you use the equation you wrote out, a + b + c = avg. 3 and plug in –c for a + b Then you get –c + c = avg 3 0 = avg Therefore, the average is 0 and the statement is sufficient.

14. (B) Statement (1) is not sufficient, though it may appear to be at first glance. If Loraine got married in January 1964, then Carson and Joan got married in July 1966. But if Loraine got married in December 1964, then Carson and Joan got married in June 1967. Therefore you can't be sure what year Carson and Joan got married.

12. (C) Statement (1) is not sufficient. Test out a few

15. (C) This question can be simplified a great deal by thinking of it algebraically.

examples. When is k an integer? It turns out, 2 k whenever k is even, is an integer. When k is 2 k odd, is not an integer. Therefore statement (1) 2 merely tells us that k is even. Statement (2) by itself is definitely not sufficient. There are lots of prime numbers: 2, 3, 5, 7, 11, 13, 17, 19… The 2 statements together are sufficient. Statement (1) tells us that k is even and statement (2) tells us k is prime. There is only 1 even prime number, 2, so we have determined the value of k.

Statement (2) is sufficient. No matter what month Carson and Joan's wedding anniversary takes place, their marriage was exactly 16 years earlier, and must have therefore been in 1966.

Statement (1) is not sufficient. There are 2 unknowns: the number of color photographs (call it x) and the number of black-and-white photographs (call it y). We have only 1 equation and therefore cannot solve for the 2 variables. If you wanted to set up the equation, you could write: x =8 y+5 5 There is no way to solve this equation. Statement (2) is also not sufficient, as knowing that there are 35 more color photographs than blackand-white photographs doesn't indicate how many there actually are. The 2 statements combined are sufficient, as we now have 2 equations and 2 unknowns and can therefore solve. The second equation, by the way, is: x – 35 = y

13. (B) Questions with exponents and inequalities can be difficult. Make sure to consider negatives and fractions. And remember, when statement (1) looks hard, don't give up. Go on to statement (2).

16. (A) Statement (1) is sufficient. If 3 y  9 , then y  2 , and y = 4. If you know exactly what y is, then you can figure out whether 3y is greater than 50. (It is not.)

Statement (2) is sufficient. When you rewrite the equation (by adding y to both sides) you get x > y Therefore, the answer to the question is “yes” and the statement is sufficient.

Statement (2) is not sufficient. The easiest way to deal with statement (2) is to try different values for y.

Statement (1) is not sufficient, even though it may look sufficient. When is x2 > y2 ? If x = 5 and y =3, then x2 > y2. When you go back to the question, the answer is “yes.” But what about trying negatives? Try x = –7 and y = –4. Again, x2 > y2 (49 > 16). But when you go back to the question, x is not greater than y (–7 < –4). © The MBA Center

If

1

3 y

 50 , then y could be 1, in which case the

answer to the question would be “no.” But y could also be 100, in which case the answer to the question would be “yes.” Statement (2) allows two different answers to the question and is therefore insufficient.

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17. (B) Again, as this is an average question, you might first jot down the average formula: x + y = avg 2 Now, go to the statements. Statement (1) is not sufficient. You could make x = 12 and y = 6, or we could make x = 106 and y = 100. Depending on which numbers you use, you derive different averages.

Step 5.2 Homework

which case the point is in quadrant II. It therefore is impossible to determine the quadrant and the statement is not sufficient. Combined, the statements are also not sufficient. A point… such as (–8, 6) is in quadrant II, but (9, –12) is in quadrant IV. It is impossible to be sure.

Statement (2) is sufficient. When you write out the equation, you get x+5+y+7 = 17 2 This then becomes x + y + 12 = 17 2 Then, x + y + 12 = 34 Then, x + y = 22 Then, x + y = 11 2 Therefore, you know the average of x and y.

18. (C) Statement (1) looks sufficient, but actually is not. (m + n)2 = 25 tells us that m + n = 5 or –5. Since there are 2 possible answers, the statement is not sufficient. Statement (2) is definitely not sufficient. Knowing that m and n are both positive integers does not tell us what their sum is. When you combine the statements, you have enough information, because statement (1) narrowed down the sum to 2 possibilities and statement (2) eliminates the negative possibility.

19. (E) Here it is necessary to work out the possibilities. In statement (1), when pq < 0, either p is positive and q is negative, or vice versa. It is possible, for example, to have the point (3, –2), which is in quadrant IV, or (–2, 5), which is in quadrant II. Statement (1) is therefore not sufficient. Statement (2) tells us that the sum is negative. Maybe both variables are negative and the coordinates are, for example, (–5, –10), in which case the point is in quadrant III, or maybe one variable is negative and the other is positive, such as (–5, 2), in

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Step 6 Data Sufficiency Workshop

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Step 6 Workshop

Directions End

➩

Data Sufficiency – Workshop

TIME 60 MINUTES 31 QUESTIONS Directions: In each of the problems below, you will find a question followed by two statements, marked (1) and (2). You must decide whether the information given in the two statements is sufficient to answer the question, based on your understanding of the principles of mathematics and knowledge of common facts (for example, the fact that there are one hundred cents in a dollar or that north and east are perpendicular directions). You then are to select the answer A if statement (1) BY ITSELF is sufficient to answer the question but statement (2) by itself is not sufficient; B if statement (2) BY ITSELF is sufficient to answer the question but statement (1) by itself is not sufficient; C if neither statement BY ITSELF is sufficient to answer the question, but the two statements COMBINED are sufficient to answer the question; D if EACH statement BY ITSELF is sufficient to answer the question; E if NEITHER statement (1) nor statement (2) is sufficient to answer the question BY ITSELF or COMBINED.

When finished reading directions click on the icon below

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Numbers: All the numbers in this section are real numbers. Diagrams: Diagrams are drawn as accurately as possible according to the data contained in the QUESTION, but are not necessarily drawn to scale as far as the new information in the two STATEMENTS: Unless stated otherwise all figures lie in a plane. All lines drawn in figures may be assumed to be straight. All angles indicated must have a measurement greater than 0 degrees. The relative positions of lines, angles, points, shapes etc. may be assumed to be in the order in which they appear. For questions that ask for the value of a variable, a statement is sufficient only when it allows you to find exactly one value for the variable. Example: How much money did Bill spend on movie tickets last week? (1) Bill bought 3 movie tickets last week. (2) Bill spent an average of $6 per movie ticket that he purchased last week. Explanation: Statement (1) indicates the number of movie tickets Bill purchased last week, but not the price of the tickets. It is therefore not sufficient to answer the question. Statement (2) alone indicates the average price Bill paid per movie ticket last week, but not the number of tickets purchased. Statement (2) is thus also not sufficient by itself to answer the question. Taken together, the two statements do provide enough information to answer the question. Therefore the answer is (C).

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Data Sufficiency

A B C D E

Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. EACH statement BY ITSELF is sufficient. Statement (1) and statement (2) COMBINED are not sufficient.

EASY

6. A store sells paperback and hardcover copies of a certain book. How many hardcover copies did the store sell in May? (1) The store sold 20 percent fewer hardcover than paperback copies of the book in May. (2) The store sold 15 more paperback than hardcover copies of the book in May.

1. Does a = 1 ? (1) b = 2a (2) b = 2

2. If 60 guests attended a catered party, how many guests ordered both the salad and the soup? (1) 28 guests ordered the salad. (2) 35 guests ordered the soup.

3. If there are 9 players on a baseball team, what is the average (arithmetic mean) age of the players? (1) The oldest player is 29 and the youngest is 25. (2) Seven of the players are either 26 or 27.

4. If a and b are positive integers, what percent of a is b ? (1) 3a = 5b (2) a + b = 80

(2)

2 +1=3 y

(1) (2)

The combined length of 2 of the pieces is 130 centimeters. The shortest piece is exactly 60 centimeters long.

8. The value of a certain car depreciates by 10 percent each year. What was the original price of the car? (1) The car was purchased 2 years ago, and its present value is $10,000. (2) Two years after the car was purchased, its depreciated value was 81% of its original price.

9. If

5. What is the value of y ? (1) 4y – 2 = 2y

7. A shelf 300 centimeters long is to be cut into 4 pieces. If the 2 middle-sized pieces are the same size, then what is the length of the longest piece?

a = c , then what is the value of a ? b

(1) bc = 4 (2) b = 8 and c =

1 2

10. What is the value of integer x ? (1) x4 < 25 (2) x = x2

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A B C D E

Step 6 Workshop

Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. EACH statement BY ITSELF is sufficient. Statement (1) and statement (2) COMBINED are not sufficient.

MEDIUM y° 13. Is x3 > x2 ?

c b z°

(1) x2 > 1 (2) x > –1

y° a

11. Is the triangle above a right triangle?

14. If xy ≠ 0, is xy > 0 ?

(1) a2 + b2 = c2 (2) z = 2y

(1) x3 < 0 (2) x = –y

A

B I

II

s r 15. What is the value of 2 + 2 ?

III C

D

(1)

s r 3+ 3 = 6

(2) r + s = 18

12. What is the area of rectangle ABCD ? (1) The sum of the areas of rectangles I and II is 28. (2) The sum of the areas of rectangles II and III is 24.

16. Does c = 8 ? (1) The average of a, b, and c is 8. (2) a – b = 0

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Data Sufficiency

A B C D E

Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. EACH statement BY ITSELF is sufficient. Statement (1) and statement (2) COMBINED are not sufficient.

A

B

Q

P

D

R S C

17. The circular base of a statue is set on a quadrilateral stand, as indicated in the figure above, such that the circular base just reaches the edge of the stand at points P, Q, R, and S. What is the area of the circular base?

20. Of the positive integers v, w, x, y, and z, which is the greatest? (1) v + w = z (2) w + x = y

21. What is the value of a + b ? (1) 2a + 3b = 15 (2) 6a + 9b = 45

(1) The diagonal AC of the stand is 12. (2) The circumference of the base is 8π.

18. If Lydia is exactly 1.5 times as old as Francis, how old is Francis? (1) Seven years ago Lydia was exactly twice as old as Francis. (2) Fourteen years from now Lydia will be exactly 25 percent older than Francis.

19. If a, b, and c are positive integers, does a = b2 ? c (1) c = b ac (2) c =

b a

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A B C D E

Step 6 Workshop

Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. EACH statement BY ITSELF is sufficient. Statement (1) and statement (2) COMBINED are not sufficient.

DIFFICULT

22. What is the value of ab ? c (1)

a = 3 and b = 2 c 4 3 c

(2)

c =6 ab

23. An omega sequence is an infinite sequence of positive integers that contains an infinite number of prime integers. If D is an infinite sequence of positive integers, is D an omega sequence? (1) D contains an infinite number of odd integers. (2) The integer 3 is not an element of D.

24. A credit card company offered a promotion in 1995 such that all users of credit card X would get a travel voucher at the end of the year equal in value to a fixed percentage of the amount of money charged on the credit card for that year. Mr. Pavlov charged d dollars on credit card X and Mrs. Pavlov charged $3,400 on credit card X. If Mr. Pavlov got a travel voucher equal in value to $380, what was the value of Mrs. Pavlov’s travel voucher? (1) The vouchers were equal in value to $0.05 for each dollar charged to credit card X in 1995. (2) d = 7,600

25. On a new manager’s first day at an express mail delivery company, 25 percent of the first 60 packages were delivered late. After the first 60, all other packages that day were delivered on time. What is the total number of packages delivered on time on the manager’s first day? (1) A total of 120 packages were delivered on the manager’s first day. (2) Of the packages delivered on the manager’s first day, 87.5 percent were delivered on time.

26. In a clothing store, 60 percent of the shirts are short-sleeved and 70 percent of the shirts are cotton. If 20 percent of the cotton shirts are white, how many of the cotton shirts are white? (1) There are 300 short-sleeved shirts in the store. (2) Of the shirts that are not cotton, 1 are white. 3

✪ x❐ ▲❋ 27. In the multiplication problem shown above, each of the symbols ✪, ❐, ▲, and ❋ represents a positive digit (not including 0). If ▲ > ❋ and ✪ > ❐, what is the value of ❐ ? (1) ✪ = 8 (2) ▲ = 3

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Data Sufficiency

A B C D E

Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. EACH statement BY ITSELF is sufficient. Statement (1) and statement (2) COMBINED are not sufficient.

28. Is abc = 1 ?

30. If n is an integer, is 3n less than 100 ?

(1) ab = 1 (2) bc = 1

(1) 3n + 1 > 100 (2) 3n – 1 = 3n – 162

b?

29. What is the average (arithmetic mean) of a and

(1) The average (arithmetic mean) of a + 4 and b + 4 is 12. (2) The average (arihmetic mean) of a, b, and 10 is 26 . 3

31. Is ab < 6 ? (1) a < 3 and b < 2 (2)

1
and b2 < 64

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Step 6 Workshop

DATA SUFFICIENCY WORKSHOP ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.

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Verbal Section Introduction

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Verbal Section

GENERAL OUTLINE

The Verbal Section of the GMAT CAT is designed to test your abilities in three subject areas: logic, grammar, and reading. For each subject area there is a corresponding question type: Critical Reasoning, Sentence Correction, and Reading Comprehension. Both Sentence Correction and Reading Comprehension questions test traditional verbal skills. Sentence Correction questions assess your ability to correct grammatical errors and Reading Comprehension questions evaluate your critical reading skills. Critical Reasoning questions, though included in the Verbal Section, test analytical skills and assess your abilities in logic. This introduction is designed to familiarize you with the Verbal Section of the GMAT CAT and the material covered. The lessons that follow this preview will discuss Critical Reasoning, Sentence Correction, and Reading Comprehension questions in detail and will give you specific strategies to help you improve your score on the Verbal Section of the GMAT CAT.

THE

FOLLOWING TOPICS WILL BE COVERED IN THIS LESSON:

The GMAT Verbal Section: An Overview What the Verbal Section Tests CAT Strategy What About Guessing on the CAT?

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Introduction

The GMAT Verbal Section: An Overview The Verbal Section of the GMAT CAT is a 75-minute section designed to test your mastery of basic logic and verbal skills as well as your ability to perform basic analyses. In this section there are 41 multiple-choice questions which fall into three categories: Critical Reasoning, Sentence Correction, and Reading Comprehension. Critical Reasoning questions are analytical problems presented as formal arguments that include inferences, premises, and a conclusion. The eight Critical Reasoning question types cover eight ways to test logical analysis, for example making intuitive deductions. Sentence Correction questions test your ability to identify and correct grammatical mistakes in sentences which are either partially or completely underlined. Your job is to determine whether the underlined section is right or wrong and, if wrong, to choose which of the answer choices best corrects the error. No sentences will appear which have not been underlined. Reading Comprehension questions test your ability to read and understand what is stated or implied in a text within a short amount of time. These questions always appear with a passage of between 250 and 450 words, and you do not have the option to select from several passages. You should expect approximately 14 Critical Reasoning questions, 14 Sentence Correction questions, and 13 Reading Comprehension questions in this section. However, because the number of each question type is decided by the computer, the actual allocation of questions may vary. The three question types in the Verbal Section do not test the same skills. Therefore, each type requires different strategies and techniques. For these reasons Critical Reasoning, Sentence Correction, and Reading Comprehension questions will be taught separately in this course.

HINT Note-taking materials are very important. Use them for drawing a scoring grid (see The MBA Center Approach to the GMAT CAT), for diagramming Reading Comprehension passages, and for outlining the premises and conclusion of a Critical Reasoning argument. We recommend that you take notes when you take the practice GMAT CATs.

What the Verbal Section Tests The Verbal Section of the GMAT requires knowledge of basic skills in logic, grammar, and reading. These concepts are the same for every GMAT and are tested in similar ways on each test. The two most commonly tested skills in the Verbal Section of the GMAT are making inferences (Critical Reasoning and Reading Comprehension) and spotting subjectverb agreement (Sentence Correction). Inferences are implied in every Critical Reasoning argument, and typically about one-third of the Critical Reasoning questions are inference questions. In Reading Comprehension, inference questions were once somewhat rare, though now you are likely to see two or three inference questions for each passage. Sentence Correction questions which test subject-verb agreement are more frequently asked than any of the other nine question types reviewed in your Sentence Correction lesson. Though questions are mixed on the CAT Critical Reasoning, Sentence Correction, and Reading Comprehension, the logic, grammar, and reading tested are distinct skills, each requiring separate mastery and strategy. The sections are designed to test precise concepts that contribute to a comprehensive assessment of general verbal skills. Each general verbal skill is broken down into a certain number of testing points designed to measure more specific verbal skills, which we’ve simplified into question types. For instance, in Sentence Correction there are ten testing points, Critical Reasoning has eight, and Reading Comprehension contains four. The ideal GMAT assessment is a thorough assessment. Many students learned grammar long ago and, as with math, need a reminder of basic rules. Since the grammar rules tested are basic, if unfamiliar, and count toward roughly one-third of your score on the Verbal Section (based on 14 or so Sentence Correction questions) we recommend that you take a look at the Grammar Review in this book before you begin the Sentence Correction lesson in Step 7.

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HINT The 41 questions in the Verbal Section include 11 experimental questions which are unrecognizable from any other question: the experimental questions are not designed to assess new testing points, they are designed to assess old testing points in new ways.

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Verbal Section

THE CHALLENGE The Verbal Section tests not only your mastery of certain verbal skills, but also your ability to determine answers to difficult questions quickly and accurately. The principal challenge of the Verbal Section of the GMAT is time. If you were given an unlimited amount of time, you could probably answer all or nearly all of the questions correctly. However, the testmaker designed each question in this section to confuse you, and the time allowed is limited. As a result most test takers have difficulty finishing the section in the time allowed. For these reasons, the MBA Center approach stresses both mastery of necessary basic verbal skills and use of the time-saving strategies in the Critical Reasoning, Sentence Correction, and Reading Comprehension lessons which follow. The Verbal Section also challenges your command of standard written English. All of the material in each of the three subject areas, Critical Reasoning, Sentence Correction, and Reading Comprehension presumes a high level of competence in the stylistic conventions and grammar rules of standard written English. Though the GMAT has been given in nonnative English speaking countries for many years, the test is still written in American English, which can prove challenging for many test takers whose first language is not English. While understanding the language in which the test is written is a significant challenge for many who take the test, nearly all test takers are challenged by the analytical skills required by over 60 percent of Verbal Section questions. The analytical skills tested involve your ability to reason, to make inferences, and to understand logical relationships. While completing the lessons which follow and practicing on your own it is important to understand how these analytical skills are tested in the Verbal Section, since all Critical Reasoning questions and at least two or three Reading Comprehension questions per passage are designed to measure these skills. Though the skills tested in the Verbal Section should not be unfamiliar to you, the challenge on the GMAT is to correctly answer questions which have been designed to confuse you within the limited amount of time you are given.

THE GMAT VERBAL SECTION

AND THE

CAT

How the CAT Works When you begin the Verbal Section of the GMAT CAT, the computer will give you a question (either Critical Reasoning or Sentence Correction) of medium difficulty. A medium difficulty question is one that roughly half of all test takers get right and roughly half get wrong. If you answer the first question correctly the computer will give you a harder question. Likewise, if you answer the first question incorrectly the computer will give you an easier question. This process is repeated for the rest of the section. Every time you answer a question correctly the computer gives you a more difficult question. Similarly, each time you answer a question incorrectly, the computer gives you an easier question. As you progress through the section each successive jump gets smaller and smaller as the computer focuses in on your level. In theory, you will eventually arrive at a point where every question will be at your level. The score you receive for the section depends not on the number, but on the difficulty level of the questions you answer correctly. The idea is to award more points for difficult questions than for easy ones. Therefore, correct answers to difficult questions increase your score more than do correct answers to easy questions. CAT Strategy In order to maximize your score on the Verbal Section of the GMAT it is important to keep in mind how the CAT arrives at a score. Remember, the computer tries to find your level of ability and assign questions to you accordingly. Early in the section, the computer makes large jumps in level of difficulty in order to find your general level of ability. As the section progresses the jumps get smaller and smaller as the computer focuses in on your level. Because your final score depends on the level of difficulty of the questions you answer

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Introduction

correctly, it is important that you correctly answer the early questions in order to get quickly to the harder, more valuable questions. Also worth noting is that not all questions in the Verbal Section require the same amount of time to answer. For example, general questions in Reading comprehension take less time to answer than do detail questions. Time Management on the CAT Because of the incredible time pressure on the CAT, it is important that you have a strategy for managing time. Use the chart below to help pace yourself on the Verbal Section of the CAT. Note that test takers who are weaker in verbal skills may want to spend a bit more time on the first nine questions in order to be sure to answer them correctly. Likewise, test takers who are stronger in verbal skills should move a bit more quickly through the early questions in order to conserve time for the difficult questions later in the section.

Time

9

27

41

Out of the Blocks - Questions 1–9 The first nine questions are by far the most important questions. Because the CAT is making large jumps at this stage of the test, a wrong answer is far more damaging to your score than is a wrong answer later on in the section. You can spend a bit more time per question here than you can later in the test. Take your time, check your work, and avoid guessing. Try to finish the first nine questions before 25 minutes have elapsed in the section. Cruising - Questions 10–27 These questions are still quite important, but a wrong answer here won’t be as damaging to your score as a wrong answer in the first nine questions. You should move through these quickly and efficiently. Make an honest attempt to answer all of these questions, but if you get stuck, go ahead and guess. You should be done with this block of questions before an hour has elapsed in the section. The Final Stretch - Questions 28–41 These questions are not as important as the previous questions. You should move quickly from question to question and don’t hesitate to guess if you find a question too difficult. Just be sure to answer all 41 questions. If you are about to run out of time, guess on the remaining questions.

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WHAT ABOUT GUESSING

Verbal Section

ON THE

CAT?

Guessing is especially important on the CAT for two reasons: 1) You can’t skip questions on the CAT. Until you answer the question you are currently on, the computer will not let you move on to the next question. So if you don’t know the answer to a question, go ahead and guess. Don’t worry, there isn’t a guessing penalty on the CAT. 2) Because the computer adapts to your level, you should find that nearly every question on the test is difficult. For this reason you will have to guess more often than you would on the pencil-and-paper test. Because guessing is necessary on the CAT, it is important that you become good at it. By using the techniques and strategies described in the Critical Reasoning, Sentence Correction, and Reading Comprehension lessons, you will be able to eliminate several wrong answer choices and improve your chances of guessing the correct answer. Answer every question in the section even if you have to guess. When time expires, every question left unanswered in the section is considered wrong. For this reason you should answer every question in the section, even if you have to take random guesses at the end. Remember: there is no penalty for getting a question wrong. Even if you take a random guess on a question, you have at least a 20 percent chance of getting it right. So make sure to allow enough time at the end to guess on the final questions if you have to. You should of course try to eliminate any wrong answers you can, but if you can’t, taking a guess is better than not answering a question at all.

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Step 7 Grammar and Style Review

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Step 7.1 Lesson

GENERAL OUTLINE

If you want to be able to choose the grammatically correct answers to multiple-choice Sentence Correction questions and to know how to write Analytical Writing Assessment essays that conform to the stylistic conventions of Standard Written American English, you need to know what the rules and conventions are. This lesson presents all the rules and conventions you need to know, in 100 bite-sized pieces, grouped into ten top grammar and style problem areas.

THE

FOLLOWING TOPICS WILL BE COVERED IN THIS LESSON:

Sentence Structure Subject-Verb Agreement Noun Number Verb Tense Pronouns Modifiers Comparisons Parallelism Idioms Style

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Grammar and Style Review

STANDARD WRITTEN AMERICAN ENGLISH (SWAE) If you want to join the club, you have to learn the code. A prerequisite for admission to the educated American elite of government, academia, or business is mastery of Standard Written American English, or SWAE. This is the language you are expected to use when you write an academic essay, a journal article, a formal letter, a legal brief, a business plan, or a diplomatic communiqué.

THE RULES OF SWAE The rules of SWAE are not codified in any one document or managed by any particular academy. The rules are established by precedent and formalized by consensus. About the great majority of rules there is no dissent. There are people who say “I knows” or “he be,” but they generally know not to write that way. About some rules, however, there are disputes. And these disputes can become surprisingly heated in some circles. In one corner, there are the rigid traditionalists who learned grammar from pedants and who cannot abide a split infinitive or a preposition at the end of a sentence. In the other corner, there are the radicals eager to abandon all rules and to accept the demise of “whom” or the use of “they” as a singular pronoun.

PHINEAS AND THE RULES OF SWAE The people who write GMAT questions and who grade GMAT essays fall somewhere between these two extremes. To avoid controversy, they do not test you on rules about which there is little consensus. You will not need to worry about split infinitives or prepositions at the ends of sentences. Nor do GMAT writers test you on rules that every literate native speaker knows. You will not have to watch out for “I knows” or “he be.” The rules tested on the GMAT are those that editors and scholars generally agree on but that many educated Americans have trouble with. These are the rules presented on the following pages. Learning these rules is critical to success on the GMAT. In one of the multiple-choice Verbal question types, Sentence Correction, your task is to detect violations of the rules of SWAE and to identify the answer choices that correct these violations. And in the Analytical Writing Assessment, your task is to produce essays that conform to the rules of SWAE. Learn the 100 rules on the following pages, and you will be ready to find and correct just about any mistake in a Sentence Correction question and to avoid the most common pitfalls in writing AWA essays.

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Step 7.1 Lesson

1. SENTENCE STRUCTURE The first issue to consider in proofing a sentence is its structure. Is it a sentence? SWAE has quite strict notions about what constitutes a sentence. Beware the sentence fragment — that is, an incomplete sentence, a string of words that does not have all it takes to make a sentence. Beware also the run-on sentence — an overcomplete sentence, a string of words that should actually be written as two sentences. Rule 1

Every sentence must have a subject and a conjugated verb.

In speech and casual writing it may be acceptable to produce sentences without verbs, but it is not acceptable in SWAE. Violence on television. That is what makes today’s young people so indifferent to human suffering. CORRECT: Violence on television is what makes today’s young people so indifferent to human suffering.

INCORRECT:

Rule 2

A clause beginning with a subordinating conjunction cannot be the main clause of a sentence.

Conjunctions like “before,” “after,” “although,” “because,” “if,” “when,” or “while” are subordinating conjunctions. A clause that begins with a subordinating conjunction cannot stand alone. Such a clause must be attached to another clause. Why was the move postponed? Because the new location was not yet ready for occupancy. CORRECT: The move was postponed because the new location was not yet ready for occupancy.

INCORRECT:

Although every attempt was made to rescue the agreement, ranging from compromise through concession to threats. CORRECT: Every attempt was made to rescue the agreement, ranging from compromise through concession to threats.

INCORRECT:

The conjunctions “and,” “but,” “or,” “nor,” “for,” “so,” and “yet” are coordinating conjunctions. A clause that begins with one of these conjunctions can be attached to another clause, but such a clause can also stand alone. Some traditionalists object to the practice, but in contemporary SWAE it is acceptable to begin a sentence with “and” or “but.” Rule 3

A clause beginning with a “which” or “who” cannot be the main clause of a sentence (unless the sentence is a question).

“Which” and “who” are relative pronouns. A clause that begins with a relative pronoun is a subordinate clause and needs another clause to attach to. The president has a degree from Harvard, and the vice president has a degree from the University of Virginia. Which is the Harvard of the South. CORRECT: The president has a degree from Harvard, and the vice president has a degree from the University of Virginia, which is the Harvard of the South.

INCORRECT:

Rule 4

Do not join two independent clauses with a comma.

If two clauses can each stand alone as a sentence, then they must be separated by something more final than a comma. A period usually works

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best, but a semicolon will work as well. The tomato is not a vegetable, it is a fruit. The tomato is not a vegetable. It is a fruit. CORRECT: The tomato is not a vegetable; it is a fruit.

INCORRECT: CORRECT:

INCORRECT: CORRECT: CORRECT:

The forecasts were accurate, the market is rebounding. The forecasts were accurate. The market is rebounding. The forecasts were accurate; the market is rebounding.

A monetary donation is not required, there are other ways to contribute. CORRECT: A monetary donation is not required. There are other ways to contribute. CORRECT: A monetary donation is not required; there are other ways to contribute.

INCORRECT:

Be aware that American readers find the semicolon pretentious. Usually a period is all you need. Use semicolons sparingly. Rule 5

Do not use adverbs to join clauses.

The following words are adverbs: thus therefore

however nevertheless

instead

These words are not conjunctions and should not be used to join clauses. Begin a new sentence, or at least use a semicolon. The quadrilateral is a parallelogram, therefore opposite angles are equal. CORRECT: The quadrilateral is a parallelogram. Therefore, opposite angles are equal. CORRECT: The quadrilateral is a parallelogram; therefore, opposite angles are equal.

INCORRECT:

No former President has ever served in the Senate, however one did serve in the House of Representatives. CORRECT: No former President has ever served in the Senate. However, one did serve in the House of Representatives. CORRECT: No former President has ever served in the Senate; however, one did serve in the House of Representatives.

INCORRECT:

Auto emissions and industrial waste are under control, nevertheless air pollution is on the increase. CORRECT: Auto emissions and industrial waste are under control. Nevertheless, air pollution is on the increase. CORRECT: Auto emissions and industrial waste are under control; nevertheless, air pollution is on the increase.

INCORRECT:

The meeting was not held in the conference room as planned, instead it took place in the director’s office. CORRECT: The meeting was not held in the conference room as planned. Instead, it took place in the director’s office. CORRECT: The meeting was not held in the conference room as planned; instead, it took place in the director’s office.

INCORRECT:

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EXERCISE 1 (SENTENCE STRUCTURE) Directions: Rewrite the following sentences to correct any sentence structure errors. (Note that some sentences may be correct as written.) 1. The secretary arrived too late, the meeting had already begun.

2. The dangers of secondhand smoke have been exaggerated, therefore the government should consider repealing some of the more restrictive antismoking laws.

3. The reasons for the price adjustment: increasing costs and decreasing demand.

4. English is not the most widely spoken language in the world, nevertheless it is the most practical language for international business.

5. Martinez and Johnson were commended for the new layout. But Chung deserves some credit as well.

6. Ask the librarian, he will know.

7. Because the head writer was in the hospital — appendicitis — and the artist was on vacation — honeymoon — progress ceased.

8. Because it has not rained in two months — the worst drought on record — and reservoir levels are dangerously low.

9. Call Novak, he is the only one who can help us now.

10. Test scores across the state have risen sharply under this administration. However, there is still room for improvement.

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2. SUBJECT-VERB AGREEMENT Once you have verified that the sentence has a subject and a verb, the next step is to make sure the subject and verb agree. Singular subjects and plural subjects take different verb forms. No native speaker has difficulty with agreement in the typical sentence in which the verb immediately follows the subject. You would never mistakenly say “he are” or “they is.” But when the sentence is more complicated — when the subject and verb are separated, or when the subject comes after the verb — subject-verb agreement becomes more complicated. Rule 6

The subject and verb must agree no matter what comes between them.

No matter how many words and what kind of words come between them, the subject and verb must agree. Do not let extra information clauses distract you. The rate at which falling objects accelerate are unrelated to their mass. CORRECT: The rate at which falling objects accelerate is unrelated to their mass.

INCORRECT:

Rule 7

For most subjects in the form “X of Y,” the verb agrees with X.

Usually the subject form “X of Y” consists of the subject X followed by a prepositional phrase “of Y” that provides extra information about X. As with any extra information clause that separates the subject and verb, the “of Y” clause should have no effect on the agreement of the verb with the true subject. The original intention of the tax cut measures were to jumpstart a sluggish economy. CORRECT: The original intention of the tax cut measures was to jumpstart a sluggish economy.

INCORRECT:

Rule 8

When X in the subject form “X of Y” is a quantity word, the verb agrees with Y.

Sometimes the subject form “X of Y” actually consists of the subject Y preceded by a statement of quantity “X of.” This is the case when X is a fraction, a percent, or a word such as “all,” “most,” “rest,” or “majority.” INCORRECT: CORRECT:

One quarter of the investments is bonds. One quarter of the investments are bonds.

INCORRECT: CORRECT:

Seventy-five percent of the portfolio are stocks. Seventy-five percent of the portfolio is stocks.

INCORRECT: CORRECT:

The majority of the House of Representatives are Republican. The majority of the House of Representatives is Republican.

Rule 9

“A number of” is plural. “The number of” is singular.

“A number of” is a quantity expression, and so verb agrees with the word that follows “of,” which will always be plural. (You cannot use “number” with a singular.) In the phrase “the number of,” the singular noun “number” is the subject.

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INCORRECT: CORRECT:

A number of reforms has been proposed. A number of reforms have been proposed.

INCORRECT:

The number of duplications are negligible. The number of duplications is negligible.

CORRECT:

Rule 10 Only the word “and” can make a plural subject out of two

or more singulars.

Such phrases as “together with,” “combined with,” “along with,” and “as well as,” do not create plural subjects. The Senator, along with her husband and children, were expected to attend. CORRECT: The Senator, along with her husband and children, was expected to attend.

INCORRECT:

The Times, the Post, as well as the Daily News have called for the judge’s resignation. CORRECT: The Times, the Post, and the Daily News have called for the judge’s resignation.

INCORRECT:

Rule 11 When a compound subject is formed using “or” or “nor,”

the verb agrees with the nearer subject.

If two plural nouns are combined with “or” or “nor,” the verb is plural. But if two singular nouns are combined this way, the verb is singular. Either the Senator or her spokesperson are expected to make a statement shortly. CORRECT: Either the Senator or her spokesperson is expected to make a statement shortly.

INCORRECT:

When one part of an “or” or “nor” subject is singular and the other part is plural, the verb agrees with the part that is closer to the verb — usually the part after “or” or “nor.” Neither her sons nor her daughter have been seen publicly in recent weeks. CORRECT: Neither her sons nor her daughter has been seen publicly in recent weeks.

INCORRECT:

Rule 12 The verb “be” agrees with the subject, not the complement.

Even when the complement is plural, if the subject is singular, then the verb must be singular. INCORRECT: CORRECT:

The only furniture were a lamp and a mattress. The only furniture was a lamp and a mattress.

INCORRECT: CORRECT:

But the true greatness of America are the people. But the true greatness of America is the people.

Rule 13 In a sentence beginning with “there,” the subject follows

the verb.

The word “there” at the beginning of a sentence is not the subject. Do not write “there is” or “there was” when what follows is plural.

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INCORRECT: CORRECT:

There is a number of possible explanations. There are a number of possible explanations.

There is not enough people in the department to get the job done. CORRECT: There are not enough people in the department to get the job done.

INCORRECT:

Each year there was more and more of what the administration euphemistically termed “inoperative statements.” CORRECT: Each year there were more and more of what the administration euphemistically termed “inoperative statements.”

INCORRECT:

Rule 14 In a sentence beginning with an adverbial phrase of

location, the subject is often postponed.

Sometimes, for reasons of emphasis or variety, a writer may choose to move an adverbial phrase of location to the front of a sentence, in which case the usual subject-verb order is reversed. Nevertheless, even if the subject comes after the verb, the subject and verb must agree. INCORRECT: CORRECT:

Between Fifth and Sixth Avenues stand a famous little church. Between Fifth and Sixth Avenues stands a famous little church.

INCORRECT: CORRECT:

At the back of the book is to be found a glossary and an index. At the back of the book are to be found a glossary and an index.

Rule 15 In a sentence beginning with a negative adverb or adverbial

phrase, the interrogative form is used, with the subject following the verb.

A writer may choose to accentuate the negative by moving a word or phrase such as “hardly,” “never,” “rarely,” or “not in a long time” to the head of a sentence. In that case, the interrogative form is used. That is, “do” or “have” or some modal verb is needed before the subject. INCORRECT: CORRECT:

Never he had seen so many elephants. Never had he seen so many elephants.

INCORRECT:

Rarely it snows in New Orleans. Rarely does it snow in New Orleans.

CORRECT:

The verb still agrees with the subject even when the subject is postponed. INCORRECT: CORRECT:

Hardly does the returning veterans recognize their home town. Hardly do the returning veterans recognize their home town.

INCORRECT: CORRECT:

In no other U.S. state does more people go to college. In no other U.S. state do more people go to college.

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EXERCISE 2 (SUBJECT-VERB AGREEMENT) Directions: Rewrite the following sentences to correct any subject-verb agreement errors. (Note that some sentences may be correct as written.) 1. The only thing he values more than his career are his wife and children.

2. The majority of the people of California supports recycling.

3. In the last ten years, the number of professional sports teams have doubled.

4. The only person who knows where the keys are is Wilson.

5. Heavy rain combined with gusty winds has caused widespread damage.

6. Not in several days have the mother or the children been seen.

7. Nuclei that are too large or ones in which the neutron-to-proton ratio is unfavorable are radioactive.

8. No less astonishing than the dimensions of the surviving examples are their variety.

9. On the ground floor of the office building is a newsstand, a coffee shop, and a restaurant.

10. Never before in the history of the state has Montana’s vote-counting procedures received more attention.

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3. NOUN NUMBER It can be a challenge to verify that the verb agrees with the subject when it is not clear whether the subject is singular or plural. Rule 16 There are some plural nouns that do not end in -s.

Some words borrowed directly from Greek or Latin have plural forms that do not end in -s. singular criterion phenomenon datum medium curriculum memorandum bacterium nucleus radius stimulus alumnus

plural criteria phenomena data media curricula memoranda bacteria nuclei radii stimuli alumni

Do not use plural forms such as “criteria,” “phenomena,” “bacteria,” or “alumni” as singular nouns. INCORRECT: CORRECT: INCORRECT: CORRECT:

The first criteria in the selection was experience. The first criterion in the selection was experience. He is an alumni of Harvard University. He is an alumnus of Harvard University.

In contemporary usage, the plural forms “data” and “media” are often used as singular nouns. “data” In the old days, English teachers taught that you must say “the data are,” but today “the data is” has become so common that it cannot be considered incorrect. CORRECT: CORRECT:

The data is inconclusive. The data are inconclusive.

“media” This word is still used as the plural of “medium.” Oil painting is one “medium,” pastel is another “medium,” and oil painting and pastel are two “media.” Do not use “media” as a singular this way: INCORRECT: CORRECT:

Television is the preferred media for political advertising. Television is the preferred medium for political advertising.

However, “media” is today very often used as a singular noun to refer to all the agencies of mass communication as an entity. This usage is so widespread that it can no longer be considered incorrect. CORRECT: CORRECT:

Everywhere the princess goes, the media follow. Everywhere the princess goes, the media follows.

Remember, however, that someone may object if you use “data” or “media” as a singular noun. To be on the safe side, treat them as plurals, just like “criteria” and “phenomena.”

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Rule 17 Uncountable nouns have no plural form.

Nouns such as “money,” “gasoline,” “smog,” “wheat,” beauty,” “grammar,” and “darkness” denote concepts that cannot be counted. Nouns of this type go by various names: uncountable nouns, noncount nouns, mass nouns. Whatever you call them, they have no plural form. Do not put -s on the end of “information,” “advice,” “baggage,” or “luggage.” INCORRECT: CORRECT:

Each passenger is allowed two carry-on baggages. Each passenger is allowed two pieces of carry-on baggage.

INCORRECT:

The counselor offered two advices. The counselor offered two pieces of advice.

CORRECT:

Rule 18 Some nouns have both a countable and an uncountable

meaning.

CORRECT: CORRECT:

Business is booming. It is always risky to start a new business.

Some doctors believe that red wine, in moderation, is good for heart. CORRECT: The wines of California have an excellent reputation. CORRECT:

Rule 19 There are some nouns that look plural but are in fact

singular.

Here are some nouns that end in -s in the singular form and are unchanged in the plural: means

series

species

The two specimens look different but are actually members of the same specie. CORRECT: The two specimens look different but are actually members of the same species.

INCORRECT:

Here are some nouns that look like plurals but generally act like uncountable singulars: news measles INCORRECT: CORRECT: INCORRECT: CORRECT:

mathematics statistics

physics economics

The news are bad. The news is bad. Quantum physics were all that the guests discussed. Quantum physics was all that the guests discussed.

Some of these words do have a countable, plural use: CORRECT: CORRECT: CORRECT: CORRECT:

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Economics is a popular major. The economics of the situation demand a tax cut. Elementary statistics is a prerequisite for this course. Statistics suggest that people drive more safely now than ten years ago.

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Rule 20 Collective nouns are usually singular.

In American usage, collective nouns such as “government,” “committee,” “public,” “family,” “team,” “band,” “choir,” and “audience” are almost always singular. INCORRECT: CORRECT:

The government were responsible. The government was responsible.

INCORRECT:

The Senator’s family have left town. The Senator’s family has left town.

CORRECT: INCORRECT: CORRECT:

The choir have arrived and are ready to sing. The choir has arrived and is ready to sing.

It should be noted that, in British English, collective nouns are often treated as plurals. The three “incorrect” versions above will sound just fine to most British ears. Rule 21 Collective nouns are sometimes used as expressions of

quantity, in which case they can be either singular or plural.

When designating a cohesive unit, a collective noun is singular. But when a collective noun is used to designate individuals acting separately, it can be plural. CORRECT:

After winning the championship, the team went their separate ways.

This construction sounds funny to most American ears, and so the sentence would normally be restated something like this: CORRECT:

After winning the championship, the team members went their separate ways.

The word “group,” however, sounds fine as either a singular or a plural. You can’t go wrong! CORRECT: CORRECT:

A group of people are waiting for the bus. A group of people is waiting for the bus.

Rule 22 Amounts of money and units of measure are generally

singular.

Two hundred dollars are not too much to spend for a business suit. CORRECT: Two hundred dollars is not too much to spend for a business suit.

INCORRECT:

Rule 23 Titles and compounds that are thought of as units are

generally singular.

Sometimes the word “and” is just a connecting word in the middle of an expression that is in reality felt to be a singular unit. Expressions such as “bacon and eggs,” “gin and tonic,” and “pride and joy” are singular. INCORRECT: CORRECT:

Bacon and eggs were once considered a healthful breakfast. Bacon and eggs was once considered a healthful breakfast.

Titles and names of organizations are generally singular. INCORRECT: CORRECT:

“Romeo and Juliet” are Shakespeare’s most popular play. “Romeo and Juliet” is Shakespeare’s most popular play.

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INCORRECT: CORRECT:

The United Nations are debating the issue. The United Nations is debating the issue.

Rule 24 Most indefinite pronouns are singular.

These indefinite pronouns are always singular: each either neither INCORRECT: CORRECT:

anything anyone anybody

everything everyone everybody

nothing no one nobody

Neither of the proposed solutions are likely to succeed. Neither of the proposed solutions is likely to succeed.

Rule 25 The indefinite pronouns “none,” “all,” “any,” and “some”

can be either singular or plural.

It depends on the context. The show has more than 12 original songs and all are tuneful and engaging. CORRECT: Most of the music is new, and all is tuneful and engaging. CORRECT:

Sometimes you have a choice. CORRECT: CORRECT:

None of the singers were especially memorable. None of the singers was especially memorable.

Rule 26 Use “many” with countable nouns and “much” with

uncountable nouns.

Do not use “much” with a countable noun. INCORRECT: CORRECT:

The goal was realized at the cost of much sweat and tears. The goal was realized at the cost of much sweat and many tears.

Rule 27 Use

“few/fewer/fewest” with countable “little/less/least” with uncountable nouns.

nouns

and

Do not use “less” or “least” with a countable noun. The theater has the most empty seats on Monday nights and the least on Saturday nights. CORRECT: The theater has the most empty seats on Monday nights and the fewest on Saturday nights.

INCORRECT:

Rule 28 Use “number” with countable nouns and “amount” with

uncountable nouns.

Do not use “amount” with a countable noun. INCORRECT: CORRECT:

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Order was assured by the presence of a large amount of police. Order was assured by the presence of a large number of police.

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EXERCISE 3 (NOUN NUMBER) Directions: Rewrite the following sentences to correct any noun number errors. (Note that some sentences may be correct as written.)

1. Anyone requiring additional informations should consult the company's website.

2. The United Nations have been debating a human rights resolution.

3. A group of people are waiting for the shuttle bus.

4. A solar eclipse is a phenomena that is worth a journey to witness.

5. The public are opposed to the proposed legislation.

6. This year’s promotional event attracted less people than last year’s did.

7. On Sundays, when admission is free, the amount of people at the museum is astonishing.

8. Everyone sang well and were heartily applauded.

9. For the first time there were less species on the endangered list than in the previous year.

10. None of students was able to complete the assignment in the allotted time.

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4. VERB TENSE Rule 29 Use the past perfect (“had” + past participle) if one clause

takes place at an earlier time than another clause that is in the past.

INCORRECT: CORRECT:

The performance already started when they arrived. The performance had already started when they arrived.

The Civil War forced the United States to decide issues that the framers of the Constitution raised but left unresolved. CORRECT: The Civil War forced the United States to decide issues that the framers of the Constitution had raised but left unresolved.

INCORRECT:

Do not use the past perfect unnecessarily. From 1920 to 1930, the number of automobiles in the state had more than tripled. CORRECT: From 1920 to 1930, the number of automobiles in the state [...] more than tripled.

INCORRECT:

In recent years, the corporate dress code had relaxed considerably. CORRECT: In recent years, the corporate dress code has relaxed considerably.

INCORRECT:

Rule 30 Use the future perfect (“will have” + past participle) if one

clause takes place at an earlier time than another clause that is in the future.

INCORRECT: CORRECT:

By the time the lecture ends, it will stop raining. By the time the lecture ends, it will have stopped raining.

Rule 31 Use the infinitive perfect (“to have” + past participle) if the

infinitive takes place at an earlier time than the rest of the clause.

INCORRECT: CORRECT:

The sculptor is believed to be born before 1400. The sculptor is believed to have been born before 1400.

Rule 32 After “when” referring to a future event, use the present

tense.

INCORRECT: CORRECT:

When the sun will come out, the temperature will rise. When the sun comes out, the temperature will rise.

When Jenkins will submit his report tomorrow morning, the governor will have all the information needed to make a decision. CORRECT: When Jenkins submits his report tomorrow morning, the governor will have all the information needed to make a decision.

INCORRECT:

Rule 33 After “if” referring to a possible future event, use the

present tense, and in the other clause use “will” or “can.”

INCORRECT: CORRECT:

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If the sun comes out tomorrow, we go on a picnic. If the sun comes out tomorrow, we will go on a picnic.

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If the value of the dollar be higher this summer than last, more Americans will vacation abroad. CORRECT: If the value of the dollar is higher this summer than last, more Americans will vacation abroad.

INCORRECT:

INCORRECT: CORRECT:

If our proposal will be accepted, we can get funding. If our proposal is accepted, we can get funding.

Rule 34 In a sentence beginning with “if” or “when” and referring

to a scientific fact or general truth, you may use the present tense in both clauses. CORRECT: CORRECT: CORRECT:

If a triangle has two equal sides, it also has two equal angles. When water is heated to 100 degrees Celsius, it boils. Whenever it rains more than an inch in one week, the river floods.

Rule 35 To express a condition that is contrary to fact in the

present, use the past tense in the “if” clause, and use “would” or “could” in the other clause. (Technically, it’s not the past tense, but the contrary-to-fact conditional. But the form is the same as the past tense for every verb except “to be.”) If the director has an assistant, the department runs more smoothly. CORRECT: If the director had an assistant, the department would run more smoothly.

INCORRECT:

INCORRECT: CORRECT:

If Young earns a bigger salary, the family would travel more. If Young earned a bigger salary, the family would travel more.

Rule 36 In the case of the verb “be,” use “were” in the “if” clause

even for the singular. If this was a school with enormous enrollment, students would have less personal contact with professors. CORRECT: If this were a school with enormous enrollment, students would have less personal contact with professors.

INCORRECT:

More and more often now one hears and reads “was” in this situation, although “If I was you...” still sounds illiterate to most educated Americans. To avoid offending the traditionalists, use “were.” Rule 37 “Was” is correct in an “if” clause when it is expressing

uncertainty about the past, not contrary to fact. If the department head were on vacation last week, then she will be relaxed for today’s meeting. CORRECT: If the department head was on vacation last week, then she will be relaxed for today’s meeting.

INCORRECT:

If Martha were able to get a ticket to the opera, she probably got home late last night. CORRECT: If Martha was able to get a ticket to the opera, she probably got home late last night.

INCORRECT:

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Rule 38 To express a condition that is contrary to fact in the past,

use the past perfect (“had” + past participle) in the “if” clause, and use “would have” + past participle in the other clause.

If the rain continued another hour, the river would have overflowed its banks. CORRECT: If the rain had continued another hour, the river would have overflowed its banks.

INCORRECT:

Rule 39 Do not use “would” in the “if” clause.

If writers would refer to the dictionary more often, there would be fewer misspellings. CORRECT: If writers referred to the dictionary more often, there would be fewer misspellings.

INCORRECT:

If the student would have studied harder, he would have passed the test. CORRECT: If the student had studied harder, he would have passed the test.

INCORRECT:

Rule 40 In a “that” clause following a verb of recommendation,

request, or requirement, use the subjunctive.

The subjunctive form is the same for all subjects. There is no -s suffix in the third person singular. INCORRECT: CORRECT:

The advisor recommended that the student repeats the test. The advisor recommended that the student repeat the test.

The Constitution requires that the President reports regularly to Congress on the state of the nation. CORRECT: The Constitution requires that the President report regularly to Congress on the state of the nation.

INCORRECT:

The subjunctive form for the verb “be” is “be.” The management suggests that valuables are to be secured in the safe. CORRECT: The management suggests that valuables be secured in the safe.

INCORRECT:

Rule 41 In a “that” clause following a noun or adjective derived

from a verb of recommendation, request, or requirement, use the subjunctive.

Next time the associates will take seriously our insistence that everyone is on time for a meeting. CORRECT: Next time the associates will take seriously our insistence that everyone be on time for a meeting.

INCORRECT:

Rule 42 Do not use “should” or “must” with the subjunctive. INCORRECT: CORRECT:

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The law requires that a motorcyclist must wear a helmet. The law requires that a motorcyclist wear a helmet.

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EXERCISE 4 (VERB TENSE) Directions: Rewrite the following sentences to correct any verb tense errors. (Note that some sentences may be correct as written.) 1. If two objects are dropped simultaneously from the same height, they reach the ground at the same time.

2. If the stationery store was open yesterday, the office manager probably bought some paper and pens.

3. If the team would have started the project a month earlier, they would be finished by now.

4. If Americans would eat less red meat, they would have lower cholesterol levels.

5. Financial experts recommend that one should diversify one’s investments.

6. He resents the suggestion that he rewrites the paper.

7. He resents the suggestion that he plagiarized.

8. The lecturer began with a quick plot synopsis for the benefit of those who did not read the novel.

9. The civilization is believed to flourish in the fifteenth century.

10. Once the student will pass the comprehensive oral examination, she has satisfied all the requirements for the degree.

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5. PRONOUNS Rule 43 Pronoun reference must be logical and unambiguous.

A pronoun must generally have an antecedent. The bill; CORRECT: The bill;

INCORRECT:

President objected to several provisions and vetoed the however, Congress overrode it. President objected to several provisions and vetoed the however, Congress overrode the veto.

And it must be absolutely clear what the antecedent is. It is better to repeat the noun than to make the reader figure out what you mean. It is not surprising that Jackson produced a more incisive analysis that Jones did, because he has less firsthand experience. CORRECT: It is not surprising that Jackson produced a more incisive analysis that Jones did, because Jones has less firsthand experience.

INCORRECT:

Rule 44 Pronouns must agree with their antecedents.

Agreement is a matter of grammar, not reality. An antecedent is a noun. If the noun is singular, any pronoun referring to it must be singular, even when it designates more than one individual. The government should not spend money on space exploration; they should pay more attention to citizens’ basic needs. CORRECT: The government should not spend money on space exploration; it should pay more attention to citizens’ basic needs.

INCORRECT:

Rule 45 Do not confuse subject and object pronouns.

“I,” “we,” “he,” “she,” “they,” and “who” are used as subjects. “Me,” “us,” “him,” “her,” “them,” and “whom” are used as objects of verbs and prepositions. Native speakers rarely have trouble with the distinction. You know perfectly well never to say or write, “Me love she,” or, “Whom is him?” The distinction becomes a little more complicated when you have a compound subject or object. Use subject pronouns for all parts of compound subjects or complements. Use object pronouns for all parts of compound objects. Do not let the word “and” or “or” confuse you. You teach a child to read, and he or her will be able to pass a literacy test. CORRECT: You teach a child to read, and he or she will be able to pass a literacy test.

INCORRECT:

Between you and I, the state of American education is alarming. CORRECT: Between you and me, the state of American education is alarming.

INCORRECT:

The distinction between “who” and “whom” seems to be the most difficult for native speakers. The incorrect versions of the following two sentences are encountered more frequently than the correct versions. INCORRECT: CORRECT:

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INCORRECT: CORRECT:

Who is the new computer for? Whom is the new computer for?

“Whom” has virtually disappeared from the spoken language. As a matter of fact, if you use “whom” in everyday speech, your listeners will think you are showing off. In writing, however, you should use “whom” when it is appropriate. A good way to decide between “who” and “whom” is to try answering the question with “he” or “him.” The answer to the question “Who/whom did the director choose?” would be: “The director chose him.” Likewise, the answer to the question “Who/whom is the new computer for?” would be: “The computer is for him.” When “him” is the answer, “whom” is the question. Rule 46 Use subject pronouns after “it is” and “it was.”

“Be” is not a transitive verb, but a linking verb. A pronoun after “is” or “was” is not a direct object, but a complement. Use the subject pronouns after “is” and “was.” INCORRECT: CORRECT:

It is him who must decide. It is he who must decide.

INCORRECT:

It was them who won the competition. It was they who won the competition.

CORRECT:

Rule 47 Use the relative pronoun “which” for things only. Use “who”

or “whom” for people.

Do not use “which” for people. The film director which this reviewer most admires is Hitchcock. CORRECT: The film director whom this reviewer most admires is Hitchcock.

INCORRECT:

Rule 48 In a subordinate clause, use “who” or “whom,” and

“whoever” or “whomever,” according to the pronoun’s grammatical function in that clause.

The distinction between “who” and “whom” is even more difficult when they are relative pronouns introducing subordinate clauses. In that case, it’s the pronoun’s grammatical function within the subordinate clause that determines the form to use. INCORRECT:

The protagonist, who the author calls Mr. X, is handsome and mysterious.

In this sentence the relative pronoun refers to the subject “protagonist,” but within the subordinate clause the pronoun is the object of the verb “calls.” Therefore, the object pronoun “whom” is correct. CORRECT:

The protagonist, whom the author calls Mr. X, is handsome and mysterious.

You can use the “he/him” test here, too. Take the clause that the pronoun “who” or “whom” is to be a part of. Think of it as a question, and then answer that question with “he” or “him.” In the above example, the relative clause is “who/whom the author calls Mr. X.” Think of it as a question: “Who/whom does the author call Mr. X?” The answer to that question is “The author calls him Mr. X.” When the answer is “him,” the correct pronoun is “whom.”

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Here is another example: INCORRECT:

They will award the prize to him whom they truly believe deserves it.

This time the relative pronoun refers to the object “him,” but within the subordinate clause the pronoun is the subject of the verb “deserves.” Therefore, the subject pronoun “who” is correct. CORRECT:

They will award the prize to him who they truly believe deserves it.

Use the “he/him” test. The clause is “who/whom they truly believe deserves it.” Think of it as a question: “Who/whom do they truly believe deserves it?” The answer is “They truly believe he deserves it.” When the answer is “he,” the correct pronoun is “who.” Do not let the words “they truly believe” confuse you. That is a grammatically irrelevant extra information clause. If you omit that phrase, it may become clearer why “who” is correct. CORRECT:

They will award the prize to him who deserves it.

The same rule applies to the relative pronouns “whoever” and “whomever.” It is the clauses they introduce that tell you which form to use. INCORRECT: CORRECT:

This letter is addressed to whoever you think it may concern. This letter is addressed to whomever you think it may concern.

Here the pronoun is the object of “may concern.” You would say “you think it may concern him,” and so “whomever” is correct. This letter is addressed to whomever you think may be interested. CORRECT: This letter is addressed to whoever you think may be interested.

INCORRECT:

This time the pronoun is the subject of “may be interested.” You would say “you think he may be interested,” and so “whoever” is correct. Rule 49 You may use either “which” or “that” for a restrictive

relative clause, but for a nonrestrictive relative clause you must use “which.”

A restrictive clause is one that limits, that tells you which one. A restrictive clause is essential to the meaning of a sentence. Some old-fashioned grammarians insist that you must use “that” in restrictive clauses. Today it is common and acceptable to use “which.” “The Queen of Spades” is a story that had a profound influence on all subsequent Russian prose. CORRECT: “The Queen of Spades” is a story which had a profound influence on all subsequent Russian prose. CORRECT:

A nonrestrictive clause is one that does not limit the word or phrase it refers to. A nonrestrictive clause is not essential to the understanding of the sentence, and is always set off from the rest of the sentence with commas. Do not use “that” at the start of a nonrestrictive clause. You must use “which.” David was born in the province of Saskatchewan, that is located between Manitoba and Alberta. CORRECT: David was born in the province of Saskatchewan, which is located between Manitoba and Alberta.

INCORRECT:

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Rule 50 Do not use “which” to refer to a whole idea.

“Which” should always have a specific antecedent. The material is expensive and the workmanship is faultless, which is why the price is high. CORRECT: The price is high because the material is expensive and the workmanship is faultless.

INCORRECT:

Rule 51 If the antecedent is “everyone,” “everybody,” “anyone,” “no

one,” etc., the pronoun should be singular. “Everyone” and “everybody” are particularly troublesome, in that they denote more than one person but are grammatically singular. INCORRECT: CORRECT:

Everyone must do their part if democracy is to succeed. Everyone must do his or her part if democracy is to succeed.

Rule 52 Do not use “they” or “them” to avoid specifying the sex of

a singular antecedent. If casual conversation it is common to use “they” and “their” to refer to a singular antecedent of unspecified sex. The intention is laudable, but the method is ungrammatical. Someone phoned this morning, but they did not leave a message. CORRECT: Someone phoned this morning, but he or she did not leave a message.

INCORRECT:

A good way to be both politically and grammatically correct is to use the gender-neutral plural throughout the sentence. Every student is required to submit their final schedule by October first. CORRECT: All students are required to submit their final schedules by October first.

INCORRECT:

Rule 53 Do not use “they” or “them” as a general person pronoun.

“They” should always have a specific antecedent. They just announced on the radio that the two biggest banks in the state are merging. CORRECT: It was just announced on the radio that the two biggest banks in the state are merging.

INCORRECT:

Rule 54 Do not switch pronouns mid-sentence.

Use either “one” or “you” for the general person pronoun, but do not mix them. INCORRECT: CORRECT: CORRECT:

If one works hard, you will succeed. If one works hard, one will succeed. If you work hard, you will succeed.

Rule 55 The possessive form of “one” is “one’s.”

Do not use “your,” “his,” “his or her,” or “their.” One should always remember to bring his or her calculator to class. CORRECT: One should always remember to bring one’s calculator to class.

INCORRECT:

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EXERCISE 5 (PRONOUNS) Directions: Rewrite the following sentences to correct any pronoun errors. (Note that some sentences may be correct as written.)

1. My partner invited my wife and me to join him and his wife for dinner.

2. No one will buy such an expensive product unless they really need it.

3. The directors are looking for someone who they can trust to abide by the rules.

4. When one considers the candidate’s youth and inexperience, you have to say that the victory was unexpected.

5. If the television viewer loses interest for just a few seconds, they will switch channels.

6. It is sunny and hot today, but they say it will rain tomorrow.

7. If one invests early and wisely, one will be able to enjoy his or her retirement.

8. Because the parties have been unable to resolve the dispute, a judge will have to do it.

9. After questioning the two suspects, the investigator became convinced that it was them who committed the crime.

10. The judges will award the scholarship to whoever they feel will benefit the most.

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6. MODIFIERS Rule 56 Use adjectives to modify nouns, and adverbs to modify

anything else. Adverbs are words that answer the questions “how?” “when?” and “where?” Most adverbs of manner (adverbs that answer the question “how?”) are formed by adding the suffix “-ly” to an adjective. There are, however, some adverbs of manner that do not take the “-ly” suffix. The most important ones are “fast,” “hard,” and “late.” There is no such word as “fastly,” and the words “hardly” and “lately” have completely different meanings from “hard” and “late.” INCORRECT: CORRECT:

The day went fastly. The day went fast.

The student worked hardly on the essay and got the good grade she deserved. CORRECT: The student worked hard on the essay and got the good grade she deserved.

INCORRECT:

Do not use an adjective to modify a verb. INCORRECT: CORRECT:

He takes his career serious. He takes his career seriously.

The adjective “good” must never be used as an adverb. The adverb is “well.” INCORRECT: CORRECT:

The soprano sang good. The soprano sang well.

Rule 57 Use an adjective after a linking verb to modify the subject.

Use an adverb to modify the verb. Verbs that describe a state of being (“be,” “remain,” and “become,” for example) and verbs that relate to the five senses (“feel,” “seem,” “look,” “sound,” “smell,” and “taste,” for example) are called linking verbs. After a linking verb it makes sense to use an adjective because it is intended to modify the subject. INCORRECT: CORRECT:

The reheated coffee smelled and tasted bitterly. The reheated coffee smelled and tasted bitter.

INCORRECT: CORRECT:

The show was canceled because the star felt badly. The show was canceled because the star felt bad.

However, if the word is intended to modify the verb, use an adverb. Note the differences in the following examples. CORRECT: CORRECT: CORRECT: CORRECT:

The evidence proved conclusive. The evidence proved conclusively that the accused was guilty. A suitcase left unattended will look suspicious. Security agents will look suspiciously at a suitcase left unattended.

Rule 58 Absolute adjectives (“unique,” “perfect,” “impossible,” etc.)

cannot be qualified with words such as “very” or “most.” INCORRECT: CORRECT:

Madagascar is the most unique tourist destination. Madagascar is a unique tourist destination.

Rule 59 Avoid misplaced modifiers.

Modifying phrases must be placed unambiguously close to the element they are modifying.

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INCORRECT: CORRECT: INCORRECT: CORRECT:

Whether baked, fried, or mashed, everyone loves potatoes. Everyone loves potatoes, whether baked, fried, or mashed. She met a man who owns three beach houses in Phoenix. In Phoenix, she met a man who owns three beach houses.

Rule 60 Avoid squinting modifiers.

A modifying phrase must be placed unambiguously. A squinting modifier is one that is situated between two possible referents. How is the reader to decide? The following sentence, for example, can be interpreted two ways: AMBIGUOUS:

People who jog frequently develop knee problems.

It is not clear whether “frequently” modifies “jog” or “develop.” To make it clear, rewrite the sentence. CORRECT: CORRECT:

Frequent joggers develop knee problems. Joggers frequently develop knee problems.

Rule 61 Place limiting modifiers (“only,” “just,” “hardly,” “almost,”

etc.) immediately before the elements they modify. Be especially careful with the placement of “only.” There is a tendency to place it ambiguously before the verb no matter what it modifies. AMBIGUOUS:

The dean only takes appointments with undergraduates on Mondays and Wednesdays.

Proper placement of “only” resolves the ambiguity. The dean takes appointments only with undergraduates on Mondays and Wednesdays. CORRECT: The dean takes appointments with undergraduates only on Mondays and Wednesdays. CORRECT:

Rule 62 Avoid dangling modifiers.

Modifying phrases must have something to modify. A dangling modifier is one that has no referent in the sentence. It just hangs there. Having read the book and seen the film, there is no question that the book is better. CORRECT: Having read the book and seen the film, I can say with certainty that the book is better.

INCORRECT:

Rule 63 An introductory modifying phrase must modify the subject

of the sentence. When a modifying phrase is placed at the start of a sentence, the phrase is felt to modify the subject of the sentence, which should generally be found right after the comma. With a population of more than five million, some visitors find the city overwhelming. CORRECT: With a population of more than five million, the city overwhelms some visitors.

INCORRECT:

An introductory modifying phrase cannot modify a noun in the possessive (-’s) form. A modifying phrase at the beginning of a sentence is felt to modify the subject, not the subject’s possessor. Having recently secured several lucrative contracts, Goldberg’s reputation in the office is on the rise. CORRECT: Having recently secured several lucrative contracts, Goldberg enjoys his reputation in the office being on the rise.

INCORRECT:

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EXERCISE 6 (MODIFIERS) Directions: Rewrite the following sentences to correct any modifier errors. (Note that some sentences may be correct as written.)

1. Driving quickly became his favorite pastime.

2. She tries to attract men with makeup and perfume.

3. Born and raised near the Mexican border, Spanish came easily to her.

4. There is a sculpture on the facade that represents the rise of technology.

5. He hired a crew with a truck that is accustomed to handling delicate antiques.

6. Having decided to get the story at any cost, nothing could stop the reporter.

7. Straight out of the oven and still piping hot, the family devoured the whole pie.

8. Even after providing explicit instructions, the new employee did not know what to do.

9. Dressed in a T-shirt and jeans, the supervisor ordered the assistant to go home and change into more professional attire.

10. No longer sworn enemies, relations between the United States and Russia have improved considerably since the end of the Cold War.

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7. COMPARISONS Rule 64 Items that are compared must be logically comparable.

A carefully written sentence will compare a quality to a quality, a quantity to a quantity, or a thing to thing. Make sure the sentence does not, when taken literally, actually compare a quality to a thing or a quantity to a thing. The taste of the artificial substitute is indistinguishable from the real thing. CORRECT: The taste of the artificial substitute is indistinguishable from that of the real thing.

INCORRECT:

INCORRECT: CORRECT:

The population of California is greater than Canada. The population of California is greater than that of Canada.

If a sentence compares two things, make sure they are comparable. INCORRECT: CORRECT:

The operas of Verdi are more tuneful than Wagner. The operas of Verdi are more tuneful than those of Wagner.

The ink cartridges for the new printer cost twice much as the old printer. CORRECT: The ink cartridges for the new printer cost twice much as those for the old printer.

INCORRECT:

Rule 65 Items

that comparable.

are

The mother opportunities CORRECT: The mother opportunities

INCORRECT:

compared

must

be

grammatically

envies her son because he has had more than her. envies her son because he has had more than she.

Rule 66 Avoid incomplete comparisons. A comparison must be clear

and unambiguous. INCORRECT: CORRECT: CORRECT:

Martin likes asparagus more than his wife. Martin likes asparagus more than his wife does. Martin likes asparagus more than he does his wife.

Executives are more concerned about profits than employees. Executives are more concerned about profits than employees are. CORRECT: Executives are more concerned about profits than about employees.

INCORRECT: CORRECT:

Rule 67 When comparing something with other members of the

same group, use the word “other” or “else.” The population of California is greater than that of any American state. CORRECT: The population of California is greater than that of any other American state.

INCORRECT:

INCORRECT: CORRECT:

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Tanya earns a bigger salary than anyone in her family does. Tanya earns a bigger salary than anyone else in her family does.

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Rule 68 Use the comparative form of the adjective with two items.

Use the superlative form with three or more items.

Her children are both in college, the oldest at Harvard and the youngest at Yale. CORRECT: Her children are both in college, the older at Harvard and the younger at Yale.

INCORRECT:

Of all the films this reviewer has seen in the past year, this one is the more memorable. CORRECT: Of all the films this reviewer has seen in the past year, this one is the most memorable.

INCORRECT:

Rule 69 Use the “-er” and “-est” suffixes to form the comparative

and superlative of one-syllable adjectives and some twosyllable adjectives. Use “more” and “most” for longer adjectives.

For adjectives of one syllable, the comparative/superlative is formed with the “-er/-est” suffixes. tall big

taller bigger

tallest biggest

For adjectives of three or more syllables, the comparative/superlative form is “more/most” + adjective. beautiful expensive

more beautiful more expensive

most beautiful most expensive

Most two-syllable adjectives also take the “more/most” form, but some take the “-er/-est” form. cheerful happy

more cheerful happier

most cheerful happiest

A few adjectives have irregular comparative and superlative forms. good bad far many much little

better worse farther more more less

best worst farthest most most least

Rule 70 Use the short comparative or superlative form if it exists.

Otherwise, use the “more” or “most.”

Do not invent “-er” and “-est” forms. INCORRECT: CORRECT:

The interior of the island is peacefuler than the coast. The interior of the island is more peaceful than the coast.

Rule 71 Do not use “more/most” or “less/least” with the “-er/est”

form.

Use one or the other. Never use both on the same adjective. It would be more easier to do business with Johnson if he were a more pleasanter person. CORRECT: It would be easier to do business with Johnson if he were a more pleasant person.

INCORRECT:

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EXERCISE 7 (COMPARISONS) Directions: Rewrite the following sentences to correct any comparison errors. (Note that some sentences may be correct as written.)

1. Americans eat more corn than Europeans.

2. The second of the author’s two published works sold best.

3. The critic maintained that it was the worse film she ever saw.

4. Unlike Los Angeles, most New Yorkers use public transportation.

5. Every year, more foreign tourists visit Paris than any European city.

6. The United States is the most rich and wasteful country in the world.

7. Alice may be younger than her husband, but she is more experienced than he.

8. His job title is director of marketing, but his salary is still less than a secretary.

9. Abraham Lincoln was perhaps one of the most wisest men ever to serve as President.

10. Choose either regular or express service: the former is least expensive and the latter is fastest.

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8. PARALLELISM Rule 72 Items in a list must be parallel.

If the first item in a list is a noun or a noun phrase, all items must be nouns or noun phrases. Last month’s drop in sales was due to increased competition, poor publicity, and because many clients were away for the holidays. CORRECT: Last month’s drop in sales was due to increased competition, poor publicity, and the fact that many clients were away for the holidays.

INCORRECT:

If the first item in a list is a conjugated verb or verb phrase, all items must be similarly conjugated verbs or verb phrases. Our team is successful because we communicate effectively, work well together, and we respect one another. CORRECT: Our team is successful because we communicate effectively, work well together, and [...] respect one another.

INCORRECT:

If the first item in a list is a gerund construction, all items must be gerund constructions. Air travel means sitting in the same position for hours, watching a bad print of a tiresome film, eating food that has no flavor, and you have to refrain from smoking. CORRECT: Air travel means sitting in the same position for hours, watching a bad print of a tiresome film, eating food that has no flavor, and refraining from smoking.

INCORRECT:

If the first item in a list is a prepositional phrase, all items must be prepositional phrases. He searched for the lost item everywhere: in the house, car, and at the office. CORRECT: He searched for the lost item everywhere: in the house, in the car, and at the office.

INCORRECT:

Rule 73 If a preposition is repeated once in a list, it must be

repeated every time. The train stops in Stamford, Bridgeport, and in New Haven. The train stops in Stamford, in Bridgeport, and in New Haven. CORRECT: The train stops in Stamford, [...] Bridgeport, and [...] New Haven.

INCORRECT: CORRECT:

The same goes for the function word “to” in infinitives. If it is repeated once, it must be repeated every time. His dream is to graduate from MIT, develop an original theory, and to win a Nobel prize. CORRECT: His dream is to graduate from MIT, to develop an original theory, and to win a Nobel prize. CORRECT: His dream is to graduate from MIT, [...] develop an original theory, and [...] win a Nobel prize.

INCORRECT:

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Rule 74 In the structures “both X and Y,” “either X or Y,” and

“neither X nor Y,” X and Y must be parallel.

Architects today must consider both how much a material costs and its durability. CORRECT: Architects today must consider both a material’s cost and its durability. CORRECT: Architects today must consider both how much a material costs and how long it will last.

INCORRECT:

The speaker will go either by train or fly to the conference in Philadelphia. CORRECT: The speaker will go either by train or by plane to the conference in Philadelphia. CORRECT: The speaker will either go by train or fly to the conference in Philadelphia.

INCORRECT:

Rule 75 In the structures “not X but Y” and “not only X but also Y,”

X and Y must be parallel.

The restaurant’s success is due not to the quality of food but where it is located. CORRECT: The restaurant’s success is due not to the quality of food but to its location.

INCORRECT:

Thomas Edison was not only a brilliant inventor, but he was also a shrewd businessman. CORRECT: Thomas Edison was not only a brilliant inventor but also a shrewd businessman.

INCORRECT:

Rule 76 When you use “be” to equate or compare two elements, the

elements must be parallel.

A noun can be likened to a noun: CORRECT:

Vanilla is more popular than chocolate.

A gerund can be compared to a gerund: CORRECT:

Seeing is believing.

An infinitive can be compared to an infinitive: CORRECT:

It is better to give than to receive.

Avoid mixing grammatical forms in a comparison: Having a spouse with whom one can openly discuss failure and self-doubt is to be happily married. CORRECT: To have a spouse with whom one can openly discuss failure and self-doubt is to be happily married.

INCORRECT:

To learn a foreign language means discovering another way to categorize reality. CORRECT: Learning a foreign language means discovering another way to categorize reality.

INCORRECT:

Do not use a clause beginning with “when” to define a noun: INCORRECT: CORRECT:

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The novel’s saddest event is when the heroine dies. The novel’s saddest event is the death of the heroine.

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EXERCISE 8 (PARALLELISM) Directions: Rewrite the following sentences to correct any parallelism errors. (Note that some sentences may be correct as written.)

1. To be a celebrity means having no privacy.

2. The meeting is not scheduled for today but tomorrow.

3. The dieter resolved neither to eat too much nor too little.

4. He is not only responsible for the design, but also the execution.

5. The turning point in the plot is when the protagonist disappears.

6. A teacher’s job is to inspire creativity as well as imparting knowledge.

7. The artist is neither naturally talented nor is she independently wealthy.

8. The two biggest events in his life were when he got married and when his first child was born.

9. By the time Baldwin arrived to help, his colleagues had already laid out the site, cleared the land, and began to excavate.

10. The changeover to the metric system did not succeed because people could not become accustomed to using meters instead of feet, grams instead of ounces, or to using liters instead of quarts.

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9. IDIOMS Rule 77 “From” goes with “to,” and “between” goes with “and.”

Do not use “between” with “to.” Between 1980 to 1990, the population of Centerville grew by 50 percent. CORRECT: From 1980 to 1990, the population of Centerville grew by 50 percent. CORRECT: Between 1980 and 1990, the population of Centerville grew by 50 percent.

INCORRECT:

No preposition is needed with a hyphen to indicate a range of dates. The symposium will take place in the nation’s capital between August 11–16. CORRECT: The symposium will take place in the nation’s capital [...] August 11–16.

INCORRECT:

Rule 78 “Either” goes with “or,” and “neither” goes with “nor.”

Do not use “neither” with “or.” Neither profit warnings or gloomy unemployment news deterred investors. CORRECT: Neither profit warnings nor gloomy unemployment news deterred investors.

INCORRECT:

Do not use “either” with “nor.” The young scholar did not intend either to contradict his mentor’s theses nor even to question them. CORRECT: The young scholar did not intend either to contradict his mentor’s theses or even to question them.

INCORRECT:

Rule 79 “Not only” is always followed by “but also.”

A common mistake is to follow “not only” with a mere “but.” Do not forget the “also.” Alaska is not only the biggest American state in area, but the smallest in population. CORRECT: Alaska is not only the biggest American state in area, but also the smallest in population.

INCORRECT:

Rule 80 “Different” is normally followed by “from.”

In casual English it is acceptable to say or write “different than” before a clause. But in SWAE it is always “different from.” INCORRECT: CORRECT:

College life is different than most new students expect. College life is different from what most new students expect.

It is true that in Britain one hears and reads “different to,” but in the U.S. it is “different from.” In any case, the phrase “different than” is almost never correct. Remember that “than” is used only with comparatives — words with “more” in front of them or with “-er” attached at the end. “Different than” can be correct only when it is “more different than”: CORRECT:

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She knew serving in the Senate would be different from serving in the House of Representatives, but it turned out to be more different than she expected.

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Rule 81 “Lay” is transitive. “Lie” is intransitive.

Use “lie” when there is no direct object. INCORRECT: CORRECT:

She felt ill and decided to go lay down for a while. She felt ill and decided to go lie down for a while.

What makes “lay” and “lie” so difficult to distinguish is that the word “lay” is also the past tense of “lie.” (Now isn’t that confusing!) The simple past and past participle forms for “lie” are “lay” and “lain.” The simple past and past participle forms for “lay” are “laid” and “laid.” INCORRECT: CORRECT:

He went to the beach and laid in sun all day. He went to the beach and lay in sun all day.

INCORRECT: CORRECT:

He has lain all his cards on the table. He has laid all his cards on the table.

Rule 82 “Raise” is transitive. “Rise” is intransitive.

Use “rise” when there is no direct object. INCORRECT: CORRECT:

If the embargo is not lifted, prices will continue to raise. If the embargo is not lifted, prices will continue to rise.

The past forms for “rise” are “rose” and “risen.” The past forms of “raise” are “raised” and “raised.” INCORRECT: CORRECT:

Because of the embargo, fuel companies have risen prices. Because of the embargo, fuel companies have raised prices.

Rule 83 Use the idiomatic preposition after a verb.

The vast majority of verb + preposition idioms are no problem. A native speaker knows perfectly well not to say “participate to the event” or “approve at the choice.” But even smart native speakers have trouble with a few, including “prefer + to,” “prevent + from,” “prohibit + from,” and “credit + with.” “prefer to” Do not write “prefer over” or “prefer as opposed to.” It is “prefer to.” INCORRECT: CORRECT:

Our customers prefer chocolate over vanilla. Our customers prefer chocolate to vanilla.

“prevent from” You do not “prevent” someone “to do” something. You “prevent” someone “from doing” something. INCORRECT: CORRECT:

The fence was erected to prevent cattle to escape. The fence was erected to prevent cattle from escaping.

“prohibit from” You do not “prohibit” someone “to do” something. You “prohibit” someone “from doing” something. INCORRECT: CORRECT:

A new law prohibits one to use a mobile phone while driving. A new law prohibits one from using a mobile phone while driving.

“credit with” You do not “credit” someone “as having done” something. You “credit” someone “with” something. Schoenberg is credited as having invented the dodecaphonic system of musical composition. CORRECT: Schoenberg is credited with the invention of the dodecaphonic system of musical composition.

INCORRECT:

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Some verbs take different prepositions for different meanings. “differ with” and “differ from” When people disagree, they “differ with” each other. When things are not alike, they “differ from” each other. The son differs from his mother on the merits of movie musicals. CORRECT: The son differs with his mother on the merits of movie musicals.

INCORRECT:

The son differs with his mother in that he is creative and talented. CORRECT: The son differs from his mother in that he is creative and talented.

INCORRECT:

“compare to” and “compare with” To “compare to” is to point out the similarities. To “compare with” is to point out the differences. Shakespeare asked his lover, “Shall I compare thee to a summer’s day?” CORRECT: When we compare this year’s numbers with last year’s, we see that revenues are up and expenses are down. CORRECT:

Do not use “compare to” when the comparison is about differences. INCORRECT: CORRECT:

Attendance is up, compared to last year. Attendance is up, compared with last year.

Rule 84 Use “like” to compare nouns. Use “as” to compare clauses.

In comparisons, “like” is a preposition, and “as” is a conjunction. What follows a preposition is a noun, and what follows a conjunction is a clause with a conjugated verb. As many working parents, Jones usually rises before dawn and retires well after midnight. CORRECT: Like many working parents, Jones usually rises before dawn and retires well after midnight.

INCORRECT:

INCORRECT: CORRECT:

This peach is firm but juicy, like a ripe peach should be. This peach is firm but juicy, as a ripe peach should be.

“As” as a preposition means “in the capacity of.” CORRECT:

As a friend and financial advisor, he recommended selling.

Rule 85 Use “such as” to introduce a list of examples. Do not use

“like.”

There is a difference between “such as” and “like.” If you say you went to a party and saw “people such as Bill Clinton and Madonna,” then Bill Clinton and Madonna were there. But if you say you went to a party and saw “people like Bill Clinton and Madonna,” then Bill Clinton and Madonna were probably not there. You just saw people that were “like” them. Nineteenth-century Russian writers produced great epic novels like “Crime and Punishment” and “War and Peace.” CORRECT: Nineteenth-century Russian writers produced great epic novels such as “Crime and Punishment” and “War and Peace.”

INCORRECT:

Rule 86 The correct expressions are: “with regard to,” “in regard

to,” and “as regards.”

In the expressions “with regard to” and “in regard to,” the word “regard” is

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a noun. In “as regards,” the word “regards” is a verb. In SWAE, “with regards to” and “in regards to” are unidiomatic. The architectural firm has filed several complaints with regards to city zoning laws. CORRECT: The architectural firm has filed several complaints with regard to city zoning laws.

INCORRECT:

All of these expressions are stuffy and wordy. Usually a simple “concerning” or “about” is enough. CORRECT:

The architectural firm has filed several complaints about city zoning laws.

Rule 87 Use “between” with two items. Use “among” with three or

more. The search committee has narrowed it down to a choice between Jefferson, Kilmer, and Nardo. CORRECT: The search committee has narrowed it down to a choice among Jefferson, Kilmer, and Nardo.

INCORRECT:

Rule 88 When referring to an alternative, “whether” is better than

“if.” “If” is common in everyday English, but “whether” is preferred in SWAE. Scholars have been unable to determine if the frescoes were painted by Giotto. CORRECT: Scholars have been unable to determine whether the frescoes were painted by Giotto.

INCORRECT:

Rule 89 Be careful with commonly confused words.

Here are a few sets of words that even smart people sometimes confuse. “affect” and “effect” “Affect” is usually a verb, meaning “influence.” The noun form of that meaning is “effect.” In other words, to “affect” means to “have an effect.” Farmers wonder how the winter drought will effect next summer’s crops. CORRECT: Farmers wonder how the winter drought will affect next summer’s crops. CORRECT: Farmers wonder what effect the winter drought will have on next summer’s crops.

INCORRECT:

As a verb, “effect” means “do” or “cause.” CORRECT:

It is always difficult to effect fundamental change.

As a noun, “affect” means “consciousness of emotion.” Unless you are writing about psychology, you will probably never need to use “affect” as a noun. “alternately” and “alternatively” Use “alternately” to describe an action that switches back and forth. Use “alternatively” when you are suggesting another option. CORRECT: CORRECT:

The weather was unsettled, alternately sunny and rainy. The company could declare bankruptcy. Alternatively, it could restructure, consolidate, and perhaps emerge from this troubled period.

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Do not confuse the words. Because of the scholarship offer, she will probably go Princeton; alternately, she could take out a loan and go Harvard. CORRECT: Because of the scholarship offer, she will probably go Princeton; alternatively, she could take out a loan and to Harvard.

INCORRECT:

to to to go

“appraise” and “apprise” “Appraise” means “estimate, judge the value of.” “Apprise” means “inform.” Before deciding whether to move, they had their house appraised. CORRECT: This notice is to apprise our faithful customers of a change in opening hours. CORRECT:

Do not confuse the words. He asked his friend to keep him appraised of any further developments. CORRECT: He asked his friend to keep him apprised of any further developments.

INCORRECT:

“assure,” “ensure,” and “insure” “Assure” means “promise.” CORRECT:

The clerk assured her that the manager would see her shortly.

“Ensure” means “make certain.” CORRECT:

Proper planning will ensure success.

“Insure” means “guarantee legally or financially.” CORRECT:

Our firm is insured against theft.

“continually” and “continuously” Something that happens repeatedly can be said to happen “continually.” Something that happens without interruption can be said to happen “continuously.” CORRECT: CORRECT:

Reporters continually ask questions about private matters. The factory never closes because the furnaces must burn continuously.

Do not confuse the words. INCORRECT: CORRECT:

It snowed continually for 24 hours. It snowed continuously for 24 hours.

“discreet” and “discrete” These are two different words. They are pronounced the same but have distinct meanings. “Discreet” means “prudent.” CORRECT:

The officer observed the suspect from a discreet distance.

“Discrete” means “separate, distinct.” CORRECT:

The manager broke the project down into discrete tasks.

“farther” and “further” “Farther” refers to a greater distance. “Further” refers to a continuation. CORRECT: CORRECT:

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“imply” and “infer” To “imply” is to suggest; to “infer” is to read into. The speaker or writer implies. The listener or reader infers. She did not say so directly, but she implied that she would be available to help. CORRECT: The reader can infer from the passage that Raphael and Michelangelo were contemporaries. CORRECT:

Do not use “infer” when you mean “imply.” Although he does not say so explicitly, the writer of this editorial infers that capital punishment ought to be abolished. CORRECT: Although he does not say so explicitly, the writer of this editorial implies that capital punishment ought to be abolished.

INCORRECT:

“incredible” and “incredulous” “Incredible” means “unbelievable.” “Incredulous” means “unbelieving, skeptical.” CORRECT:

After he told an incredible story about having been abducted by aliens, his listeners were incredulous.

In formal writing, do not use “incredible” to mean “excellent.” INCORRECT: CORRECT:

All were sated after the incredible meal. All were sated after the excellent meal.

A story or a fact can never be “incredulous.” Only people can be “incredulous.” INCORRECT: CORRECT:

The film is said to be based on fact, but I found it incredulous. The film is said to be based on fact, but I found it incredible.

Rule 90 Be careful with commonly misused words.

“anticipate” To “anticipate” is to “act in advance of, prepare for.” CORRECT:

Residents anticipated potentially damaging winds by boarding up windows.

Do not use “anticipate” to mean “expect.” INCORRECT: CORRECT:

We do not anticipate any further delays. We do not expect any further delays.

“anxious” To be “anxious” is to be “worried.” CORRECT:

The patient was anxious about the results of the blood test.

Do not use “anxious” to mean “eager, excited.” After waiting months for approval, the team was anxious to get started. CORRECT: After waiting months for approval, the team was eager to get started.

INCORRECT:

“could care less” For some reason the trite expression “couldn’t care less” is often shortened to the illogical “could care less.” More apathetic than ever, voters could care less who wins the election. CORRECT: More apathetic than ever, voters could not care less who wins the election.

INCORRECT:

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You can get away with the expression in speech, but do not write “could care less” unless that is really what you mean. CORRECT:

I do not care enormously about the Academy Awards, but I could care less.

“due to” Use “due to” only after the verb “be.” CORRECT:

This morning’s departure delays are due to inclement weather.

Do not use “due to” at the beginning of a sentence or anywhere else to mean “because of.” Due to circumstances beyond our control, the event has been canceled. CORRECT: Because of circumstances beyond our control, the event has been canceled.

INCORRECT:

“epitome” The “epitome” of something is the most ordinary, typical example. CORRECT:

The epitome of the suburban commuter, he spends four hours a day in heavy traffic.

It is a common mistake to use “epitome” to mean “extreme example.” He is the epitome of a baseball fan: nobody knows more about the game than he. CORRECT: He is the extreme example of a baseball fan: nobody knows more about the game than he.

INCORRECT:

“ironic” An event that is the opposite of what one would expect is “ironic.” CORRECT:

It is ironic that such a sinner would become such an accomplished religious painter.

Do not use “ironic” to mean “a curious coincidence.” It is ironic that Verdi and Wagner, the antipodes of nineteenthcentury opera composers, were born in the same year. CORRECT: It is a curious coincidence that Verdi and Wagner, the antipodes of nineteenth-century opera composers, were born in the same year.

INCORRECT:

“literally” Taken literally, “literally” means “actually,” or “exactly as the words say.” CORRECT:

He took the boss’s advice literally and jumped in a lake.

Do not use “literally” in a weak attempt at emphasis. In particular, do not use “literally” when you really mean “figuratively.” The best solution is usually just to delete it. Congressional leaders literally held a gun to the President’s head. CORRECT: Congressional leaders [...] held a gun to the President’s head.

INCORRECT:

“peruse” Contrary to popular usage, “peruse” means “read thoroughly.” Do not use “peruse” to mean “glance over, skim, read superficially.” The department head did not have time to read the report thoroughly, so she just perused it. CORRECT: The department head did not have time to peruse the report, so she just skimmed it.

INCORRECT:

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EXERCISE 9 (IDIOMS) Directions: Rewrite the following sentences to correct any idiom errors. (Note that some sentences may be correct as written.)

1. There were something between twenty to thirty thousand people in attendance.

2. The candidate is not inclined either to debate his opponent face to face nor even to respond to questions about the accusations.

3. Fletcher is not only the youngest member of the team, but, with three university degrees, he is the most educated.

4. The world is a totally different place now than it was before the advent of the personal computer.

5. The children were anxious to start eating, but they knew they had to wait until everyone was served.

6. The director of human resources uses quaint Southern colloquialisms like “fixin’ to.”

7. Just like a child does, he uses his finger to point at the words as he reads them.

8. Her elocution coach taught her to pronounce her r’s like they are pronounced in Britain.

9. The experience of war in the trenches had a profound affect on the young English poets.

10. The jury must first decide if the defendant is telling the truth.

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10. STYLE Rule 91 Avoid redundancy.

It is bad form to repeat ideas unnecessarily. We are ready for any unforeseen event that may or may not occur. CORRECT: We are ready for any unforeseen event [...].

INCORRECT:

Some common examples of redundancy are simply forbidden in SWAE. Editors and essay graders shriek at the sight of the following notorious bugbears: reason is because equally as reason why hardly never return back each and every repeat again in any way, shape, or form The reason the business failed was because of mismanagement. CORRECT: The business failed because of mismanagement

INCORRECT:

Here are some more examples of redundancies to be avoided: advance planning consensus of opinion safe haven blue-colored

five in number PIN number ATM machine GMAT test

Rule 92 Omit unnecessary words.

Avoid wordiness. If you can delete a word or series of words without changing or obscuring the meaning, do so. Do not, for example, write “considered as” or “considered to be” when “considered” will do. INCORRECT: CORRECT:

He is considered to be a leading expert on Etruscan art. He is considered [...] a leading expert on Etruscan art.

And why write “whether or not” when “whether” means the same thing? INCORRECT: CORRECT:

The committee will decide whether or not to call witnesses. The committee will decide whether [...] to call witnesses.

Avoid flabby expressions. as of yet at this point in time due to the fact that in spite of the fact that of a ____ nature in a _____ manner In spite of the fact that the director is more than eighty years of age, the film which he recently directed can been said to be fresh as well as fast, and it is funny also. CORRECT: Although the director is more than eighty years old, his film is fresh, fast, and funny.

INCORRECT:

Rule 93 Do not omit necessary words.

Economy is a virtue in SWAE. You want to use as few words as possible to express your meaning. If a word is unnecessary — if the sentence has the same meaning without it — delete it. But do not omit words that are grammatically or logically necessary.

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INCORRECT: CORRECT: BETTER: INCORRECT: CORRECT:

This year’s event should be as big if not bigger than last year’s. This year’s event should be as big as, if not bigger than, last year’s. This year’s event should be at least as big as last year’s. This team has not yet and never will surrender. This team has not yet surrendered and never will surrender.

Rule 94 Avoid slang and colloquialisms.

You probably know better than to write something like “he ain’t got none” or “That kid is awesome.” Slang obviously has no place in SWAE. The dividing line between formal and casual is a fuzzy one. The following words are usually too casual for SWAE: pretty (as in “a pretty tough question”) real (as in “a real important job”) awful or awfully

a lot nice stupid

INCORRECT: CORRECT:

Ten thousand dollars is an awful lot of money. Ten thousand dollars is a great deal of money.

INCORRECT:

This company is a pretty nice place to work. This company is a rather pleasant place to work.

CORRECT:

Rule 95 Be careful with jargon and trendy expressions.

Conservative editors and English teachers despise fashionable businessspeak. They cringe at words like “prioritize,” “proactive,” and “outsource.” But these words are so widely used and understood that they have to be accepted now. Use one of these words if it expresses your meaning precisely and unambiguously, but be aware that some old-fashioned readers may object. As always, consider your audience. But a line has to be drawn somewhere. The following examples cross that line and are unacceptable. The job was in-sourced because we had all the people we needed. CORRECT: We did the job in house because we had all the people we needed.

INCORRECT:

Because of budget cuts, the department had to dehire several employees. CORRECT: Because of budget cuts, the department had to lay off several employees.

INCORRECT:

Conservatives particularly dislike the wanton use of nouns as verbs. INCORRECT: CORRECT:

We want to know how a tax cut would impact the economy. We want to know what impact a tax cut would have on the economy.

Rule 96 Prefer the active to the passive.

A passive sentence construction is one that turns an object into a subject. “John ate the cake” is active. “The cake was eaten by John” is passive. Sometimes the passive construction is appropriate, particularly when the true subject is unknown. CORRECT:

Twelve paintings were stolen.

But when the true subject is known, it is usually better to make it the grammatical subject as well. INCORRECT:

One thousand likely voters were interviewed by the pollsters.

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CORRECT:

The pollsters interviewed one thousand likely voters.

Do not write “able to be.” INCORRECT: CORRECT:

This problem is not able to be solved. This problem cannot be solved.

Rule 97 Avoid weak intensifiers.

Writers often use words such as “very” or “really” in a vain effort to render their writing more forceful or profound. Be sparing with “very.” And watch out for “really,” “incredibly,” “totally,” and “absolutely.” These feeble attempts to make bolster your words can sometimes lead to nonsense. INCORRECT: CORRECT:

The story was incredibly believable. The story was [...] realistic.

Rule 98 Opt for the specific over the vague.

When you are tempted to use a vague word such as “interesting” or “important,” consider whether there is a more specific word to use instead. WEAK: STRONG:

That was a very interesting play. That was a thought-provoking play

Look at the following sentence from a White House aide’s testimony at a Congressional hearing. WEAK:

I was provided with additional input that was radically different from the truth. I assisted in furthering that version.

This speaker uses vague expressions intentionally. He wants to soften (if not obscure) the truth, which is simply: “They lied, and I helped.” Rule 99 Avoid illogical and meaningless sentences.

Here are several gems of illogical and meaningless nonsense that have been attributed to various U.S. politicians: NONSENSE: NONSENSE: NONSENSE: NONSENSE:

If we don’t succeed, we run the risk of failure. When people are out of work, unemployment results. More and more of our imports come from overseas. It isn’t pollution that’s harming the environment; it’s the impurities in our air and the water that are doing it.

Rule 100 Avoid awkwardness.

Awkwardness is an ill-defined and subjective criticism. There are no hardand-fast rules for recognizing and eliminating awkwardness. But there is no doubt that some sentences are awkward and need to be rewritten. Apart from the master bedroom, which has its own, all the other bedrooms share a bathroom. CORRECT: The master bedroom has its own bathroom; all the other bedrooms share a bathroom.

INCORRECT:

Writers sometimes find themselves in quagmires of awkwardness in efforts to avoid sexism. “He or she” and “his and her” may be politically correct, but they are awkward. Try to rewrite the sentence in the gender-neutral plural if you can. If a student wishes to change his or her area of concentration, he or she must obtain written permission from his or her academic advisor. CORRECT: Students who wish to change areas of concentration must obtain written permission from their academic advisors.

INCORRECT:

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EXERCISE 10 Directions: Rewrite the following sentences to correct any style errors. (Note that some sentences may be correct as written.)

1. Our nation must come together to unite.

2. When he goes to his country house for the weekend, he hardly never returns back before Monday afternoon.

3. Due to the fact that it sold more than a million copies, the book was considered to be a success.

4. The experiences are not able to be compared.

5. He says that he has not, does not, and never will eat broccoli.

6. According to her itinerary, the consultant will airplane it to New York and from there train it to Boston.

7. Pricewise the possible new office is a bargain, but locationwise it is a gamble.

8. The 1969 World Series will never be forgotten by the old baseball fan.

9. The judges, who were five in number, could not reach a consensus of opinion on a winner.

10. The employee complained that the supervisor disrespected him.

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ANSWERS TO EXERCISES EXERCISE 1 (SENTENCE STRUCTURE)

EXERCISE 3 (NOUN NUMBER)

1. The secretary arrived too late. The meeting had already begun. 2. The dangers of secondhand smoke have been exaggerated; therefore, the government should consider repealing some of the more restrictive antismoking laws. 3. The reasons for the price adjustment are increasing costs and decreasing demand. 4. English is not the most widely spoken language in the world; nevertheless, it is the most practical language for international business. 5. No error. 6. Ask the librarian. He will know. 7. No error 8. Because it has not rained in two months — the worst drought on record, reservoir levels are dangerously low. 9. Call Novak. He is the only one who can help us now. 10. No error.

1. Anyone requiring additional information should consult the company's website. 2. The United Nations has been debating a human rights resolution. 3. No error. 4. A solar eclipse is a phenomenon that is worth a journey to witness. 5. The public is opposed to the proposed legislation. 6. This year’s promotional event attracted fewer people than last year’s did. 7. On Sundays, when admission is free, the number of people at the museum is astonishing. 8. Everyone sang well and was heartily applauded. 9. For the first time there were fewer species on the endangered list than in the previous year. 10. No error.

EXERCISE 4 (VERB TENSE) 1. No error.

EXERCISE 2 (SUBJECT-VERB AGREEMENT) 1. The only thing he values more than his career is his wife and children. 2. The majority of the people of California support recycling. 3. In the last ten years, the number of professional sports teams has doubled. 4. No error. 5. No error. 6. Not in several days has the mother or the children been seen. 7. No error. 8. No less astonishing than the dimensions of the surviving examples is their variety. 9. On the ground floor of the office building are a newsstand, a coffee shop, and a restaurant. 10. Never before in the history of the state have Montana’s vote-counting procedures received more attention.

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2. No error. 3. If the team had started the project a month earlier, they would be finished by now. 4. If Americans ate less red meat, they would have lower cholesterol levels. 5. Financial experts recommend that one diversify one’s investments. 6. He resents the suggestion that he rewrite the paper. 7. No error. 8. The lecturer began with a quick plot synopsis for the benefit of those who had not read the novel. 9. The civilization is believed to have flourished in the fifteenth century. 10. Once the student passes the comprehensive oral examination, she will have satisfied all the requirements for the degree.

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EXERCISE 5 (PRONOUNS)

EXERCISE 7 (COMPARISONS)

1. No error. 2. No one will buy such an expensive product unless he or she really needs it. 3. The directors are looking for someone whom they can trust to abide by the rule. 4. When one considers the candidate’s youth and inexperience, one has to say that the victory was unexpected. 5. If the television viewer loses interest for just a few seconds, he or she will switch channels. 6. It is sunny and hot today, but forecasters say it will rain tomorrow. 7. If one invests early and wisely, one will be able to enjoy one’s retirement. 8. Because the parties have been unable to resolve the dispute, a judge will have to do so. 9. After questioning the two suspects, the investigator became convinced that it was they who committed the crime. 10. No error.

1. Americans eat more corn than Europeans do. 2. The second of the author’s two published works sold better. 3. The critic maintained that it was the worst film she ever saw. 4. Unlike Los Angelenos, most New Yorkers use public transportation. 5. Every year, more foreign tourists visit Paris than any other European city. 6. The United States is the richest and most wasteful country in the world. 7. No error. 8. His job title is director of marketing, but his salary is still less than that of a secretary. 9. Abraham Lincoln was perhaps one of the wisest men ever to serve as President. 10. Choose either regular or express service: the former is less expensive and the latter is faster.

EXERCISE 8 (PARALLELISM) EXERCISE 6 (MODIFIERS) 1. Driving soon became his favorite pastime. 2. With makeup and perfume, she tries to attract men. 3. Born and raised near the Mexican border, she easily picked up Spanish. 4. On the facade there is a sculpture that represents the rise of technology. 5. He hired a crew that has a truck and that is accustomed to handling delicate antiques. 6. Deciding to get the story at any cost, the reporter could not be stopped. 7. The family devoured the whole pie, straight out of the oven and still piping hot. 8. Even after receiving explicit instructions, the new employee did not know what to do. 9. The supervisor ordered the assistant, dressed in a Tshirt and jeans, to go home and change into more professional attire. 10. Because they are no longer sworn enemies, relations between the United States and Russia have improved considerably since the end of the Cold War.

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1. To be a celebrity means to have no privacy. 2. The meeting is scheduled not for today but for tomorrow. 3. The dieter resolved to eat neither too much nor too little. 4. He is responsible for not only the design, but also the execution. 5. The turning point in the plot is the disappearance of the protagonist. 6. A teacher’s job is to inspire creativity as well as to impart knowledge. 7. The artist is neither naturally talented nor independently wealthy. 8. The two biggest events in his life were his marriage and the birth of his first child. 9. By the time Baldwin arrived to help, his colleagues had already laid out the site, cleared the land, and begun to excavate. 10. The changeover to the metric system did not succeed because people could not become accustomed to using meters instead of feet, grams instead of ounces, or liters instead of quarts.

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EXERCISE 9 (IDIOMS) 1. There were something between twenty and thirty thousand people in attendance. 2. The candidate is not inclined either to debate his opponent face to face or even to respond to questions about the accusations. 3. Fletcher is not only the youngest member of the team, but, with three university degrees, he is also the most educated. 4. The world is a totally different place now from what it was before the advent of the personal computer. 5. The children were eager to start eating, but they knew they had to wait until everyone was served. 6. The director of human resources uses quaint Southern colloquialisms such as “fixin’ to.” 7. Just like a child, he uses his finger to point at the words as he reads them. 8. Her elocution coach taught her to pronounce her r’s as they are pronounced in Britain. 9. The experience of war in the trenches had a profound effect on the young English poets. 10. The jury must first decide whether the defendant is telling the truth.

EXERCISE 10 (STYLE) 1. Our nation must come together. 2. When he goes to his country house for the weekend, he hardly ever returns before Monday afternoon. 3. Because it sold more than a million copies, the book was considered a success. 4. The experiences cannot be compared. 5. He says that he has not eaten, does not eat, and never will eat broccoli. 6. According to her itinerary, the consultant will fly to New York and from there go by train to Boston. 7. The price of the possible new office is a bargain, but the location is a gamble. 8. The old baseball fan will never forget the 1969 World Series. 9. The five judges could not reach a consensus on a winner. 10. The employee complained that the supervisor showed him disrespect.

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HOMEWORK/PRACTICE TEST GRAMMAR REVIEW ANSWER GRID B !

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Grammar Review – Homework

Directions: In the following questions, each sentence has four underlined words or phrases. The four underlined parts of the sentence are marked (A), (B), (C), and (D). Identify the one underlined word or phrase that must be changed in order for the sentence to be correct.

Directions

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Grammar Review

1. The Organization of American States, stretching A from the North Pole to the Southern tip of Patagonia and including virtually every nation in B the Western Hemisphere, display a surprising ability C to confront important issues facing the Americas. D

2. Dorothy, in addition to Jill and Craig, who also A ran for office in the State Senate, were defeated in B C D the primaries.

3. The Federal Government recently judged that

6. Because of the severe hailstorms and the repeated A B flash floods that have struck the area, the police C demand that everyone should stay indoors. D

7. Although he was always an excellent student, he A B did not deserve getting the highest grade on the C D biology exam.

8. Joe explained that if he arrives on time, and A B everything goes according to plan, he wants to C go to the movies. D

many than 10,000 Eskimos is sufficient to sustain A B C D their ancient culture and traditions.

4. After finishing the grueling, six-hour ironman race, A Hercules was so thirsty that he ran up to the first B C unsuspecting soul - who happened to be Apollo - to ask for a water. D

5. On the Amazon river, although one must beware of A B the man-eating piranha, you can safely travel C from beginning to end in under one month. D

9. The Acme Car Rental Company became worldA famous thanks to its slogan: "Our cars break B C down less than do our competitors!” D

10. Joe asked his attorney for just two things on the A B eve of his 10- year sentence: a last meal of roast C duck and to call his beloved mother. D

11. The police searched for the infamous Mr. McGoo A B in his office, the grocery store, and in his car, C D before giving up the futile petty larceny investigation.

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12. The second product built by Henry Ford's A company, the Model "A" was modeled from its B C predecessor, the simplistic Model "T." D

13. While walking to Scarborough Fair, Osirus came A across a woman who asked him if it was necessary B C that he should go in that direction. D

14. Scientists have determined that fewer of the small A number of not many tree frogs found in the B C Brazilian rainforest are alive today than ever. D

15. Neil Armstrong, who was the first human being to A set foot on the Moon, was waIking only fifteen B C steps in the difficult lunar environment. D

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GRAMMAR REVIEW HOMEWORK/PRACTICE TEST ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

C C A D C D C C D D C C D B C

EXPLANATIONS FOR GRAMMAR REVIEW HOMEWORK/PRACTICE TEST 1. (C) Subject/verb agreement error The subject is ”The Organization,” a singular collective noun which takes the plural verb, ”displays” instead of ”display.” 2. (C) Subject/verb agreement error The main subject is ”Dorothy,” which is singular and therefore requires the singular verb, ”was” instead of ”were.” 3. (A) Noun number error The correct expression for this noun number error is ”more than”; ”many than” is not a correct expression of a countable quantity in English. 4. (D) Noun number error The non-count noun ”water” cannot take the indefinite article ”a,” it must take the indefinite term ”some” instead. 5. (C) Pronoun error Since the possessive pronoun ”one” is used in the beginning of the sentence, ”one must beware,” then it must be matched by ”one can safely ...” in the latter part of the sentence. 6. (D) Verb tense error After ”demand that,” you need the subjunctive. Do not use the modal ”should” with the subjunctive. 7. (C) Verb tense error Infinitive form is needed here. The gerund ”getting” must be changed to the infinitive form ”to get.” 8. (C) Conditional error In a conditional construction with the present tense in the ”if” clause, you should use the future tense in the following clause: ”he will want to go to the movies.” 9. (D) Comparison error The two terms of comparison here, cars and competitors are not of the same type. To draw a correct comparison, ”our competitors,” must be changed to ”our competitors' cars.”

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10. (D) Parallelism error All the items in a parallel list must be of the same form: ”and to call ...” must be changed to ”and a call to” in order to agree with the form of the first item in the list, ”a last meal.” 11. (C) Parallelism error All the items in a parallel list must be in the same form: ”the grocery store” is not in the same forrn as the other two items in the list, ”in his office” and ”in his car,” and would need to be changed or eliminated to make this sentence correct. 12. (C) Idiom error The correct idiomatic phrasal verb in this sentence should be ”modeled after” instead of ”modeled from.” 13. (D) Conditional error After ”it was necessary that,” you need the subjunctive. Do not use the modal ”should” with the subjunctive. 14. (B) Redundancy error Since ”a small number” and ”not many” have roughly the same meaning, then to correct the redundancy in this sentence, one of them must go. Eliminate ”not many” to make this sentence correct. 15. (C) Verb tense error For an action performed in the past and completed, use the simple past tense. Change ”was walking” to ”walked” to make this sentence correct.

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Step 8 Grammar Workshop

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Step 8 Workshop

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Grammar Review – Workshop

Directions: In the following questions, each sentence has four underlined words or phrases. The four underlined parts of the sentence are marked (A), (B), (C), and (D). Identify the one underlined word or phrase that must be changed in order for the sentence to be correct.

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Grammar Review

GMAT GRAMMAR WORKSHOP TEST ONE: 1. The amount of people in the school district A who signed up for Mr. Evergreen’s beginning swim B class corresponded to the Olympic boogie C boarding team that made it all the way to the D semi-finals last year.

2. The much aquatic resources recently discovered on A B C the Moon have been the subject of much debate. D

3. The new law in London, surely passing in the rest A of England, dictates that it is illegal to obstruct foot B traffic on train platforms with public displays of C D affection.

4. John asked me if I had heard the news today and, A B as I knew that he was working on a thesis on C reactions to the popular media, I told him that I have. D

5. When living abroad and are looking for work, A there is often a discrepancy between one’s abilities B C and the kind of job one must accept due to D competition and a reluctance to hire foreigners;

6. Thinking she has not completed her forms on time, A Karen is always concerned at the end of April when B tax are due although she doesn’t make C nearly enough money for the Internal Revenue D Service to waste time to prosecute her if she does happen to file late.

7. Blake and Lori decided to start a band, as they both A felt the desire to play instruments and express their creativity through music, but they B couldn’t see how them would find a bass player C whom they could rely on. D

8. Eddie, who is always late to work despite using five A alarm clocks, realized that instead of taking the bus every day and spending thirty minutes waiting for it B C to arrive, he decided to get his driver’s license and D buy a car.

9. Since I never take sugar in my coffee, a habit I A have maintained since I was 20, I don’t think that B when I will go to Greece and am offered strong C tea I will be tempted to sweeten the drink. D

this is commonly referred to as the “immigrant’s compromise”.

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10. The operation, although newer and more A experimental than it of traditional techniques, to B remove the tumor from the philosopher’s head was unsuccessful and no more useful than the C radiation which caused his hair to fall out. D

11. Fabrice,

like Mark, is full of spirit and A B energized with hope, both of which he learned C from his older brother, and he is motivated to D complete each task well, a quality he inherited from his mother.

12. Doing well in college requires study, dedication, A and knowing how to create meaningB ful relationships with professors; doing poorly in college is often the result of too much partying, not enough concentration, and lacking sleep. C D

13. Justine, who studied art history for ten years, is an A B expert on Medieval painting, Renaissance drawing, sculptures of the Pre-Raphaelite, and C period identification. D

14. My new neighbor, who reminds me of James, an old English friend living in Los Angeles, has a kind heart, a patient ear, and an easy laugh very A B similar as those of James. C D

15. Composed by tequila, coconut milk, and pineA apple juice, the Pina Colada is very popular in B C places near Mexico, particularly in Southern California where the sun shines most of the time. D

16. Violet was ashamed with her parents when she A B was growing up, but after she met her boyfriend’s C parents she changed her mind. D

17. The costume director of the Marseilles Opera insisted, after seeing the scraps of cloth left over A from the last show’s needlework, that every actor B and actress should collect and donate the extra C pieces of fabric to the local charity. D

18. While it is likely that Mr. Schrempf might be the A B culprit, the detectives have had a difficult time finding conclusive evidence against him. C D

STOP IF YOU FINISH BEFORE TIME IS EXPIRED YOU MAY CHECK YOUR WORK 260

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Grammar Review

GMAT GRAMMAR WORKSHOP TEST TWO: 1. The

Michaelsons,

after

visiting their sick A grandmother in Iowa City, intends to travel to Italy B because their son Edward has a master’s degree in C Italian and wishes to continue his studies in D Florence.

2. Is she really considering to go to Europe after she A B C graduates instead of inheriting her father’s business D and carrying on the family name?

3. Even though the man knew that he would A probably not win a significant sum of money, he B bought him a lottery ticket in the hope that just C once he would be able to call himself a winner. D

4. All the women including the child was considered A B part of the demonstration which shook the C foundation of Bender Hall and created a precedent for all future demonstrations against war. D 5. When Virginia looked at the study on environmental A problems in the Russian sector, she learned that B there wasn’t many information to be collected from C D the old documents and asked her assistant to begin

6. Frequent travelers have learned that it is A easier and faster to board a commercial airplane if B they carry no more than two luggages. C D

7. The many Indian owners of motel chains in the A B United States expect to borrow from and only do C business to each other. D

8. The history of Latin America is slowly gaining importance in North American schools A evident in their curricula, which are now C books and art by Latin American D and writers.

like is B full of artists

9. The agency who created the marketing campaign A B for Nike products is, despite its success, still located in Portland, Oregon, the city where C D it began.

10. Unless Anne will put in the time to research her A B C science project independently, her teacher will never give her the grade she needs for her parents to give her permission to go to the dance. D

a new analysis.

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11. Eddie and Susan will walk forever tonight should A they not to find a warm dry place to put the new B baby; even a tree with thick branches would suffice for shelter from the driving rain. C D

12. The volume of a cube is determined by its length, A B wide, and height multiplied together. C D

16. Plato’s theories of justice, the forms, and his A B theories of the political structure of the state are B C still studied today while some ideas of more D modern thinkers have already been forgotten.

17. Kirsten, who is charming, intelligent, and openA minded is so different to Mary, who is constantly B C depressed, perpetually tired, and never willing to D go out and have a good time.

13. Jennifer’s dress, which has lace trim and a thick A black bodice, has more style than Emily’s: the B C two girls constantly compete for the title of D “Fairest at the Ball”.

14. By many numerous critics, Glenn Gould was A considered to be the most enigmatic concert B pianist of the twentieth century. C D

15. Neutrinos they are so unpredictable that A physicists have difficulty measuring their precise B C D mass.

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Grammar Review

GRAMMAR WORKSHOP TEST ONE ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

A A A D A C C D C B D D C C A A C B

EXPLANATIONS TEST ONE

FOR

GRAMMAR WORKSHOP

1. (A) noun number error Since “people” is a count noun it must take the phrase “number of” instead of “amount of,” which is used to modify only noncount nouns. 2. (A) noun number error The count noun “resources” must take the modifying phrase “many” instead of “much,” which is used to modify only noncount nouns. 3. (A) style error Change “surely passing” (passive) to “sure to pass” (active) to correct this sentence. 4. (D) verb tense error Part (B) correctly uses the past perfect — the speaker’s hearing took place before John’s asking. Part (D) should also use the past perfect. Change “have” to “had” to correct the sentence. 5. (A) parallelism error All of the parts in a list must be of the same grammatical type or be expressed in the same form: to make the correction here, change “are looking” to “looking” to match the form of the first item in the list, “living abroad.” 6. (C) subject/verb agreement error The singular subject here, “tax,” must be changed to the plural, “taxes,” to agree with the conjugated plural verb “are” in order to correct this sentence. 7. (C) pronoun error Change the object pronoun “them” to the subject pronoun “they” to make the correction in this sentence. 8. (D) pronoun error It is redundant and ungrammatical to include the subject pronoun ”he” when the sentence has already a subject “Eddie.”

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9. (C) verb tense error Only the present and past tenses are used after the connector word “when,” never the future tense. Since the future tense is used here, “when I will go,” replace “will go” with the present tense “go” to make this sentence correct. 10. (B) comparison error To correctly state a comparison here change the invalid form “than it of” to the valid comparison phrase “than that of”: “newer...than that of...”

Step 8 Workshop

17. (C) redundancy error After “insisited,” use the subjunctive, which is simply “collect.” It is redundant and ungrammatical to include the modal “should.” 18. (B) redundancy error Since “it is likely” and “might be” express the same idea, one of them is unnecessary: to make the correction in this sentence change “might be” to “is.”

11. (D) parallelism error All the parts in a list must be of the same grammatical type or be expressed in the same form: to make the correction here eliminate “he” from “he is motivated” to match the form of the first item in the list, “is full of spirit and energized with hope.” 12. (D) parallelism error All the parts in a list must be of the same grammatical type or be expressed in the same form: to make the correction here change “lacking sleep” to “lack of sleep” to match the form of the previous items in the list. 13. (C) parallelism error All the parts in a list must be of the same grammatical type or be expressed in the same form: to make the correction here change “sculptures of the Pre-Raphaelite” to “Pre-Raphaelite sculptures” to match the form of the previous items in the list. 14. (C) idiom error To make the correction in this sentence change “similar as” to the proper idiom of comparison “similar to.” 15. (A) idiom error To make the correction in this sentence change “Composed by” to the proper prepositional idiom “Composed of.” 16. (A) idiom error To make the correction in this sentence change “ashamed with” to the proper prepositional idiom “ashamed of.”

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Grammar Review

GRAMMAR WORKSHOP TEST TWO ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

B C C B C D D B A B B C C A A B B

EXPLANATIONS TEST TWO

FOR

GRAMMAR WORKSHOP

1. (B) subject/verb agreement error Since the subject, “The Michaelsons,” is plural, the conjugated verb which corresponds to it must also be plural: to make the correction in this sentence change the singular verb “intends” to the plural verb “intend.” 2. (C) verb tense error When the verb “consider” takes a verb as an object, it always takes the gerund, or -ing form of that verb: to make the correction in this sentence change the infinitive “to go” to the gerund “going.” 3. (C) pronoun error The personal pronoun “him” in answer choice (C) is unnecessary: to make the correction in this sentence eliminate “him” from “him a lottery ticket.” 4. (B) subject/verb agreement error Since the third-person subject “...the women” is plural, the conjugated verb which corresponds to it must also be plural: to make the correction in this sentence change the singular verb “was” to the plural verb “were.” 5. (C) noun number error Since “information” is a noncount noun in English, it must be modified by the quantity word “much” instead of “many,” which is used only for count nouns. 6. (D) noun number error In order to specify one or more individual items with a noncount noun such as “luggage,” the appropriate form of the expression “a piece of” can be used: to make the correction in this sentence change “two luggages” to “two pieces of luggage.” 7. (D) idiom error To make the correction in this sentence change “do business to each other” to the proper reciprocal idiom “do business with each other.” 8. (B) comparison error To correctly state the comparison here between two verb clauses change the invalid “like” to “as.”

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9. (A) pronoun error The pronoun “who” is only used to refer to people, not things such as an advertising agency: to make the correction here change “who” to “which.” 10. (B) verb tense error The correct verb tense here after the time signature “Unless” should be the present not the future tense: to make the correction in this sentence change “will put” to “puts.” 11. (B) verb tense error Use the dictionary form after the modal “should.” To correct the sentence, change “to find” to “find.” 12. (C) parallelism error All the parts in a list must be of the same grammatical type or be expressed in the same form: to make the correction in this sentence change “wide” to “width.” 13. (C) comparison error To make a valid comparison between nouns such as “Jennifer’s dress” and “Emily’s dress,” a verb must be used after the comparison word “than”: to make the correction here change “than Emily’s” to “than does Emily’s.” 14. (A) redundancy error Since “many” is similar in meaning to “numerous” it is unnecessary and awkward in this sentence: to make the correction, eliminate “many.” 15. (A) redundancy error The pronoun “they” is unnecessary here since the subject “Neutrinos” is placed next to the verb clause “are so”: to make the correction in this sentence eliminate “they.” 16. (B) parallelism error All the parts in a list must be of the same grammatical type or be expressed in the same form: to make the correction in this sentence change “and his theories” to “theories.” 17. (B) idiom error To make the correction in this sentence change “so different to” to the proper idiom “so different from.”

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Step 9 Sentence Correction

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Step 9.1 Lesson

GENERAL OUTLINE

The objective of Sentence Correction questions is to test the rules of English grammar and usage. The rules required to master these kinds of questions seem intimidating, especially for non-native English speakers. What makes the problem more complicated is that, unlike in the Quantitative section, GMAC does not predetermine the content for these questions. Fortunately, the number of grammar and usage rules for English tested on the GMAT is reasonably limited, and you are never required to correct punctuation or spelling. The lesson which follows will discuss Sentence Correction question types in detail and give you specific strategies for answering each one of them.

THE

FOLLOWING TOPICS WILL BE COVERED IN THIS LESSON:

The Most Common Testing Points for Sentence Correction Learning to Spot and Eliminate Wrong Answers A Systematic Approach to Sentence Correction Questions A Review of the Top 10 Mistakes in Sentence Correction

KEY

TERMS

Statement: This is the original sentence located above the five answer choices. It is either completely or partially underlined. Answer choices: The five choices lettered (A) through (E) located below the numbered sentence. They often appear in patterns such as the “3-2” and the “2-2-1,” which are explained later in this lesson. Same Error Answers: Answer choices that contain the same error as that in the original sentence and change something else in the sentence to tempt those who don’t identify the original mistake. There is rarely a set of answer choices without at least one of these. Almost Right Answers: Answer choices that correct the error in the original sentence but introduce new errors elsewhere. There is rarely a set of answer choices without at least two of these. The Best Answer: The answer choice that is not only error-free, but is also stylistically preferable. This is the one true answer to the question. There is never a set of answer choices without one of these.

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Sentence Correction

READY… The Sentence Correction questions appear in the Verbal Section of the GMAT and are the only grammar-based questions on the test. The Verbal Section includes about 14 Sentence Correction questions mixed randomly with Critical Reasoning and Reading Comprehension questions. Since it is impossible for Reading Comprehension questions to appear at the beginning of the section, it is very likely that among the first five questions you will find between two and three Sentence Correction questions of medium difficulty. As previously discussed, the first five questions are especially important in determining your final score for the section. It is therefore very important that you answer these early Sentence Correction questions correctly because they will have a disproportionately large impact on your final Verbal score. Although there are literally hundreds of grammatical rules governing sentence structure and form in American English, you should not be intimidated by Sentence Correction questions. The GMAT tests your ability to recognize only a very limited number of common grammatical and stylistic errors. In this lesson we will show you how to quickly identify and repair those errors and zero in on the best answer choice.

DIRECTIONS On the CAT, you can click on the HELP button, and the directions for the current question type will appear on the screen. Since you will need every available minute to work on the questions, it is important that you become familiar with the directions now so you will not waste time reading them on test day. Below are the directions for the Sentence Correction questions. Learn them now. They are always the same. GMAT CAT – Section 4 : Verbal End

When finished reading directions click on the icon below

Directions: For each question below, part or all of the sentence is underlined. Following the sentences are five versions of the underlined part. The first version repeats the original; the other responses change the underlined part. Choose the best version of the sentence. If you think the original is best, choose the first version. Otherwise select one of the other responses. These questions test your ability to identify correct and effective writing. Select your response based on the rules of standard written English. You should consider grammar, choice of words, and sentence construction. Select the response which most clearly and effectively expresses the meaning intended in the original sentence. This choice should avoid awkwardness, ambiguity, redundancy, and grammatical error. To review these directions for subsequent questions of this type, click on HELP.

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Step 9.1 Lesson

Thus, according to Phineas, the Sentence Correction section tests your ability to: – Distinguish correct from incorrect English – Avoid ambiguous and awkward expressions – Eliminate unnecessarily wordy constructions

WHAT

THE DIRECTIONS MEAN

The directions that the test makers give you do not offer much guidance for answering Sentence Correction questions. You know that each sentence will be completely or partially underlined, and that the first answer choice (choice (A)) will always be the same as the original sentence. Certainly, you are supposed to choose the best answer, but what the test makers mean by this is not entirely clear. Note that the directions do not say “choose the right answer.” This is because there may be more than one answer choice that is grammatically correct. The second paragraph of the instructions explains what the test makers believe the “best answer” to be, but there is no mention of spelling, punctuation, or the range of grammar rules tested. As it turns out, you don’t need to know how to spell, you don’t need to know much about punctuation, and you will see later in this section that the number of grammar rules tested is quite small.

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Sentence Correction

AIM… ANATOMY

OF A

SENTENCE CORRECTION QUESTION:

Sentence Correction questions are composed of a statement, which may or may not contain a grammatical or stylistic error for you to identify, and five answer choices. The first answer choice is the same as the original statement and the other four are different. Your job is to choose the best version of the statement from among the five answer choices. The “best” answer choice is the one that eliminates grammatical mistakes and expresses the meaning of the original statement in the most clear and straightforward manner. Each statement will be either completely or partially underlined.

Check your work Use the un-underlined part of the sentence to your advantage: it is the one part of the sentence you know is right.

Let’s look at a typical Sentence Correction statement:

STATEMENT Although less impressive than the great masterpieces, contemporary artists are more in touch with issues relevant to modern life. Note that the un-underlined part is indisputable. You should use the ununderlined part to help you figure out how the underlined part should be corrected.

ANSWER CHOICES (A) (B) (C) (D) (E)

contemporary artists are more in touch with issues relevant contemporary artists have more relevance the work of contemporary artists are more in touch with issues relevant the work of contemporary artists are more relevant the work of contemporary artists is more relevant

If you read the initial statement you can identify the problem: a modifier. The sentence compares masterpieces (works of art) to artists (persons who create works in art). Such a comparison is nonsensical. You are looking for an answer choice that fixes the mistake. (Don’t worry, we’ll discuss modifiers later.) After scanning the answer choices (never read the first answer choice: it is always exactly the same as the initial statement) you can see that the second proposal (choice (B)) has been changed, but still doesn’t fix the mistake. The third proposal (choice (C)) fixes the initial mistake but introduces a new mistake: faulty subject/verb agreement between “the work” and “are.” The fourth proposal (choice(D)) changes what was awkward in choice (C) – “in touch with issues relevant” – but keeps the same mistake: faulty subject/verb agreement between “the work” and “are.” The last proposal (choice (E)) is the best one. It fixes the modifier mistake and has correct subject/verb agreement.

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Questions that are completely, or almost completely, underlined tend to be the most difficult because there is nothing correct with which to compare the incorrect underlined part.

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Step 9.1 Lesson

Standardized tests = standardized mistakes

Looking in vain Sometimes there is no error in the statement. In fact, you should expect (A) to be correct as often as any other choice – about once in five questions.

In Step 1 of this manual we saw that Phineas has an agenda. His goal in giving the GMAT is to tell business schools which candidates have average abilities, less than average, more than average, unusually high, etc. He must therefore create wrong answer choices that tempt test takers. Specifically, there must be some choices that are not completely wrong and yet have something attractive to tempt some test takers. There are some questions that are almost right, so that competent test takers will get them right half the time and get them wrong the other half. Only the most competent test takers get all, or nearly all, the questions right. We call the technique of producing wrong answers according to the principles of standardization the Wrong Answer Factory. There are generally three types of answer choices for Sentence Correction questions: Same Error Answers: Answer choices that repeat the error from the initial statement, but change something else in the answer choice. Most of the time, you will see at least one same error answer choice. This is apparent in choice (B). Almost Right Answers: Answer choices (in this case (C) and (D)) that fix the error from the original sentence, but introduce new errors. Best Answers: Answer choices that are grammatically correct, straightforward, and clearly express the meaning of the initial sentence. There will never be errors in spelling or punctuation. Understanding the Wrong Answer Factory is a sure way of finding the best answer. Once you have identified Same Error and Almost Right Answers, using the Process of Error Identification to find the Best Answer is easy.

Many questions are made difficult by the addition of distracting words. By identifying a key word, phrase, or clause, you will spot the testing patterns and focus on the initial errors, making elimination easier.

ANSWER CHOICE PATTERNS “3-2” - You can quickly see a “3-2” pattern in the answer choices. In this example, there are two choices that compare great masterpieces to “contemporary artists” and three choices that compare great masterpieces to “the work of contemporary artists.” You don’t have to zero in on the right choice immediately. Instead, look for patterns and eliminate answer choices with the same mistakes. “2-2-1” - Sometimes you see a “2-2-1” pattern, in which two choices have one expression, another two choices have a different expression, and a fifth choice is completely different from all the others. These questions tend to be a little harder, but after recognizing the “2-2-1” pattern you can begin to eliminate any answer choices that contain the same mistake.

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Sentence Correction

THE MBA CENTER APPROACH Knowing that the number of question types is limited and that all the questions are written according to the Wrong Answer Factory principles, we have designed an approach to Sentence Correction appropriate for each of the question types. Step 1: Read the initial statement and identify the type of problem The least advised approach to Sentence Correction would be to read the answer choices instead of the question to determine the type of problem. First look at the original sentence to determine the problem (if any – always check). Once you do, you’ll know what error to focus on in the answer choices, and can use the Process of Error Identification to eliminate wrong answer choices.

DRILL 1 DIRECTIONS: FOR EACH SENTENCE 1.

BELOW IDENTIFY THE TYPE OF ERROR (IF ANY):

The Secretary of State’s strategic advisor, together with her staff of three top aides, are accompanying her on a diplomatic tour of capitals in the Middle East.

Type of problem: ________________________________________________ 2.

Unlike previous hypotheses concerning climate changes, paleontological circles have introduced a new theory for the extinction of the dinosaurs in the form of a lethal comet.

Type of problem: ________________________________________________ 3.

The French are renowned for their eating habits, not only for the quality and preparation of their food, but also for the refined manner in which they eat it.

Type of problem: ________________________________________________ 4.

While some of the blood samples were contaminated today, rendering them useless for further experiments, the scientists already finished their research.

Type of problem: ________________________________________________ 5.

Whereas warriors in centuries past counted among their nations’ heroes, so too do today’s sports stars, such as Michael Jordan and Ronaldo, embody the physical and competitive aspirations of their countrymen.

Type of problem: ________________________________________________

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Statistically, 20% of the time the first answer choice is correct. No error, or answer choice (A), is more common than you might think. How to make sure? Even if you are right and think there is no error to identify, scan for differences among answer choices to make certain there is nothing wrong in the initial statement.

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Step 9.1 Lesson

Step 2: Do not reread the first answer choice What is the difference between the underlined part and answer choice (A)? Economists are hard pressed to explain why, occasionally, out of many years of steady economic growth emerge the twin problems of unemployment and large income gaps. Answer choice (A): emerge the twin problems of unemployment and large income gaps. Notice that the first answer choice, (A), is always the same as the underlined part in the initial statement. Keep in mind as you go through this lesson that you always have choice (A) as an option for best answer. To gain time, if you’re not satisfied with the initial statement, move directly down to answer choice (B) and begin comparing all the answer choices. Step 3: Identify the Same Error Answers Identifying Same Error Answer choices is the first step in the Process of Error Identification. Same Error Answer choices are the easiest to spot, so they’re a natural place to start. To spot Same Error Answers, find the answer choices that repeat the error from the initial statement.

DRILL 2 DIRECTIONS: FOR THE QUESTIONS BELOW, DETERMINE ERROR ANSWERS IN EACH SET OF ANSWER CHOICES.

THE

SAME

Score Value: 500

GMAT CAT – Section 4 : Verbal

1 of 41

The Secretary of State’s strategic advisor, together with her staff of three top aides, are accompanying her on a diplomatic tour of capitals in the Middle East. ! ! ! ! !

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(A) together with her staff of three top aides, are (B) as well as her staff of three top aides, is (C) also her staff of three top aides, are (D) bringing along with her staff of three top aides, are (E) additionally with her staff of three top aides, is

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Sentence Correction

Score Value: 600

GMAT CAT – Section 4 : Verbal

2 of 41

Unlike previous hypotheses concerning climate changes, paleontological circles have introduced a new theory for the extinction of the dinosaurs in the form of a lethal comet.

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! (A) paleontological circles have introduced a new theory for the extinction of the dinosaurs in the form of a lethal comet ! (B) paleontologists are examining a new theory for the extinction of the dinosaurs, one involving a lethal comet ! (C) a new theory for the extinction of the dinosaurs has made its way into paleontological circles, this time citing a lethal comet as the cause of the extinction ! (D) a new theory citing a lethal comet as the cause of the extinction of the dinosaurs has made its way into paleontological circles ! (E) the introduction of a new theory, citing a lethal comet as the cause of dinosaur extinction, has made its way into paleontological circles

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Score Value: 650

GMAT CAT – Section 4 : Verbal

3 of 41

The French are renowned for their eating habits, not only for the quality and preparation of their food, but also for the refined manner in which they eat it.

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! (A) the quality and preparation of their food, but also for the refined manner in which they eat it ! (B) the quality and preparation of their food, but by the refined manner in which they eat it ! (C) the quality and preparation of their food, but also the refined manner in which they eat it ! (D) their food’s quality and preparation, but for the refined manner in which they go about eating it ! (E) the quality and preparation of their food, and the refined manner in which they eat it

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Score Value: 650

GMAT CAT – Section 4 : Verbal

4 of 41

While some of the blood samples were contaminated today, rendering them useless for further experiments, the scientists already finished their research.

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! (A) While some of the blood samples were contaminated today, rendering them useless for further experiments, the scientists ! (B) While some of the blood samples had been contaminated today, rendering them useless for further experiments, the scientists ! (C) Some of the blood samples had been contaminated today, rendering them useless for further experiments; fortunately, the scientists had ! (D) While some of the blood samples were contaminated today, rendering them useless for further experiments, the scientists had ! (E) Today some of the blood samples were contaminated, rendering them useless for further experiments, but the scientists

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Score Value: 700

GMAT CAT – Section 4 : Verbal

5 of 41

Whereas warriors in centuries past counted among their nations’ heroes, so too do today’s sports stars, such as Michael Jordan and Ronaldo, embody the physical and competitive aspirations of their countrymen. ! ! ! ! !

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(A) Whereas warriors in centuries past (B) Much like warriors in centuries past, who (C) Just like warriors in centuries past, who (D) Just as warriors in centuries past (E) Just as warriors in centuries past, who

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Sentence Correction

Step 4: Identify the Almost Right Answers Once you have identified and eliminated all the Same Error Answers, only Almost Right Answers and the best answer remain. Because they are more difficult to spot, look for Almost Right Answers only after you’ve located and eliminated all the Same Error Answers. At this point, compare slight differences in wording between the remaining answer choices and look for Almost Right Answers, which correct the original problem and add an error to another part of the sentence to distract you. Spotting and eliminating Almost Right Answer choices requires a bit more attention and skill than for Same Error Answers. This stage of error identification is critical and is where most mistakes are made.

DRILL 3 DIRECTIONS: IDENTIFY

THE ALMOST FOLLOWING ANSWER CHOICES.

RIGHT ANSWERS

AMONG THE Score Value: 550

GMAT CAT – Section 4 : Verbal

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Some popular music lyrics written during the late 1960’s and early 1970’s, including those of Bob Dylan and Creedence Clearwater Revival, were revolutionary for their time, as it eschewed romantic musings for declarations of political protest. ! ! ! ! !

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(A) as it eschewed (B) as they eschewed (C) in its eschewance of (D) in that they eschewed (E) as they had eschewed

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Score Value: 600

GMAT CAT – Section 4 : Verbal

7 of 41

Ernest Hemingway, one of the most acclaimed American writers of the twentieth century, has been credited for revolutionizing modern English prose, which had become, in the Victorian era, excessively verbose. ! ! ! ! !

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(A) for revolutionizing (B) as revolutionizing (C) with revolutionizing (D) for the revolutionization of (E) with having had revolutionized

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Step 9.1 Lesson

Score Value: 510

GMAT CAT – Section 4 : Verbal

8 of 41

Before the introduction of the Miranda Rights, persons suspected of having committed a crime was subject to search and interrogation without the benefit of legal counsel. ! ! ! ! !

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(A) was subject to (B) which were subjected to (C) were subjected by (D) being subject to (E) were subject to

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Score Value: 550

GMAT CAT – Section 4 : Verbal

9 of 41

The committee investigating the charges have found no evidence of wrongdoing on the senator’s part, and will announce their report next week.

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! (A) have found no evidence of wrongdoing on the senator’s part, and will announce their ! (B) have found no evidence of wrongdoing on the part of the senator and will announce their ! (C) has found no evidence of wrongdoing on the senator’s part, and will announce their ! (D) has found no evidence of wrongdoing on the senator’s part, and as a result it will announce its ! (E) has found no evidence of wrongdoing on the senator’s part, and will announce its

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Sentence Correction

Score Value: 610

GMAT CAT – Section 4 : Verbal

10 of 41

Having survived public disgrace and subsequent resignation as President of the United States in the wake of the notorious Watergate scandal, Richard Nixon’s image managed to alter from political pariah to senior statesman in the latter years of his life. ! ! ! ! !

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(A) Richard Nixon’s image managed to alter (B) Richard Nixon’s image altered (C) Richard Nixon managed to alter his image (D) Richard Nixon had managed an alteration of image (E) the alteration of Richard Nixon’s image

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Step 5: By the Process of Error Identification arrive at the right answer. After completing all four steps, only the best answer should remain. However, when you cannot determine the type of problem, the four-step approach is not of much use.

WHAT

IF

I

CANNOT IDENTIFY THE TYPE OF PROBLEM?

If you cannot identify the type of problem, compare the answer choices for differences and similarities. Identify a key word or clause that appears in all the sentences, and compare it with key words or clauses in the answer choices. From this work you’ll be in a position to identify both the Same Error Answers, in which the main error is the same as that of the original sentence; and the Almost Right Answers, which correct the original error but introduce new mistakes. Following these steps, and using the Process of Error Identification, you can find the best answer, even if you cannot identify the type of problem.

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Step 9.1 Lesson

Now try one on your own!

DIRECTIONS: CHOOSE THE BEST VERSION OF THE SENTENCE FROM THE ANSWER CHOICES BELOW. Score Value: 710

GMAT CAT – Section 4 : Verbal

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Before he wrote his masterpiece Notre-Dame de Paris, otherwise known as The Hunchback of Notre Dame, Victor Hugo saw a small sculpture along the northern wall of the Notre Dame cathedral in Paris that inspired the character Quasimodo.

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! (A) Before he wrote his masterpiece Notre-Dame de Paris, otherwise known as The Hunchback of Notre Dame, Victor Hugo saw a small sculpture along the northern wall of the Notre Dame cathedral in Paris that inspired the character Quasimodo. ! (B) Before writing his masterpiece Notre-Dame de Paris, otherwise known as The Hunchback of Notre Dame, a small sculpture along the northern wall of the Notre Dame cathedral in Paris inspired Victor Hugo to create the character Quasimodo. ! (C) The character of Quasimodo, who appears in Victor Hugo’s masterpiece Notre-Dame de Paris, otherwise known as The Hunchback of Notre Dame, was inspired by a small sculpture along the northern wall of the Notre Dame cathedral in Paris. ! (D) Quasimodo, the character appearing in Victor Hugo’s masterpiece Notre-Dame de Paris, otherwise known as The Hunchback of Notre Dame, had been an inspiration which Victor Hugo had after seeing a small sculpture along the northern wall of the Notre Dame cathedral in Paris. ! (E) The inspiration for Victor Hugo’s Quasimodo, the character in his masterpiece Notre-Dame de Paris, otherwise known as The Hunchback of Notre Dame, was inspired by a small sculpture which appears along the northern wall of the Notre Dame cathedral in Paris.

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Sentence Correction

STRATEGY

AT WORK

Read the statement and answer choices below then turn the page for practice with our five-step approach to find the best answer for Sentence Correction questions. Score Value: 650 GMAT CAT – Section 4 : Verbal

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A recent study from the Center for Disease Control has concluded that much of the currently uncontrolled carcinogens to which residents of northeastern states are exposed has not been the major cause of increased breast cancer in the region.

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! (A) much of the currently uncontrolled carcinogens to which residents of northeastern states are exposed has ! (B) much of the currently uncontrolled carcinogens to which residents of northeastern states are exposed to has ! (C) much of the carcinogens that are currently uncontrolled and that residents of northeastern states are exposed to has ! (D) many of the carcinogens that are currently uncontrolled and residents of the northeastern states are exposed to have ! (E) many of the currently uncontrolled carcinogens to which residents of northeastern states are exposed have

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Step 1: Identify the problem in the statement. What is the grammar problem in the statement? Step 2: Do not reread the first choice If you are not satisfied with the initial statement, go directly to the second answer choice. Step 3: Identify the Same Error Answers On the grid below, cross out the Same Error Answer choices.

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Step 9.1 Lesson

Score Value: 650

GMAT CAT – Section 4 : Verbal

12 of 41

A recent study from the Center for Disease Control has concluded that much of the currently uncontrolled carcinogens to which residents of northeastern states are exposed has not been the major cause of increased breast cancer in the region.

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! (A) much of the currently uncontrolled carcinogens to which residents of northeastern states are exposed has ! (B) much of the currently uncontrolled carcinogens to which residents of northeastern states are exposed to has ! (C) much of the carcinogens that are currently uncontrolled and that residents of northeastern states are exposed to has ! (D) many of the carcinogens that are currently uncontrolled and residents of the northeastern states are exposed to have ! (E) many of the currently uncontrolled carcinogens to which residents of northeastern states are exposed have

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Step 4: Identify the Almost Right Answers. On the grid below, cross out the Almost Right Answer choices.

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A B C D E Step 5: By elimination, you come to the best answer. The best answer is ________________.

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FIRE! Let’s look at the specific errors tested on Sentence Correction. Remember, there are many, many grammar points that could be tested. In this section we are going to look at the ten most common errors on Sentence Correction.

Rule: The subject of a verb must agree in number and person with that verb. It is a simple rule, but leave it to Phineas to find complications.

A. SUBJECT-VERB AGREEMENT ERROR Rule: The main subject of the sentence must always agree in number with the main verb of the sentence. Be careful: Phineas is fond of using collective nouns as subjects that, though describing a plural group, use a singular verb. (See the Grammar Review for a complete explanation of this rule.)

DRILL 4 DIRECTIONS: FROM BETTER.

THE TWO CHOICES SELECT THE ONE THAT IS

1. A) The National Rifle Association, seeking to defend the rights of lawabiding citizens and sportsmen, are lobbying to preserve free access to armor-piercing bullets. or, B) The National Rifle Association, seeking to defend the rights of lawabiding citizens and sportsmen, is lobbying to preserve free access to armor-piercing bullets. The main subject is the “National Rifle Association,” which, although made up of a plural number of politically active members, is a singular noun. 2. A) After working on the computers for what seemed like days, the group decided that the project was finished and that the members could go home for the day. or, B) After working on the computers for what seemed like days, the group decided that the project were finished and that the members could go home for the day. What is the subject? “Group” or “project”? Both are subjects with verbs (group - decided) (project - was). The mistake is simple, despite the long and difficult sentence. “Project” is a count noun, and, since it is singular, we must use the verb “was.” 3. A) The publisher is given to arguing with his writers, but in this case the agreement, although 25 pages in length, has no room for negotiation. or, B) The publisher is given to arguing with his writers, but in this case the agreement, although 25 pages in length, have no room for negotiation.

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Step 9.1 Lesson

The subject in question is “agreement.” Again, don’t let the extra information clause (despite … long) confuse you. “Agreement” can be a count or non-count noun; in this sentence it is count because of the article “the” and must therefore take a singular verb, “has.” 4. A) The legislative wing of the government, the group of politicians and staff members charged with the writing and prosecution of all the national laws, is prone to controversy. or, B) The legislative wing of the government, the group of politicians and staff members charged with the writing and prosecution of all the national laws, are prone to controversy. Is the subject “wing” or “government”? Any expression following “of the…” is a modifier. “Government” is modifying “wing.” (What kind of “wing”? A government wing). “Wing” is a simple, non-count noun in the singular form, therefore use the singular form of the verb to be: “is.” 5. A) From all walks of life, students, teachers, professionals, and performers alike must wait in line because employment, although available through the government agency, is given based not on experience, but on the applicant’s willingness to try new things. or, B) From all walks of life, students, teachers, professionals, and performers alike must wait in line because employment, although available through the government agency, are given based not on experience, but on the applicant’s willingness to try new things. What is the subject here? Phineas will always try to confuse you. It is your job to break down the sentence into its critical parts. The subject here is “employment,” a noncount noun that takes the singular verb, “is.” 6. A) Even though he had driven around town all afternoon to get the right papers, neither his passport nor the statements from his bank were sufficient to prove his residency. or, B) Even though he had driven around town all afternoon to get the right papers, neither the statements from his bank nor his passport was sufficient to prove his residency. Both are correct. Can you see why? Fortunately, the test makers would never do this to you. If you are tested on Subject/Verb Agreement with a “neither … nor” or an “either … or” construction, your tendency is to use a plural verb anyway, right? So watch out for two singular subjects.

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EXAMPLE

OF A

SUBJECT-VERB AGREEMENT QUESTION Score Value: 680

GMAT CAT – Section 4 : Verbal

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Out of America’s fascination with all products low in fat have grown a market for diet brands of foods and soft drinks that are forcing marketing specialists to change the way they advertise and package their food and beverage products.

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! (A) products low in fat have grown a market for diet brands of foods and soft drinks that are forcing ! (B) products low in fat has grown a market for diet brands of foods and soft drinks that is forcing ! (C) products that are low in fat has grown a market for diet brands of foods and soft drinks that force ! (D) low-fat products have grown a market for diet brands of foods and soft drinks that are forcing ! (E) low-fat products has grown a market for diet brands of foods and soft drinks that force

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If you can, determine the mistake in the original statement. When you move down to the answer choices, remember always to skip over answer (A). The original mistake concerns the correct subject, in this case the inverted subject “market.” “Market” is a singular non-count noun and must therefore have the singular verb, “has.” Therefore you can eliminate choices (A) and (D), which both contain the plural verb “have.” What is the next mistake? Notice the second verb in the underlined section changes with each answer choice. Should it be “that is forcing,” “that force,” or “that are forcing”? Again, establish the subject of this verb: who or what is performing the action? “Market,” again. Since “market” is singular, you need a singular verb. Eliminate answers (C) and (E). Using the Wrong Answer Factory, you can easily eliminate answer choices once you have determined the original mistake. If you can’t find a mistake in the original statement, look directly at the answer choices. By comparing what Phineas has or has not changed in the answer choices, you can often find the mistake from the initial statement even if you don’t know what type of problem it is.

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Step 9.1 Lesson

B. MODIFIER PROBLEMS

Modification Breakdown Rule: Words or phrases that modify another word should be as close as possible to the word they modify. This is one of the hardest grammar rules tested on the GMAT.

Rule: A modifier will always describe the closest noun. Words or phrases that modify should be as close as possible to the noun they modify. Be careful: if the subject of the modifier is wrong, the sentence usually needs to be completely restructured.

DRILL 5 DIRECTIONS: FROM BETTER.

THE TWO CHOICES, SELECT THE ONE THAT IS

1. A) Having located the correct place where the digging and excavation was going to occur, the shovels and rakes were put to work by the laborers hired for the job. or, B) Having located the correct place where the digging and excavation was going to occur, the laborers who were hired for the job put the shovels and rakes to work. Introductory verbal modifiers are difficult at first, but once you understand how to identify them, they are quite easy. In this sentence we have an introductory modifier “Having located the place where the digging was going to occur” with no subject. It will therefore modify the closest noun. Ask yourself who or what is performing the action (who or what “has located”), “shovels and rakes”? No, the “laborers.” 2. A) Thinking about the project, although in a very thorough and organized manner, Jack would have seen the problem sooner had he just started working. or, B) Thinking about the project, although in a very thorough and organized manner, the problem would have been seen sooner had Jack just started working. It is possible to have an extra information clause between the modifier and the subject. In this sentence this clause (although … manner) is there to distract you. Who or what is “thinking about the project”? Jack, of course. 3. A) Agile and keen-witted, the introduction of the domestic cat to the Australian continent has threatened the survival of a number of usually predator-free small mammal species. or, B) Agile and keen-witted, the domestic cat, recently introduced to the Australian continent, has threatened the survival of a number of usually predator-free small mammal species. Sometimes, with an adjectival introductory phrase the same rule for modifiers applies. Ask yourself who or what is “agile and keen-witted,” the “introduction”? No, “the domestic cat.”

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4. A) Bread and Wine is a fictionalized account of a small Italian village at the beginning of the Fascist movement, which many literary critics consider Silone’s greatest work. or, B) Bread and Wine, which many literary critics consider Silone’s greatest work, is a fictionalized account of a small Italian village at the beginning of the Fascist movement. Who, that, and which are modifiers and must be as close to the words they modify as possible. Did many “literary critics” consider the “Fascist movement” to be “Silone’s greatest work,” or is it the book, “Bread and Wine”?

EXAMPLE

OF A

MODIFIER QUESTION Score Value: 650

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GMAT CAT – Section 4 : Verbal

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Important because of the skeletal material discovered there, archaeologists excavating the Choukoutien caves of northern China also found significant information of the region’s inhabitants. (A) archaeologists excavating the Choukoutien caves of northern China also found significant information of the region’s inhabitants (B) but also, archaeologists excavating the Choukoutien caves of northern Chine also found significant information about the region’s inhabitants (C) the Choukoutien caves of northern China also contained significant information about its inhabitants found by archaeologists (D) archaeologists’ excavations of the Choukoutien caves of northern China found significant information of the region’s inhabitants (E) the Choukoutien caves of northern China also contained significant information, found by archaeologists, about the region’s inhabitants

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Identify the original mistake. A modifier will describe the closest noun. What is “important because of the skeletal material discovered there”? Archaeologists? No, it must be some place, not some person. Eliminate any choices with the wrong subject, (A) and (B). What’s the next mistake? Again, refer back to the original modifier. What is “important”? The “caves,” not the “excavations.” Eliminate answer (D). We are left with answers (C) and (E). (C) looks good, because it corrects the original mistake, but we can eliminate it because it is ambiguous what was “found by archaeologists” (information or inhabitants?). Also, we can eliminate choice (C) because it uses the singular pronoun “its” to refer to the plural “caves”.

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C. PROBLEMS

Step 9.1 Lesson

WITH

PRONOUNS

Rule: Every pronoun must have a clear antecedent, agreeing in number, gender (for people), and case.

DRILL 6 DIRECTIONS: FROM BETTER.

THE TWO CHOICES, SELECT THE ONE THAT IS

1. A) The position of the Earth in relation to the Sun is always changing, as its axis tilt is not rigidly constant. or, B) The position of the Earth in relation to the Sun is always changing, as the Earth’s axis tilt is not rigidly constant. In the second clause, what does the possessive pronoun “its” refer to? Each pronoun must have a clear antecedent; “position” is not the subject that is “not rigidly constant”; therefore we must add the correct subject in the second sentence. 2. A) Peyton enjoys the company of many friends, especially Jim and Jason, but he is especially careful not to consider any one friend more important than another. or, B) Peyton enjoys the company of many friends, especially Jim and Jason, but Peyton is especially careful not to consider any one friend more important than another. “He,” in first sentence, could refer to “Peyton,” “Jim,” or “Jason.” There is no clear antecedent. Therefore we must rewrite the sentence, repeating the subject, to avoid confusion.

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Sentence Correction

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PRONOUN QUESTION

Score Value: 590

GMAT CAT – Section 4 : Verbal

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One result of the National Education Council’s recent study of undergraduate life is the realization that in a student’s last academic year, their concerns for job prospects often interfere with their academic careers.

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EXAMPLE

! (A) the realization that in a student’s last academic year, their concerns for job prospects often interfere with their academic careers ! (B) the realization that during students’ last academic year, their concerns for job prospects often interfere with their academic careers ! (C) to realize that in a student’s last academic year, his or her concerns for job prospects often interfere with his or her academic career ! (D) to realize that during a student’s last academic year, their concerns for job prospects often interfere with their academic careers ! (E) realizing that during students’ last academic year, their concerns for job prospects often interfere with their academic careers

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Whenever you see multiple pronouns in a sentence, you should be suspicious. In this sentence there are two pronouns “their” that must refer to a plural subject. What is the subject? “A student” is singular, therefore we have a pronoun mistake. First scan the answer choices for those that repeat the original mistake. Choices (A) and (D) can be eliminated. Choices (C) and (E) fix the original mistake, but add new problems. (C) incorrectly completes the construction “One result is...” with the infinitive “to realize,” and (E) incorrectly completes it with the gerund “realizing.”

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D. PROBLEMS

Step 9.1 Lesson

WITH

PARALLELISM

Rule: When making a list or a comparison, parallel concepts must be expressed in parallel constructions.

DRILL 7 DIRECTIONS: OF

THE TWO CHOICES, SELECT THE ONE THAT IS BETTER.

1. A) On his vacations, Phil always enjoys looking at the museums and the small streets, finding out-of-the-way cafes and restaurants, although he sometimes gets lost, and buys original paintings. or, B) On his vacations, Phil always enjoys looking at the museums and the small streets, finding out-of-the-way cafes and restaurants, although he sometimes gets lost, and buying original paintings. Parallel ideas must be expressed in parallel constructions. Here we have three verbs that are expressing the same idea: what Phil enjoys “doing” on his vacation. Be careful of the other verbs in the sentence; they are not part of the parallel construction. 2. A) William Blake is renowned not only for writing works of poetry, but also for the drawings and paintings that accompanied them. or, B) William Blake is renowned not only for his works of poetry, but also for the drawings and paintings that accompanied them. The idiomatic expression “not only … but also” requires that the two items listed maintain a parallel construction. In the first sentence above, “writing works of poetry” is incorrectly paired with “the drawings and paintings.” 3. A) Thomas Jefferson’s interests ranged from the study of paleontology to reading classical literature. or, B) Thomas Jefferson’s interests ranged from studying paleontology to reading classical literature. Here, the idiomatic phrase is “ranged from … to.” Again, verify parallel construction between the two items. Other expressions that require parallel construction include: Either… or, neither… nor, prefer… to , both… and, between… and, from… to, left … for.

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Sentence Correction

4. A) To say that the Middle culture is to do a great thinkers of the period. or, B) To say that the Middle culture is doing a great thinkers of the period.

Ages was a period of chaos and loss of disservice to the many great artists and Ages was a period of chaos and loss of disservice to the many great artists and

What is the comparison here? Noticing the words “to say” ought to be a big hint for you. In order to maintain parallel structure, we must repeat the infinitive “to do” and avoid the gerund “doing”.

EXAMPLE

OF A

PARALLEL CONSTRUCTION QUESTION Score Value: 700

00:43

GMAT CAT – Section 4 : Verbal

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The wings of the dodo bird resembled a turkey’s, and so were probably without flight. (A) The wings of the dodo bird resembled a turkey’s (B) The dodo bird’s wings resembled that of a turkey (C) A dodo bird’s wings were similar to a turkey (D) The dodo birds had wings that resembled a turkey (E) The dodo birds had wings that resembled those of a turkey

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The original sentence is not a proper parallel construction, since it implies that the wings of the dodo bird were without flight. Eliminate (A), (B) and (C). The two parallel items are “had wings” and “were without flight” as these are both qualities of the correct subject of the sentence, “the dodo birds”. Answer choice (D) makes the incorrect comparison between “wings” and “a turkey”. The correct answer is (E).

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E. PROBLEMS

Step 9.1 Lesson

WITH

FAULTY COMPARISONS

Rule: In comparisons, the items being compared must be of a similar nature. That is, people should be compared with people, furniture with furniture, and actions with actions.

DRILL 8 DIRECTIONS: FROM BETTER.

THE TWO CHOICES, SELECT THE ONE THAT IS

1. A) Even after the defeat of the Spanish Armada in 1588, Spain’s fleet remained greater in size and mobility than England. or, B) Even after the defeat of the Spanish Armada in 1588, Spain’s fleet remained greater in size and mobility than England’s. When making comparisons, be careful that you are comparing similar things. In the first example, the size of the “fleet” is larger than the size of the country (“England” ). Wrong sentences of this kind are not necessarily grammatically incorrect. You could say that “the parking lots in Texas are larger than Rhode Island.” (Meaning the actual size of a parking lot is larger than the actual size of Rhode Island… which is nearly true.) 2. A) The rooms of the Louvre, without exception, are more ornate than the MBA Center. or, B) The rooms of the Louvre, without exception, are more ornate than those of the MBA Center. You get the idea.

3. A) Publishing journal articles and participating in the many lecture circuits can be as important to a professor’s success as teaching classes. or, B) Publishing journal articles and participating in the many lecture circuits can be as important to a professor’s success as class. What is the comparison? “Publishing” and “participating” are being compared with “teaching,” not “class.” Make sure you are comparing similar ideas.

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4. A) When I think of the French teacher, she pales in comparison to the Spanish teacher’s beautiful spontaneity and passion for the small things in life. or, B) When I think of the French teacher’s attitude, it pales in comparison to the Spanish teacher’s beautiful spontaneity and passion for the small things in life. The comparison in this sentence is between the attitude of the French teacher and the unstated attitude of the Spanish teacher. We can eliminate the first sentence because it compares “teacher” to “spontaneity and passion.”

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FAULTY COMPARISON QUESTION

Score Value: 680

GMAT CAT – Section 4 : Verbal

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Safety belts, although known occasionally to cause injuries in automobile accidents, pose less danger to drivers and passengers than airbags.

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AN EXAMPLE

! (A) Safety belts, although known occasionally to cause injuries in automobile accidents, pose less danger to drivers and passengers than airbags. ! (B) The risks posed by safety belts, which occasionally cause injuries to drivers and passengers in automobile accidents, are fewer than airbags. ! (C) Safety belts, although known occasionally to cause injuries in automobile accidents, pose less danger to drivers and passengers than do airbags. ! (D) Although safety belts occasionally cause injuries in automobile accidents, they pose fewer risks to drivers and passengers than that caused by airbags. ! (E) The risk of safety belts is less to drivers and passengers than the risk of airbags, although they occasionally cause injuries in automobile accidents.

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This sentence may sound right at first because people talk this way all the time. (Phineas relies on the fact that you will think this sentence is correct for that reason.) But, in fact, this sentence is ambiguous. It could be interpreted to mean that safety belts pose less danger to drivers and passengers than they do to airbags. Eliminate (A). All of the other answer choices try to correct the faulty comparison, but only (C) manages it directly and correctly, by inserting the “do” in the sentence as a verb to accompany airbags. (C) should leap off the page for Correct. What is wrong with the other choices? (B) compares the risks, rather than the safety belts, to the airbags. (D) is wordy and includes a pronoun error (“that” instead of “those”). (E) makes a quantitative error (“less” instead of “smaller” or “lesser” – more on these soon), is wordy, and places the modifying phrase too far from the subject.

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Step 9.1 Lesson

F. PROBLEMS

Who makes the rules? Rule: In GMAT-land, idioms must be phrased exactly the way Phineas wants them. Any deviation and the sentence is incorrect.

WITH IDIOMS

Rule: Idioms are simply phrases that denote fixed expressions of language. The key here is to recognize the preferred usage of idioms for the GMAT, not your personal preferred usage or that of your region of the world. And therein lies the rule: idioms are learned through usage, not through memorization. Below is a list of popular idioms on the GMAT. approve/disapprove of based on composed by/of corrected by/about credit with defined as discourage from from… to modeled after not only… but also refer to regard as responsible to (a person) result from consider

DRILL 9 DIRECTIONS: OF 1. A) Research relativity or, B) Research relativity

ashamed of between… .and concerned with contrast to/with debate over different from depend on further from much as prefer… .to… . related to responsible for (something) result in composed of

THE TWO CHOICES, SELECT THE ONE THAT IS BETTER.

in astrophysics based on Einstein’s general theory of has yielded the concept of the black hole. in astrophysics based with Einstein’s general theory of has yielded the concept of the black hole.

2. A) Regarded as priceless, the Crown Jewels are some of Britain’s most heavily guarded treasures. or, B) Regarded for priceless, the Crown Jewels are some of Britain’s most heavily guarded treasures. 3. A) Visitors to California often prefer the compact, picturesque cityscape of San Francisco over the sprawling, asphalt maze of freeways that is Los Angeles. or, B) Visitors to California often prefer the compact, picturesque cityscape of San Francisco to the sprawling, asphalt maze of freeways that is Los Angeles.

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Sentence Correction

4. A) Ashamed by his job writing math questions, Chris decided to pursue his childhood dream of being an AAA manager in his hometown of Houghton Lake, MI. or, B) Ashamed of his job writing math questions, Chris decided to pursue his childhood dream of being an AAA manager in his hometown of Houghton Lake, MI.

AN

EXAMPLE OF AN IDIOM

When you see a long sentence with a very short underlined part, there’s a good chance your knowledge of idioms is being tested.

QUESTION Score Value: 580

GMAT CAT – Section 4 : Verbal

18 of 41

A great rivalry existed between the New York Yankees, who represented professionalism and success, in contrast with the Brooklyn Dodgers, perennial underdogs who appealed to diehard fans and working-class New Yorkers. ! ! ! ! !

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(A) in contrast with the Brooklyn Dodgers (B) in contrast with the Brooklyn Dodgers fans (C) against the Brooklyn Dodgers (D) as opposed to the Brooklyn Dodgers (E) and the Brooklyn Dodgers

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The idiom in question here is “between … and.” Because the ununderlined portion of the sentence cannot be altered, the underlined portion must conform to it. Here, “between” is not underlined, thus the sentence must follow with “and.”

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G. PROBLEMS

Step 9.1 Lesson

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TENSE

Rule: The verb tenses in English are relatively easy to use; however, there are some simple tricks. Unless a sentence emphasizes the sequential nature of events, tenses rely on either the verbs that come before them or a changing time signal.

DRILL 10 DIRECTIONS: FROM BETTER.

THE TWO CHOICES, SELECT THE ONE THAT IS

1. A) The long beginning phase of the Quaternary ice age has not been closely subdivided, but it is given the general name Villafranchian in Europe or Blancan in North America. or, B) The long beginning phase of the Quaternary ice age has not been closely subdivided, but it has been given the general name Villafranchian in Europe or Blancan in North America. This is another example of parallel structure. The same verb form must be used throughout the statement, in this case the present perfect tense. It is not clear which action occurred first, therefore we use the present perfect to refer to any action that occurred in the past but that is connected to the moment of speaking. 2. A) Before Hubert set up the wildly successful publishing branch of his new company, he launched an independent software venture that sought to introduce new material through the Internet. or, B) Before Hubert set up the wildly successful publishing branch of his new company, he is launching an independent software venture that sought to introduce new material through the Internet. There are two events here: the one that occurred first must be put further in the past than the more recent event. According to GMAT rules, the “Before” in the sentence clarifies the chronology of events, so “launched” does not need to be changed to “had launched.” 3. A) The teacher, although given to expressing his beliefs, had to control himself when he told Jack that it was imperative that he wrote more clearly on his final paper. or, B) The teacher, although given to expressing his beliefs, had to control himself when he told Jack that it was imperative that he write more clearly on his final paper. The phrase “it was imperative that” calls for the subjunctive, which is the dictionary form “write.”

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EXAMPLE

OF A

TENSE QUESTION Score Value: 670

GMAT CAT – Section 4 : Verbal

19 of 41

Some doctors who were faulted last week by health officials for improperly prescribing drugs not fully tested by the FDA were improperly briefed by their hospitals on new medications.

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! (A) Some doctors who were faulted last week by health officials for improperly prescribing drugs not fully tested by the FDA were ! (B) Some doctors who were faulted last week by health officials for prescribing drugs not fully tested by the FDA had been ! (C) Some doctors that health officials faulted last week for prescribing improper drugs not fully tested by the FDA have been ! (D) Last week health officials faulted some doctors for improperly prescribing drugs not fully tested by the FDA but have been ! (E) Last week some of the doctors who were faulted for prescribing improperly drugs not fully tested by the FDA but had been

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Is the order of events clear in the original sentence? Is it possible to determine when the doctors were “improperly briefed”? No. Be suspicious of the verbs immediately, since the last word in the underlined section is a verb. Scan the answer choices quickly (just the last words) and you can quickly eliminate answers because of verb problems. We need a certain order of events, which means we need the past perfect tense. Answer choice (B) has the past perfect, as does choice (E). (Eliminate (A), (C), and (D).) Of the two, which one is better? Answer (E) has seriously altered the word order so that the sentence has no meaning.

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In this sentence, you can deduce that the improper prescriptions came after the improper briefing; hence, the briefing occurred before the prescriptions, and the action should be further in the past. Notice that among the answer choices, only two of them employ the past perfect “had been”. Between those two, which one is better? The best answer is (B).

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H. PROBLEMS

Step 9.1 Lesson

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Rule: The exact repetition of an idea (even if it uses different words) already expressed in a sentence should be avoided.

DRILL 11 DIRECTIONS: OF The two expressions “at least” and “or more” both indicate minimum amount; the choice of which one to remove is the test makers', not yours.

THE TWO CHOICES, SELECT THE ONE THAT IS BETTER.

1. A) At least three hundred thousand people or more gathered in front of the White House in Washington, D.C., in 1968 to protest U.S. involvement in the Vietnam War. or, B) At least three hundred thousand people gathered in front of the White House in Washington, D.C., in 1968 to protest U.S. involvement in the Vietnam War. The expression “at least” has the same meaning as the expression “or more”. Therefore one of them is redundant. Be careful. Taking either expression out will correct the sentence. 2. A) While it is possible that the Trojan War depicted in Homer’s epic poems might have actually occurred, it is unlikely that such a large, well-coordinated expedition was motivated by a love triangle. or, B) While it is possible that the Trojan War depicted in Homer’s epic poems actually occurred, it is unlikely that such a large, wellcoordinated expedition was motivated by a love triangle. “While it is possible” and “might have” in this sentence are redundant. Both are referring to the chance that an event occurred.

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Sentence Correction

EXAMPLE

OF A

REDUNDANCY QUESTION Score Value: 550

GMAT CAT – Section 4 : Verbal

20 of 41

The Napoleonic code requires that all voting citizens must have a fixed address and at least three different kinds of identification. (A) that all voting citizens must have (B) that all voting citizens should have (C) that all voting citizens that they must have (D) that all voting citizens have (E) of all voting citizens the having of

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! ! ! ! !

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Can you spot the redundancy? The phrase “requires that” calls for the subjunctive. It is redundant and ungrammatical to include the modal “must” or “should” with the subjunctive “have.” Eliminate (A) and (B). Choice (C) adds an extra “that they.” Eliminate (C). Both (D) and (E) fix the original mistake, but look what a mess (E) is.

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I. PROBLEMS

Step 9.1 Lesson

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COMPARISON/QUANTITY WORDS

Rule: Countable nouns must be modified by countable quantity words (few, many, etc.), and noncountable nouns must be modified by noncountable quantity words (little, much, etc.). Also, be careful of comparisons between two items and comparisons among three or more items.

DRILL 12 DIRECTIONS: OF

In comparisons between only two items, only the expressions “less” and “more” can be used. In comparisons between three or more items, only the superlatives “least” and “most” can be used.

THE TWO CHOICES, SELECT THE ONE THAT IS BETTER.

1. A) Despite increased funds for political campaigning and voter registration reforms, fewer voters than ever before turned out for the recent election. or, B) Despite increased funds for political campaigning and voter registration reforms, less voters than ever before turned out for the recent election. Is “voters” a count or noncount noun? Count, of course (one voter, 50 voters). Therefore we must use a count quantity word, like “few” or “many.” 2. A) Of all the possible disasters that face the Indian elephant, the possibility of continued decline in habitat size is perhaps the more difficult to prevent. or, B) Of all the possible disasters that face the Indian elephant, the possibility of continued decline in habitat size is perhaps the most difficult to prevent. What is being compared in this sentence? Two things or more than two things? “Habitat size” is being compared to “all the possible disasters,” a plural term. We must use the superlative, “most,” because we are comparing three or more items.

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Sentence Correction

EXAMPLE

OF A

COMPARISON/QUANTITY WORD QUESTION Score Value: 550

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GMAT CAT – Section 4 : Verbal

21 of 41

A recent study from the Center for Disease Control has concluded that much of the currently uncontrolled carcinogens to which residents of northeastern states are exposed has not been the major cause of increased breast cancer in the region. (A) much of the currently uncontrolled carcinogens to which residents of northeastern states are exposed has (B) much of the currently uncontrolled carcinogens that residents of northeastern states are exposed to has (C) much of the carcinogens that are currently uncontrolled and that residents of northeastern states are exposed to has (D) many of the carcinogens that are currently uncontrolled and residents of northeastern states are exposed to have (E) many of the currently uncontrolled carcinogens to which residents of northeastern states are exposed have

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Again, here is a question where glancing at the first word of each answer choice can lead you right to the question type. Should it be “much” or “many”? That depends on whether the noun “carcinogens” is count or noncount. In fact it is a count noun. (There are only a few noncount nouns that end with “s”). Since it is a count noun, we can eliminate any answer choice with noncount quantity words (choices (A), (B), and (C)). Now we must decide between (D) and (E). (D) has changed the word order in the sentence so drastically that the sentence no longer makes sense.

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J. PROBLEMS

Step 9.1 Lesson

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Rule: The GMAT prefers a concise writing style that avoids the use of unnecessary or ambiguous phrases. Beyond your own understanding of proper writing style, it is helpful to recognize certain style errors that appear repeatedly and render an answer choice incorrect.

DRILL 13 DIRECTIONS: OF

THE TWO CHOICES, SELECT THE ONE THAT IS BETTER

1. A) Often the most difficult question for employees working in a company undergoing being merged with a larger corporation is whether or not they renegotiate a collective bargaining agreement with the new company directors. or, B) Often the most difficult question for employees working in a company undergoing a merger with a larger corporation is whether to renegotiate a collective bargaining agreement with the new directors. There are two style problems here. The first is “undergoing being merged”: whenever possible (and it is always possible), avoid the inclusion of the word “being.” Second, when given the choice between “whether” and “whether or not,” go with the former, which carries the same meaning, but fewer words. 2. A) After the First World War, the Conference of Paris was working hard to make a settlement to bring lasting peace to Europe. or, B) After the First World War, the Conference of Paris worked hard to make a settlement to bring lasting peace to Europe.

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Sentence Correction

EXAMPLE

OF A

STYLE PROBLEM Score Value: 490

GMAT CAT – Section 4 : Verbal

22 of 41

Overcrowded and antiquated prison systems are often resulting in convicted felons serving short sentences or none at all.

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! (A) are often resulting in convicted felons serving short sentences ! (B) often have as the result convicted felons serving short sentences ! (C) often are resulting in the serving of short sentences by convicted felons ! (D) result often in short sentences being served by prisoners ! (E) often result in convicted felons’ serving short sentences

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The first words of the underlined section are terrible; they “sound” wrong. Eliminate them, this is a style problem. Notice that answer (C) is using the same words although in a different order; sound any better? Nope, eliminate it. Could we say “have as the result” in a simpler way? We think so; eliminate answer (B). Only answers (D) and (E) are left. (D) has a simple modifier problem because it separates “short sentences” and “none at all.”

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Step 9.1 Lesson

SENTENCE CORRECTION LESSON ANSWER KEY DRILL 1

1. Type of problem: Subject/Verb agreement 2. Type of problem: Modifier 3. No error 4. Type of problem: Verb Tense 5. Type of problem: Idiom (just as)

DRILL 2

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DRILL 3

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DRILL 13

1. 2. 3. 4. 5.

1. 2. 3. 4. 5.

1. 2. 3. 4. 5. 6.

1. 2. 3. 4.

B D A D D

D C E E C

B A A A A A, B

B A B B

1. B 2. B

1. 2. 3. 4.

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B B B A

1. 2. 3. 4.

1. 2. 3. 4.

B B A B

A A B B

1. B 2. A 3. B

1. B 2. B

1. A 2. B

1. B 2. B

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Sentence Correction HOMEWORK/PRACTICE TEST SENTENCE CORRECTION ANSWER GRID B !

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Step 9.2 Homework

End

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Sentence Correction – Homework

TIME - 25 MINUTES 22 QUESTIONS

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Directions: For each question below, a part or all of the sentence is underlined. Following the sentence are five versions of the underlined part. Response (A) repeats the original; the other responses change the underlined part. Choose the best version of the sentence. If you think the original is best, choose (A). Otherwise select one of the other responses. These questions test your ability to identity correct and effective writing. Select your response based on the rules of standard written English. You should consider grammar, choice of words, and sentence construction. Select the response which most clearly and effectively expresses the meaning intended in the original sentence. This choice should avoid awkwardness, ambiguity, redundancy, and grammatical error.

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Sentence Correction

1. In their research, distinguishing between Total Factor Productivity growth and capital investment is one of the most difficult tasks for economists. (A) (B) (C) (D) (E)

is one of the most difficult tasks for economists are the most difficult tasks for an economist is a most difficult task for the economist are the most difficult tasks for economists are economists’ most difficult tasks

2. Since last August, the pound has soared by 18% in trade-weighted terms at its highest level since leaving Europe’s exchange-rate mechanism in September 1992. (A) (B) (C) (D) (E)

at by for reached to

3. Huddie Leadbetter’s legendary performances on the twelve-string guitar, Vincent Van Gogh’s landscape paintings done in small rural towns in France, and John Kennedy O’Toole’s A Confederacy of Dunces are all examples of talented artists who only came into full recognition after their deaths. (A) examples of talented artists who only came into full recognition after their deaths (B) examples of artistic works that came into full recognition only after the deaths of the artists (C) examples of artistic works not fully recognized when the artists were dead (D) examples of artistic works that came into full recognition only after their deaths (E) artistic works which exemplify when artists do not come into full recognition until after their deaths

4. For residents of nations that have been involved in wars in recent decades, the 110 million land mines planted that have not yet been detonated remain a deadly menace, a danger that kills or wounds 30,000 people every year.

(A) (B) (C) (D) (E)

a danger that kills or wounds as a danger killing or wounding killing or wounding as the deaths or wounds of to kill or wound

5. While there is hardly unanimous agreement in the field, some developmental psychologists have found that much of the determinants of one’s future success in life is traced to the formative years of early childhood. (A) much of the determinants of one’s future success in life is traced (B) much of the many determinants of one’s future success in life is traced (C) much of the determinants of one’s future success are traced (D) many of the determinants of one’s future success in life can be traced (E) many of the determinants of one’s future success in life are to be traced

6. In the twelfth century students and masters migrated to the portion of the Left Bank known as the Latin Quarter, of which the name, though being derived from Roman times, nevertheless continued to be appropriate, because of all medieval scholarship being in Latin. (A) though being derived from Roman times, nevertheless continued to be appropriate, because of all medieval scholarship being in Latin (B) though having derived from Roman times, nevertheless had still been aptly named, for all medieval scholarship was in Latin (C) having nonetheless derived from Roman times, continued appropriately, for all medieval scholarship had been in Latin (D) derived from Roman times, nevertheless was still appropriate, as all medieval scholarship was in Latin (E) having nonetheless derived from Roman times, had been named appropriately, as all medieval scholarship was in Latin

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7. In 1965 gold mining in Nevada accounted for forty-five percent of the gold produced in the United States; and sixty percent in 1995. (A) United States; and sixty percent in 1995 (B) United States; in 1995 the figure was sixty percent (C) United States; and in 1995 sixty percent (D) United States; and sixty percent in 1995 was the figure (E) United States that rose to sixty percent in 1995

8. Exit polls during the recent election show that the numbers of people whose primary political concern is the high level of crime grew by more than a twenty percent increase in the past four years and accounted for more than forty-two percent of the entire voting community.

Step 9.2 Homework

(C) suggests that government efforts toward expanding wildlife preserves and stiffen penalties against poachers have been successful, but that (D) suggests that government efforts to expand wildlife preserves and stiffen penalties against poachers were successful, but that (E) suggests that government efforts to expand wildlife preserves and stiffen penalties against poachers have been successful, but

10. What was as extraordinary as the numerous sightings of comets in the last decade have been the insights gained by scientists through their study on such diverse topics as the extinction of the dinosaurs and the age of the solar system. (A) What was as extraordinary as the numerous sightings of comets (B) The thing that was as remarkable as sighting many comets (C) No less extraordinary than the numerous sightings of comets (D) Sighting numerous comets has been none the less remarkable than (E) Sighting of numerous comets has been no less remarkable as

(A) numbers of people whose primary political concern is the high level of crime grew by more than a twenty percent increase (B) numbers of people whose primary political concern is the high level of crime grew more than twenty percent (C) numbers of people whose primary political concern is the high level of crime were raised by more than twenty percent (D) number of people whose primary political concern is the high level of crime increased by more than twenty percent (E) number of people whose primary political concern is the high level of crime was raised by more than a twenty percent increase

11. Economists are hard-pressed to explain why, occasionally, out of even years of steady economic growth emerge the twin problems of unemployment and large income gaps.

9. The decline in the Environmental Protection Agency’s index of threatened species suggest that government efforts to expand wildlife preserves and stiffen penalties against poachers have been successful, but that the continued decline of old-growth forests in the Pacific Northwest indicates that in the coming decades many plant and animal species are likely to be added to the EPA’s endangered species list.

(A) emerge the twin problems of unemployment and large income gaps (B) emerges twin problems, those being unemployment and an increasing income gap (C) emerge the twin problems, increasing income gaps and unemployment (D) emerge those twin problems, large income gaps and unemployment (E) emerges the twin problems of increasing unemployment and income gaps

(A) suggest that government efforts to expand wildlife preserves and stiffen penalties against poachers have been successful, but that (B) suggest that government efforts to expand wildlife preserves and stiffen penalties against poachers have been successful, but

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Sentence Correction

12. Eisuke Sakakibara’s recent book, “Beyond Capitalism,“ which extols the successes of the Japanese economy, has allowed him to advocate almost any economic policy without fear of charges that he is acting contrary to Japan’s interests. (A) Eisuke Sakakibara’s recent book, “Beyond Capitalism,“ which extols the successes of the Japanese economy, has allowed him (B) Eisuke Sakakibara’s recent book, “Beyond Capitalism,“ because of its extolling of the successes of the Japanese economy, has made him able (C) Eisuke Sakakibara’s “Beyond Capitalism,“ the recent book which extols the successes of the Japanese economy, makes it possible (D) Eisuke Sakakibara, whose recent book “Beyond Capitalism“ extols the successes of the Japanese economy, has allowed him (E) By extolling the successes of the Japanese economy in his recent book, “Beyond Capitalism,“ Eisuke Sakakibara has been able

(B) Unlike physics or other sciences, which they admit require a rigorous study of basic rules, many people are disinclined to recognize that fields in the humanities, such as literary criticism and philosophy, also require a rigorous study of basic rules. (C) Unlike physics or other sciences, fields in the humanities, such as literary criticism and philosophy, bring out a disinclination on the part of many people to recognize that they require a rigorous study of basic rules. (D) Many people, willing to admit that physics and other sciences require a rigorous study of basic rules, are disinclined to recognize that fields in the humanities, such as literary criticism and philosophy, require the same kind of rigorous study. (E) Many people have a disinclination to recognize that fields in the humanities, such as literary criticism and philosophy, require a rigorous study of basic rules while willing to admit that they need them for physics and other sciences.

13. Recent research in geophysics indicates that the severity of the destruction caused by an earthquake depends to a great extent on if the crustal movement that leads to shaking unfolds quickly.

15. Lasers, widely used today in such diverse technologies as medical endoscopes and compact disc players, were originally considered by many people to be a scientific curiosity of little practical value.

(A) if the crustal movement that leads to shaking unfolds quickly (B) whether the crustal movement that leads to shaking unfolds quickly (C) whether or not the crustal movement that can lead to shaking will unfold quickly (D) its speed for moving the crust leading to shaking (E) the speed of its crustal movement leading to shaking

(A) to be a scientific curiosity of little practical value (B) as being a scientific curiosity and of little practical value (C) as scientifically curious and of little practical value (D) scientific curiosities of little practical value (E) scientific curiosities and to be of little practical value

14. Unlike physics or other sciences, there is a disinclination on the part of many people to recognize that fields in the humanities, such as literary criticism and philosophy, require a rigorous study of basic rules. (A) Unlike physics or other sciences, there is a disinclination on the part of many people to recognize that fields in the humanities, such as literary criticism and philosophy, require a rigorous study of basic rules.

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16. Just as merchants in ancient Rome relied on naval patrols to keep trade routes free of pirates, so do producers of intellectual property today depend on international trade organizations to prevent illegal reproduction of copyrighted material. (A) Just as merchants in ancient Rome relied on naval patrols to keep trade routes free of pirates, so (B) Like merchants in ancient Rome relied on naval patrols to keep trade routes free of pirates, so (C) Merchants in ancient Rome relied on naval patrols to keep trade routes free of pirates, and in a similar way (D) As with the reliance of merchants in ancient Rome on naval patrols to keep trade routes free of pirates, so too (E) Similar to ancient Rome where merchants relied on naval patrols to keep trade routes free of pirates, just so

17. If the current rate at which fossil fuels and natural gases are consumed worldwide continues into the next century, the world’s natural energy resources have been and will continue to decline, pushing up prices and posing the risk of increased pollution. (A) (B) (C) (D) (E)

have been and will continue to decline have and will continue to decline will continue to decline, as they already did will continue to decline, as they have already will continue to decline

Step 9.2 Homework

19. Spacecraft that fail to break out of the Earth’s gravitational field either burn up completely in the atmosphere, which poses no danger of colliding into the Earth, and break up into large components capable of withstanding the intense heat and pressure of their fall back to the Earth. (A) which poses no danger of colliding into the Earth, and break up (B) posing no danger of colliding into the Earth, or breaking up (C) without the posing of any danger of colliding into the Earth, or breaking up (D) posing no danger of colliding into the Earth, or break up (E) with the posing of no danger of colliding into the Earth, and break up

20. Studies show that when there are several siblings close in age, the oldest sibling often takes on parental duties, such as supervising activities, taking the younger siblings to school and to pick them up afterwards, and reprimanding them for dangerous behavior. (A) taking the younger siblings to school and to pick (B) taking the younger siblings to school and picking (C) to take the younger siblings to school and to pick (D) to take the younger siblings to school and pick (E) to take the younger siblings to school while picking

18. One potential adverse effect of powerful hallucinogens such as LSD or acid is that not only do users experience the immediate impact of disorientation, but also they will encounter considerable suppression of the ego for a period of up to three weeks additionally. (A) but also they will encounter considerable suppression of the ego for a period of up to three weeks additionally (B) but also there’ll be a three-week period of ego suppression additionally (C) but the ego becomes suppressed for a period up to three weeks additionally (D) but also they will encounter considerable suppression of the ego for a period of up to three weeks (E) but the user’s ego is suppressed for a period of up to three weeks more

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Sentence Correction

21. The artists who did the Altamira cave paintings 15,000 years ago employed flint tools to carve outlines on the rock face, add color using brushes made of twigs, feathers, tufts of hair or fur, and clumps of moss. (A) add color using brushes made of twigs, feathers, tufts of hair or (B) and add color using twig brushes, feathers, tufts of hair and (C) and then added color using brushes made of twigs, feathers, tufts of hair or (D) using brushes to add color made of twigs, feathers, tufts of hair or (E) having added color using brushes made of twigs, feathers, tufts of hair and

22. Poets’ Corner in Westminster Abbey memorializes nearly six centuries of legendary English authors with graves and plaques inscribed with such celebrated names as Dylan Thomas, Samuel Johnson, and Lord Byron. (A) (B) (C) (D) (E)

inscribed with such celebrated names as inscribing such celebrated names like inscribed with celebrated names like that are inscribed with names as with inscriptions of such celebrated names as

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Step 9.2 Homework

SENTENCE CORRECTION HOMEWORK/PRACTICE TEST ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

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Sentence Correction EXPLANATIONS FOR SENTENCE CORRECTION HOMEWORK/PRACTICE TEST 1. (A) First notice the pronoun “their“ in the ununderlined part. This plural pronoun must have a plural antecedent, so any choice with the singular “economist“ is wrong (cross out (B) and (C)). Then, scanning the remaining choices, what main difference do you notice? There is an “is“ in (A) and an “are“ in (D) and (E). What is the subject of the verb? The gerund “distinguishing,” which is singular (verbal nouns are always singular). You need that “is.” 2. (E) If you only look at the underlined part and a few of the words that follow, this question may seem difficult. “At“ its highest level and “reached“ its highest level might sound okay. But which earlier word in the sentence determines the correct choice? “Soared.” “Soared to“ is an idiom and so (E) is the right answer. 3. (B) Scan the answer choices and compare. (A) says “examples of talented artists,” (B), (C), and (D) say “examples of artistic works,” and (E) says just “artistic works.” What actually was mentioned in the ununderlined part? “Performances,” “paintings“ and a novel. These are works, not artists. So (A) is wrong. The phrase “exemplify when“ in (E) is unidiomatic. Now you have to compare (B), (C), and (D). (B) sounds okay and is the right answer. (C) doesn't make sense; you don't talk about when people were dead, as presumably they still are dead. It should say “when the artists were alive.” (D) may sound pretty good, but notice the pronoun “their.” What is its antecedent? It is supposed to replace “artists,” but “artists“ has not yet been used. It cannot replace the artists mentioned only in the possessive form (as in Van Gogh's, etc.) 4. (C) Choice (A) is wrong because it illogically implies that the danger, and not the mines, kills or wounds people. (B) makes the same error and unnecessarily includes the word “as.” The present participles “killing“ and “wounding“ correctly modify the noun phrase “land mines that... detonated.” (D) leaves a sentence fragment, as the conjunction “as“ requires a finite verb in the clause that follows. The infinitive construction in (E) implies that the purpose of the mines is to “kill or wound 30,000 people every year“ and, grammatically, should not follow the comma after “menace.” © The MBA Center

5. (D) This is a quantity word question that also tests verb tense usage. Since “determinants” is a countable noun (presumably there are a number of them that can be counted) it requires the quantity word “many” instead of “much,” which is only used with non-count nouns. So, eliminate any answer choices that retain “much”: choices (A), (B), and (C). (E) corrects the quantity word problem but adds a verb tense error with the infinitive “to be traced” at the end of the sentence. Only (D) changes “much” to “many” and corrects the verb form from the infinitive “to be traced” to the modal “can be traced.” 6. (D) The phrase “because of all medieval scholarship being in Latin“ in choice (A) is awkward. The present participle in the continuous aspect “being derived“ is also awkward and doesn't make sense; the name is not still being derived. The past perfect “had been in Latin“ in choice (C) implies that the Latin scholarship preceded the appropriate naming of the area. Also the phrase “continued appropriately“ is not correct, as “continued“ should not be used as a finite verb; “the name continued to be appropriate“ is better. This whole question can be done rather simply by eliminating the choices that don't have parallel verb tenses: (B) uses the past perfect “had still been aptly named“ and the simple past “was in Latin.” (E) makes the same error. (D) is consistent in tense, using the simple past for both clauses. 7. (B) The right answer must state what was “sixty percent“ in 1995. In (A) and (C), is “sixty percent“ the subject, the object, or what? After the semicolon, you must have an independent clause. (A) and (C) are unclear and ungrammatical. In (D) there is a misplaced modifier; “in 1995“ should modify “the figure,” not “sixty percent.” Choice (E) makes it sound as though the United States rose to sixty percent. (B) is clear, direct, and grammatical. 8. (D) Choices (A), (B), and (C) all incorrectly use the plural “numbers.” In (A), the clause “grew by more than a twenty percent increase“ is redundant. In (E), “was raised by more than a twenty percent increase“ is also redundant. (D) is the only choice that correctly uses the singular “number“ and avoids redundancy. 9. (E) A quick scan here reveals a 3-2 split between “suggest“ and “suggests.” Which is correct? The subject is “decline,” a singular noun, and so the singular “suggests“ is required. Eliminate (A) and (B).

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(C) makes a parallelism error; “expanding“ and “stiffen“ are not parallel. (D) does not make this error, as it correctly uses the parallel “expand“ and “stiffen,” but it incorrectly includes the word “that“ at the end. Rereading the sentence just for the grammatical skeleton results in “the decline… suggests…. that the continued decline… indicates that…“ There seems to be one too many “thats.” This is a question of parallelism. The parallel structure is: “The decline in the EPA's index suggests that… but the continued decline of old-growth forest indicates that…” (E) correctly uses parallel structure and has a verb (suggests) that agrees with the subject (decline). 10. (C) Choices (A) and (B) do not have parallel tenses; they both use the past “was“ while the ununderlined part uses the present perfect “have been.” (D) incorrectly uses “none the less remarkable than“; the correct usage of the idiom for comparisons is “no less remarkable than.” (E) makes the error of using “less… as.” Only (C) avoids a tense error and uses the correct idiom for the comparison. 11. (A) A quick look should reveal a 3-2 breakdown in terms of verb number; (A), (C), and (D) use the plural “emerge,” and (B) and (E) use the singular “emerges.” What is the subject? It is a bit tricky here, as the subject follows the verb. The subject is “twin problems.” Since it is plural, eliminate (B) and (E). (C) and (D), besides being stylistically weak, are ambiguous. In (C), it is unclear whether the problems are 1) an increasing income gap and 2) unemployment, or 1) an increasing income gap and 2) increasing unemployment. In (D), does “large” modify only “income gaps,” or “unemployment” as well. (B) is the only choice with the correct verb number, a lack of ambiguity, and a clear style. Note that the ambiguity in (C) and (D) is quite minor. Phineas likes to give you choices in which the main error is style, but to avoid being accused of giving subjective questions (for, after all, style generally is a subjective issue), they (or should we say “it“?) include very minor grammatical faults as well. 12. (E) This is a question of modifiers and pronouns. (A) uses the pronoun “him.” What does “him“ replace? “Eisuke Sakakibara“ has not been mentioned, except in the possessive form, which doesn't count, as it is really “Eisuke Sakakibara's recent book“ that has been mentioned. (B) makes the same error and uses the awkward phrase “because of its extolling of the successes.” (C) is unclear because it doesn't specify who can advocate economic policy. (D) illogically states

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“Eisuke Sakakibara… has allowed him,” where it should say “… the book has… allowed him.” (E) begins with a modifying clause, followed by the correct subject of the modifier, Eisuke Sakakibara. 13. (B) Notice that (A) begins with “if,” (B) and (C) begin with “whether,” and (D) and (E) use neither, but rather begin with “its speed“ and “the speed.” “If“ should never begin an indirect question. “If“ is only used for conditional statements. (B) and (C) are similar, though (C) is longer and more awkward. The “or not“ is redundant after “whether“ and the future “will“ is also redundant. It is unclear in (D) and (E) what is “leading to shaking“ – is it the crust, the moving, or the speed? “Speed for“ in (D) is also unidiomatic. (B) correctly uses the word “whether“ and unambiguously indicates that crustal movement leads to shaking. 14. (D) This looks like a nightmare question. The sentence is long and completely underlined. Nevertheless, the word “unlike“ at the beginning of the sentence tells us that there is a comparison involved, giving us a clue of where to begin. In (A), “Unlike physics or other sciences“ should be compared to other academic fields. It cannot be followed by “there is a disinclination…” In (B), “physics or other sciences“ are erroneously compared to “many people.” (C) corrects the faulty comparison, but it uses the awkward phrase “brings out a disinclination on the part of many people“ and ambiguously uses the pronoun “they.” (Does “they“ refer to “fields in the humanities“ or “many people“? Does it matter?) (D) is clear and idiomatic, avoiding ambiguous pronouns and faulty comparisons. (E) has many flaws, including the ambiguous uses of “they“ and “them.” In the phrase “they need them,” who needs what? “Many people have a disinclination“ is also unidiomatic; “many people are disinclined“ is better. 15. (D) (D) is the only choice that uses the correct idiom of consider + adjective. Incorrect are “consider as“ and “consider to be“ used in (A), (B), (C), and (E).The other choices include other errors, too. (E), for example, is inconsistent. It uses “to be“ in front of “of little practical value“ but not in front of “scientific curiosities.” (A) and (B) use the singular “a scientific curiosity“ to describe the plural “lasers.” 16. (A) This is a question of idiom. For comparisons, “just as“ must be complemented by “so.” (B) is wrong because “like” is a preposition and cannot introduce © The MBA Center

Sentence Correction

an independent clause, that is, a clause with a subject and a verb. (C) implies that the way producers of intellectual property depend on trade organizations is similar to the way merchants in Rome relied on naval patrols. The statement does not compare how the two groups are (or were) reliant, but simply the fact that in both cases, there is (or was) a reliance. In general the GMAT doesn't like the phrase “in a similar way.” (D) makes the error of comparing “the reliance of merchants“ with “producers of intellectual property.” (E) also makes a faulty comparison, comparing “ancient Rome“ to “producers of intellectual property.” 17. (E) This is a verb tense question. “have been and will continue to decline“ is faulty, because “have been“ requires the present participle “declining.” In (B), “have“ requires the past participle “declined.” (C) and (D) are redundant; something that continues to do something must have already been doing it. (E) is simple, clear, and correct. 18. (D) Any time you see “not only” in a Sentence Correction question you should be on alert for a “but also” to follow it. A quick scan of the choices reveals a “3-2” split between 3 choices that have a “but also” and 2 that don’t. Right away, eliminate the two that don’t: choices (C) and (E). Since the best answer should be stylistically as well as grammatically correct, a redundancy error such as “but also … additionally” (also and additionally share a very similar meaning) in choices (A) and (C) is unacceptable. You can eliminate these without further evaluation. Only (D) corrects the redundancy error and correctly uses the idiom “not only … but also,” one of Phineas’ favorites. 19. (D) This question is a bit tricky. There are the issues of parallel construction and modifiers. The word “which“ in choice (A) grammatically modifies the preceding word, “atmosphere.” But this is illogical, as it should be the spacecraft, not the atmosphere, “which poses no danger of colliding into the Earth.” In (B), the participle “posing,” unlike the relative pronoun “which,” can modify a word further back, in this case “spacecraft.” The problem with (B) is that “breaking up“ should be parallel with “burn up,” not with “colliding.” The “spacecraft… either burn up… or break up.” Therefore “breaking up“ in (B) is wrong. (C) makes the same error. (E) says “and break up,” whereas “or“ is required following the word “either.” In (C), “without the posing of any danger“ is also awkward. (D) is the only choice that correctly follows “either burn up“ with the parallel “or break up.” © The MBA Center

20. (B) This is a case of parallel construction, probably easier than question 19. There is a list, beginning with “supervising,” and so we need “taking“ and “picking.” (B) is the only choice that provides these. 21. (C) Since these paintings were made 15,000 years ago, we should use the past tense to describe what the artists did. Therefore eliminate (A) and (B), as “add“ is the present tense. In (D), it sounds like the color, not the brushes, were “made of twigs, feathers, …“ (E) illogically implies that they added color before incising the outlines. Even if you like to draw in the colors before making the outlines, the word “added“ indicates that the color came after the outline, conflicting with the implication of the past participle “having added.” 22. (A) How would you know to choose (A) if you weren’t sure it contained an error? By comparing answer choices and eliminating those that have obvious errors or don’t sound “right” when you read them to yourself. Since on this difficult question there is no real pattern to spot (only (A) and (C) begin with the participle “inscribed”) among the choices, you must examine each and every one looking for differences and similarities. (B), eliminate because the continuous aspect of “inscribing” doesn’t match the simple present verb, and the comparative phrase “such … like” doesn’t exist in standard written English. (C) is a classic Almost Right Answer: it retains the correct participle “inscribed” from (A) but adds a new mistake with another nonexistent comparative “with … like.” (D) starts off OK with the formal but not necessarily incorrect “that are inscribed,” but again an error is added with the imaginary (and incorrect) “with …as.” (E) is simply wordy and awkward when inserted into the original statement. “With graves and plaques with inscriptions…” is not an improvement over the original statement. Even though it’s close, eliminate.

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Step 10 Sentence Correction Workshop

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Step 10 Workshop

Sentence Correction – Workshop End

Directions

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TIME: 50 MINUTES 30 QUESTIONS Directions: In each problem below, either part or all of the sentence is underlined. Following the sentence are five versions of the underlined part. Answer choice (A) repeats the original; the other answer choices vary. If you think that the original phrasing is best, choose (A). If you think one of the other answer choices is best, select that choice.

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This section tests your ability to identify correct and effective writing. Select your response based on the rules of standard written English. You should consider grammar, choice of words, and sentence construction. Select the response which most clearly and effectively expresses the meaning intended in the original sentence. This choice should avoid awkwardness, ambiguity, redundancy, and grammatical error.

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Sentence Correction

EASY 1. The decline in levels of educational achievement among grade-school students, whether the result of decreasing emphasis on homework or of inadequate public school systems, have been a disturbing national trend. (A) (B) (C) (D) (E)

have been a disturbing national trend have caused a national disturbance has been a cause of national disturbance has been a disturbing national trend has been disturbing the national trend

2. While some vacationers prefer destinations offering luxury and convenience, others choose more remote locations where little news or services exist. (A) (B) (C) (D) (E)

little news or services exist little news or services exists few services and little news exists there is little news or services available there are few services and little available news

3. In a surprising turnaround, the City Council announced that it would overturn the decision to impose a weekday curfew of 10:00 p.m. on minors. (A) it would overturn the decision to impose a weekday curfew (B) it would overturn the impose of a weekday curfew (C) it would overturn to impose a weekday curfew (D) they would overturn the imposition of a curfew on the weekdays (E) they would overturn the decision to impose a weekday curfew

4. Of all the efforts to prevent Napoleon's 1812 campaign into Russia, the destruction of crops, stores of grain, and livestock by the retreating Russian army was perhaps the more effective. (A) the destruction of crops, stores of grain, and livestock by the retreating Russian army was perhaps the more effective (B) the destruction of crops, stores of grain, and livestock by the retreating Russian army was perhaps the most effective (C) in the destruction of crops, stores of grain and livestock by the retreating Russian army was perhaps the most effective (D) destroying crops, stores of grain and livestock by the retreating Russian army was perhaps the more effective (E) the most effective on the part of the Russian army being perhaps the destruction of crops, stores of grain and livestock

5. We know less about prehistoric peoples that left their legacy only in stones, bones, and pottery, than we do about the Sumerians, who were the world's first writers and historians. (A) (B) (C) (D) (E)

prehistoric prehistoric prehistoric prehistoric prehistoric

peoples that left their peoples, who left their peoples and their peoples leaving its peoples leaving their

6. In industrialized nations, recent generations of parents tend to have less children than did their ancestors. (A) (B) (C) (D) (E)

tend to have less children have a tendency to have fewer children tend to have a few less children tend to have fewer children not so many children

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MEDIUM

7. Mastering both the technical complexities and physical demands of the sport, Dan Gable’s wrestling career, which culminated in an Olympic gold medal, has distinguished him as one of America’s all-time greatest wrestlers. (A) Dan Gable’s wrestling career, which culminated in an Olympic gold medal, has distinguished him as one of America’s all-time greatest wrestlers (B) Dan Gable’s wrestling career, which has distinguished him as one of America’s all-time greatest wrestlers, culminated in an Olympic gold medal (C) Dan Gable, one of America’s all-time greatest wrestlers, culminated his career by winning an Olympic gold medal (D) Dan Gable culminated his career with an Olympic gold medal, one of America’s all-time greatest wrestlers (E) the Olympic gold medal won by Dan Gable distinguished him as one of America’s all-time greatest wrestlers

8. The hospital planning commission has begun to institute new guidelines that require of health care employees the wearing of face masks and gloves. (A) that require of health care employees the wearing of face masks and gloves (B) that require health care employees wearing face masks and gloves (C) that require health care employees to wear face masks and gloves (D) requiring face masks and gloves being worn by health care employees (E) to require of health care employees that they wear face masks and gloves

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9. The challenges faced by many developing African nations include the establishment of a stable, democratic government, fighting the spread of AIDS, and nurturing their domestic industries. (A) the establishment of a stable, democratic government, fighting the spread of AIDS, and nurturing their domestic industries (B) establishing a stable, democratic government, fighting the spread of AIDS, and nurturing their domestic industries (C) the establishment of a stable, democratic government, the fight against the spread of AIDS, and nurturing their domestic industries (D) to establish a stable, democratic government, fight the spread of AIDS, and nurture their domestic industries (E) the establishment of a government which is both stable and democratic, the fight against the spread of AIDS, and to nurture their domestic industries

10. In an attempt to wage its war on drugs at all levels, the Drug Enforcement Agency has focused its efforts both on the small-time dealer, who is subject to mandatory prison sentences for drug-related offenses, and on the leaders of international trafficking rings, who are now pursued even in their own countries. (A) both on the small-time dealer, who is subject to mandatory prison sentences for drug-related offenses, and on the leaders of international trafficking rings, who are now pursued even (B) both on the small-time dealer, who is subject to mandatory prison sentences for drug-related offenses, and pursuing the leaders of international trafficking rings (C) both on the small-time dealer, who is subject to mandatory prison sentences for drug-related offenses, and on the leaders of international trafficking rings, the pursuit taking place even (D) both on the small-time dealer, being subject to mandatory prison sentences for drug-related offenses, and on the leaders of international trafficking rings, being now pursued even (E) both on the small-time dealer, who is subjected to mandatory prison sentences for drug-related offenses, and on trafficking by leaders of international trafficking rings, who are now pursued even

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Sentence Correction

11. What was as extraordinary as Beethoven’s musical development and impressive productivity has been his influence on successive generations of classical composers such as Robert Schumann, Anton Bruckner, and Gustav Mahler. (A) What was as extraordinary as Beethoven’s musical development and impressive productivity (B) The thing that was as extraordinary as Beethoven’s musical development and impressive productivity (C) No less extraordinary than Beethoven’s musical development and impressive productivity (D) Extraordinary musical development, for Beethoven, and impressive productivity (E) Development of Beethoven’s extraordinary music has been no less impressive as his productivity

12. Stephen Hawking's theories concerning the concept of the black hole suggest that the universe began from a singular point, and that it will continue to expand. (A) suggest that the universe began from a singular point, and that it will continue to expand (B) suggests that the universe began from a singular point, and that it will continue to expand (C) suggests that the universe began from a singular point, and that expansion has occurred and will continue (D) suggest that the universe began from a singular point, but that it has and will continue to expand (E) suggest a singular point as having started the universe, but expansion will continue

13. Medical researchers, alarmed by the appearance of a lethal new strain of influenza, are devoting their efforts to understanding and to develop a vaccine against it. (A) are devoting their efforts to understanding and to develop (B) are devoting their efforts in order to understand and develop (C) are devoting their efforts first to understanding it, then to developing (D) are devoting their efforts to the understanding of and the development of (E) is devoting their efforts to understand it, then develop

14. According to studies by the Commerce Department, families, which are richer than ever before, is holding much less in cash than they were only ten years ago. (A) which are richer than ever before, is much less in cash than they were (B) which are richer than ever before, are much less in cash than they were (C) which are richer than ever before, are much less in cash than (D) which are richer than ever before, are much fewer in cash than (E) which are richer than ever before, are fewer cash than they were

holding holding holding holding holding

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15. The Rosetta Stone, one of archeology's most significant and valuable finds, are on display in the British Museum. (A) (B) (C) (D) (E)

are on display in the British Museum are displayed in the British Museum is on display in the British Museum is in the British Museum, on display is a display in the British Museum

16. To create a fantastic new invention and successfully marketing it are two very different tasks. (A) successfully marketing it are two very different tasks (B) to market it successfully are two very different tasks (C) the successful marketing of it is two very different tasks (D) to market it with success is a very different task (E) having marketed it successfully are different tasks

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17. Less expensive than a long-distance telephone call and swifter and more convenient than a letter, an e-mail recipient may send and receive messages virtually instantly from around the world. (A) an e-mail recipient may send and receive messages virtually instantly from around the world (B) an e-mail recipient may send and receive messages around the world at a fraction of the cost and with infinitely greater speed than was previously possible (C) an e-mail address allows its owner to send messages and receive them as well virtually instantaneously from around the world (D) e-mail enables messages to be sent and received virtually instantly around the world (E) e-mail allows the sending and receiving of written messages to be achieved instantly around the world

18. Not only are the Chengjiang fossils from southwest China older than the Burgess fossils from the Canadian Rockies by more than one hundred million years, yet they’re not so deformed and are less difficult preparing for analysis. (A) yet they’re not so deformed and are less difficult preparing for analysis (B) but they are also less deformed and less difficult to prepare for analysis (C) they are not as deformed and are less difficult in preparation for analysis (D) but that they are less deformed and less difficult to prepare for analysis (E) yet they are not as deformed, and preparing them for analysis is less difficult

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Sentence Correction

19. The defenders against foreign invaders, the bone marrow creates white blood cells, also known as lymphocytes. (A) The defenders against foreign invaders, the bone marrow creates white blood cells, also known as lymphocytes. (B) Defending the body against foreign invaders, white blood cells are created in the bone marrow, also known as lymphocytes. (C) Created in the bone marrow, defense against foreign invaders is provided by white blood cells, also known as lymphocytes. (D) Created in the bone marrow, white blood cells, also known as lymphocytes, defend the body against foreign invaders. (E) The bone marrow creates white blood cells, the defenders against foreign invaders, also known as lymphocytes.

20. Responding to the public’s growing concern for maintaining a healthy, balanced diet, food manufacturers are marketing products that have less fat and calories than did their predecessors. (A) (B) (C) (D) (E)

less fat and calories than less fat and less calories than less fat and fewer calories than fewer fat and calories than less fat and fewer calories compared to

21. Unlike previous hypotheses concerning climate changes, paleontological circles have introduced a new theory for the extinction of the dinosaurs in the form of a lethal comet. (A) paleontological circles have introduced a new theory for the extinction of the dinosaurs in the form of a lethal comet (B) paleontologists are examining a new theory for the extinction of the dinosaurs, one involving a lethal comet (C) a new theory for the extinction of the dinosaurs has made its way into paleontological circles, this time citing a lethal comet as the cause of extinction (D) a new theory citing a lethal comet as the cause of extinction of the dinosaurs has made its way into paleontological circles (E) the introduction of a new theory, citing a lethal comet as the cause of dinosaur extinction, has made its way into paleontological circles

22. Given the choice between higher tax rates, which would fund extensive social programs, or lower tax rates, resulting in reduced resources for the socially and economically disadvantaged, the American public, judging from voting patterns, seems to opt for the latter. (A) which would fund extensive social programs, or lower tax rates, resulting in (B) funding extensive social programs, or lower tax rates, resulting in (C) which would fund extensive social programs, as opposed to lower tax rates, which result in (D) which would fund extensive social programs, and lower tax rates, which result in (E) which would fund extensive social programs, and lower tax rates, the result being

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23. Although their marriage was a tumultuous one, F. Scott Fitzgerald and Zelda maintained a regular correspondence in which they confided their most intimate thoughts only to one another. (A) (B) (C) (D) (E)

to one another one with the other one with another each other to each other

24. While some of the blood samples were contaminated today, rendering them useless for further experiments, the scientists already finished their research. (A) While some of the blood samples were contaminated today, rendering them useless for further experiments, the scientists (B) While some of the blood samples had been contaminated today, rendering them useless for further experiments, the scientists (C) Some of the blood samples had been contaminated today, rendering them useless for further experiments; fortunately, the scientists had (D) Though some of the blood samples were contaminated today, rendering them useless for further experiments, the scientists had (E) Today some of the blood samples were contaminated, rendering them useless for further experiments, but the scientists

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25. Depending on the source, the legend of King Arthur and the Knights of the Round Table take place either in the French region of Brittany or in parts of England. (A) take place either in Brittany or in (B) take place in either Brittany or in (C) takes place in either Brittany or in (D) takes place either in Brittany or in (E) either take place in Brittany or

the French region of the French region of the French region of the French region of the French region of

26. While some environmental litigators believe that environmental law should be a requirement in every law school curriculum, others maintain that students should study environmental law only if it would be offered as a separately elective course. (A) only if it would be offered as a separately elective course (B) if it would only be offered as an elective course, separately (C) if it was offered only as a course elected separately (D) if it would be offered only as a course separated and elective (E) only if it is offered as a separate, elective course

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Sentence Correction

27. Director Martin Scorsese and actor Robert De Niro have worked together on numerous films, from Taxi Driver, a disturbing portrait of one man's alienation and insanity, and Raging Bull, a biographical account of boxer Jake La Motta. (A) and Raging Bull, a biographical account of boxer Jake La Motta (B) up to Raging Bull, a biographical account of boxer Jake La Motta (C) in addition to Raging Bull, boxer Jake La Motta biographical account (D) to Raging Bull, a biographical account of boxer Jake La Motta (E) to Raging Bull, a biographical account recounting the life of boxer Jake La Motta

28. An MBA, while undoubtedly an essential degree for qualification for more satisfying, higher-paying jobs, remain an expensive and time-consuming endeavor. (A) remain an expensive and time-consuming endeavor (B) remain an endeavor both expensive and timeconsuming (C) remains an expensive and time-consuming endeavor (D) remains an expensive endeavor which is timeconsuming as well (E) is remaining an endeavor as expensive as it is time-consuming

29. While it is probable that a single mother language may very well have spawned all the world's languages, determining its specific origins has proven difficult for linguists. (A) (B) (C) (D) (E)

may very well have spawned all may very well to have spawned all is a valid possibility for having spawned all was spawning all spawned all

30. While opinions vary, William Shakespeare is considered by many literary scholars the greatest English writer of all time. (A) is considered by many literary scholars the greatest English writer of all time (B) is considered by many literary scholars to be the greatest English writer of all time (C) is considered by many literary scholars as being the greatest English writer of all time (D) is the greatest English writer of all time, as considered by many literary scholars (E) is considered as the greatest English writer of all time by many literary scholars

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Step 10 Workshop

SENTENCE CORRECTION WORKSHOP ANSWER KEY 1. D 2. E 3. A 4. B 5. B 6. D 7. C 8. C 9. B 10. A 11. C 12. A 13. C 14. B 15. C 16. B 17. D 18. B 19. D 20. C 21. D 22. D 23. E 24. D 25. D 26. E 27. D 28. C 29. E 30. A

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Step 11 Critical Reasoning

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Total PrepKit for the GMAT®

Step 11.1 Lesson

GENERAL OUTLINE

About one-third of the questions in the Verbal Section of the GMAT CAT are Critical Reasoning questions. These questions evaluate your ability to reason effectively in the areas of argument construction and argument evaluation. In this lesson, we’ll introduce the most common types of Critical Reasoning questions and show you specific strategies for answering each one of them.

THE FOLLOWING TOPICS WILL BE COVERED IN THIS LESSON Anatomy of a Critical Reasoning Question The Different Types of Inferences The MBA Center Approach to Critical Reasoning Questions The Eight Critical Reasoning Question Types

KEY TERMS Argument: Central to every Critical Reasoning question is the argument. An argument is an ordered line of reasoning composed of premises, assumptions, and a conclusion. Understanding the elements of an argument is essential to performing well in this section. Premise: Each Critical Reasoning argument contains at least one premise. Premises are pieces of factual information that provide evidence used to support the conclusion of the argument. For the purposes of Critical Reasoning arguments, premises are facts not subject to dispute. Conclusion: The conclusion is the endpoint of the line of reasoning of an argument. Think of it as the result of the argument. The line of reasoning leading to a conclusion is often where errors in logic are made. Assumption: Assumptions are unstated facts and logical connections in an argument. In order for the conclusion of an argument to be true, the assumptions upon which that argument is based must also be true.

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READY… Critical Reasoning questions test your ability to use basic logic to analyze and critique arguments made up of premises and conclusions. While they are a large part of your Verbal score, the approximately 14 Critical Reasoning questions in the Verbal Section test grammatical and verbal abilities much less than do the Reading Comprehension or the Sentence Correction questions. Rational thinking, or common sense, plus a competent display of the basic rules of logic are what these questions test. Indeed these types of questions are also part of the Analytical Section in the Graduate Record Examination (GRE), which is notoriously abstract and difficult. Critical Reasoning and Sentence Correction questions are the most important types of questions to learn and understand for the Verbal part of the GMAT. Critical Reasoning questions do not outnumber Reading Comprehension questions, but they do have a greater influence on your score. Remember too that your Verbal score depends heavily on the accuracy of your answers to the first five questions or so. (See “What Is This Thing Called the GMAT?” to review adaptive scoring.) Also, you are more likely to find Critical Reasoning questions at the beginning of the Verbal Section than the longer, more-involved Reading Comprehension passages. So, stay alert in this section, practice, and get to know these unique question types, which count for so much (you’ll soon see) on the GMAT. To begin the exam informed and with confidence is an excellent strategy. One more note: official test directions for this section state that no knowledge of the terminology and conventions of formal logic is presupposed. That may be true, but Critical Reasoning questions are not simple or familiar to most students and do require some introductory knowledge of logic in order to understand the structure of formal arguments and the question types.

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Step 11.1 Lesson

DIRECTIONS

Before starting the section, or by clicking on the Help button while answering a Critical Reasoning question, the following directions will appear: GMAT CAT – Section 4: Verbal End

Directions

When finished reading directions click on the icon below

Directions: Choose the best response for each question in this section. To review these directions for subsequent questions of this type, click on HELP.

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TRANSLATED FOR YOU

Each Critical Reasoning problem consists of a short, usually flawed, argument, a question about the argument, and five answer choices. No outside knowledge is necessary. Each question can be answered solely on the basis of the information contained in the argument.

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Score Value: 550

GMAT CAT – Section 4: Verbal

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In years past, professional baseball players lifted weights less but were also injured less often during games. Obviously, the more an athlete lifts weights, the higher the likelihood of injury.

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The conclusion above presupposes which of the following? ! (A) The increase in baseball injuries is due to a factor other than weightlifting. ! (B) The activities of baseball players represent those of athletes as a group. ! (C) Most baseball injuries today result from too much weightlifting. ! (D) There is no proven correlation between how much athletes lift weights and how likely they are to be affected by injury. ! (E) Weightlifting has always been common practice for professional athletes.

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QUESTION

Every Critical Reasoning question is made of three parts: an argument, a question, and answer choices. The Argument In years past, professional baseball players lifted weights less but were also injured less often during games. Obviously, the more an athlete lifts weights, the higher the likelihood of injury. The Question The conclusion above presupposes which of the following? The Answer choices (A) The increase in baseball injuries is due to a factor other than weightlifting. (B) The activities of baseball players represent those of athletes as a group. (C) Most baseball injuries today result from too much weightlifting. (D) There is no proven correlation between how much athletes lift weights and how likely they are to be affected by injury. (E) Weightlifting has always been common practice for professional athletes. The Argument: Each argument contains three main parts: premise, conclusion, and assumption. Take a look. 1. A premise or several premises. Here the premise is “In years past, professional baseball players lifted weights less and were injured less often during games.” A premise is a piece of information; it is factual, and for the purposes of the question, is not arguable. It is upon the premise(s) that an argument’s conclusion depends.

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Although Critical Reasoning is a part of your Verbal score, it is more a test of analytic abilities than it is of verbal abilities. You can find exactly the same kind of questions on other tests, such as the GRE, where they are in the "Analytic," and not "Verbal," section.

Step 11.1 Lesson

2. A conclusion. The conclusion constitutes the main point or opinion and is usually placed at the end of an argument – though on the GMAT it might also appear at the beginning or in the middle. Conclusions rely upon their factual premises for support but are themselves open to question and critique – your job, in fact, is to analyze their various flaws. A conclusion is sometimes easy to spot by noticing introduction words such as “thus,” “therefore,” “obviously,” or “clearly then.” But, the GMAT is a sophisticated test, and in general trigger words like these are rarely found. What is a conclusion then? A statement or sentence that cannot stand on its own. 3. An assumption. An unstated premise or idea that must be true for an argument to be valid. As these Critical Reasoning questions are constructed, an assumption, though unstated (does not appear in the text), is in fact part – the unstated part – of an argument. Some examples soon to come will illustrate this for you. 4. Some arguments also include a fourth element: the inference. You might think of an inference as a reasonable guess or estimation based on the facts, or premises, given to you. It is the result of the type of reasoning that Sherlock Holmes was so proud of – deduction. The most important concept here is that inferences on the GMAT are obvious, undeniable truths which the argument provides but are not directly stated. Get to know inferences very well for they appear in one form or another throughout the Verbal Section. One more note: though questions that test your ability to understand and recognize an assumption are not rare in this section, they’re not to be feared either. Once you’ve devoted the time to know them well, in class and in practice on your own, you’ll see assumptions for what they are: standardized, or uniform, and therefore knowable. The Questions: Eight different question types have been identified in this section and each type of question requires a specific approach. Because of the variety of available question types, you must concentrate on understanding the nature of each question. Stick closely to the text and determine precisely what you’re being asked to do. You might be asked to identify assumptions, to supply a conclusion, to strengthen, or provide support for, an argument, or to choose an answer choice that weakens, or does not provide support for, an argument. More details and question types to come. The Answer Choices: Unlike in Sentence Correction, no answer choice patterns are found in Critical Reasoning. The content of the answer choices is never the same – it varies according to the argument and question type. Answer choices must always be read very carefully and you must read each and every one. On more difficult questions a close comparison (after Process of Error Identification) between two possible answer choices is sometimes necessary, indeed unavoidable. As the language used is often dense, formal, and unfamiliar, get in the habit of patient, thorough evaluations of Critical Reasoning answer choices, questions, and arguments.

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DRILL 1 Directions: In the exercise below there are six statements containing assumptions. Your job is to identify and write down the assumption contained in each statement. When you are finished, compare your answers with those in the key below. 1- The Winavers must be planning to buy a new house, since they visited the office of the local real estate agent yesterday. 2- John’s grade point average is below 3.2, so if he wants to enter Graduate School he should apply as early as possible. 3- Unemployment in France is due to a lack of economic activity, so if the government reduces the length of the work week, the unemployment rate should decrease. 4- Professor Sully only gives good grades to European students. After all, last semester he gave good grades to Hubert and Elio who are both Europeans. 5- Anyone who wants to work as a strategy consultant wants to pursue an MBA ranked in the top ten. Giles wants to apply to Wharton, which is always ranked among the top ten MBA programs in the US. Therefore, Giles wants to become a strategy consultant. 6- Many people who describe themselves as painters are not painters by profession, since painting is not their main source of income.

Conclusions can appear at the beginning (first sentence), the middle (buried), or the end (last sentence) of an argument. Concentrate your efforts in this section on learning to pinpoint a conclusion—it does not stand on its own, but must logically follow from the meaning (stated or implied) of a statement or assertion.

Assumptions: 1- All people that visit the local real estate agent’s office want to buy new houses. 2- Applying early to graduate school makes admission easier. 3- Diminishing legal work duration increases economic activity. 4- Hubert and Elio were the only students that received good grades. 5- All who apply to Wharton want to become strategy consultants. 6- To be a painter by profession one must have painting as one’s main source of income.

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Step 11.1 Lesson

AIM… THE DIFFERENT TYPES

OF ASSUMPTIONS

Once you've learned to find the conclusion and the premises of an argument, you’ll improve your analytical skills by learning to take apart arguments step by step, looking for their logical structure (premises, conclusion) and their assumptions. If you learn to recognize the logical flaws (the assumptions behind the inference) quickly and easily, you will find that the actual questions asked on Critical Reasoning are, for the most part, straightforward.

A) ANALOGY An analogy argument is an argument in which the connection between the premises is made by analogy. For instance, take a look at the following argument: Score Value:

One way to recognize Analogy arguments is to pick out a key term in the conclusion that is not included in the premises. In the example here, “human beings” is the new term in the conclusion.

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Even though no actual cases have ever been documented, we know that human beings could transmit rabies to other human beings through a bite, since dogs can transmit rabies to all mammals through a bite. Premise: Dogs can transmit rabies through their bite. Conclusion: Human beings can transmit rabies through their bite.

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Where is the logical gap in this argument? Once again, there is something new that is introduced in the conclusion: the idea of human beings. Where did this idea come from? It doesn't exist anywhere in the premises since the premise is about dogs. How can we draw any conclusion at all about human beings based on what is true of dogs? Only if we assume that human beings are similar to dogs, with regard to the potential of their bite to transmit diseases like rabies. This argument thus rests on the assumption that human beings and dogs are analogous with regard to their potential to spread diseases through their bite. In order for this argument to be strengthened, evidence that supports this assumption (such as: human beings and dogs both carry rabies in their saliva; human beings and dogs can both transmit hepatitis through a bite, etc...) is necessary. To weaken this argument, evidence that denies this analogy between human beings and dogs (such as: human beings, unlike dogs, do not carry rabies in their saliva; the teeth of human beings do not penetrate as deeply as do those of dogs, etc...) needs to be provided.

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B) THE

PAST PREDICTS THE PRESENT/FUTURE

This sort of argument assumes that the way something happened in the past will be analogous to how it will happen in the present/future; or that the conditions in the past are similar enough to predict an outcome for the present/future. Here is an example: GMAT CAT – Section 4: Verbal

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When we hired Marizonian immigrants 10 years ago, the project was a failure. They had problems speaking English and had difficulties adjusting to American life, both of which made them unreliable workers. For all these reasons, we should not have Marizonian immigrants in our factory.

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Conclusion: We should not hire Marizonian immigrants to work in our factory. Premise: When we tried doing this 10 years ago, it was a miserable failure. Premise: Their lack of knowledge of English and their difficulties in adjusting to life in the U.S. made them unreliable workers.

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In this argument, the logical gap is a bit subtle. Note that the conclusion is in the present tense, and is a statement about the present: that we should not hire Marizonian workers today. On the basis of what evidence? Ten years ago it didn't work. But how can we draw a conclusion about what is the current situation based on evidence from 10 years ago? Only if we believe that the conditions are approximately the same today as 10 years ago, and that therefore what happened 10 years ago will repeat itself again in the present day. To strengthen this argument, give evidence to show that the conditions are approximately the same today as 10 years ago, and that therefore the past will accurately predict the present; to weaken this argument, give evidence to show that today the conditions are different, and that therefore the past may not accurately predict the present or future.

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Step 11.1 Lesson

C) CAUSAL

ARGUMENTS

A causal argument is an argument that concludes that X is responsible for (causes) Y, based on the evidence of a temporal relation between X and Y – that X accompanies Y, or that X precedes Y. For instance, we might say that because the doorbell rings when you push the button, that therefore your pushing the button causes the doorbell to ring. The problem, of course, is that not every temporal relation implies a causal relation for it's also possible that two things occur at the same time simply out of coincidence. If lightning strikes just as I step out the door, this does not give me much reason to believe that my stepping out the door caused the lightning. Thus, a temporal relation (in which one development directly precedes another, or in which two developments occur simultaneously) does not by itself justify the conclusion that there is a causal relationship. Therefore, if an argument includes only evidence of a temporal relation and draws the conclusion that there is a causal relationship, the author is making two assumptions: that the relation is, in fact, a causal relation and not mere coincidence, and that there is no other possible cause. (Remember this. It will be important when we see weaken/strengthen questions.) Here is one example. GMAT CAT – Section 4: Verbal

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The number of crimes committed in Los Angeles is highest during school hours (between 8:00 a.m. and 3:00 p.m. on weekdays). On any one given day, over 10,000 teenagers fail to attend school, and are unaccounted for during these hours. Therefore, it is these teenagers who are responsible for the high crime rate.

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Premise: Crime is highest during school hours. Premise: During school hours, many students skip school. Conclusion: These students are responsible for the crime.

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Phineas loves causal relationships: the leap from a temporal correlation in the premises to a causal correlation in the conclusion is the most common argument flaw on the GMAT.

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Here we are presented with events that occur at the same time: during the same period (8:00 a.m. - 3:00 p.m. weekdays), two things happen: a large number of crimes are committed, and a large number of students skip school. But this could be a mere coincidence of unrelated events. There is no evidence to show that these two phenomena have a more substantial, that is, less circumstantial relationship. There is no reason, based on the mere fact that these two things happen together, to believe that one is responsible for the other. Therefore, the conclusion rests on the assumption that this is not a mere coincidence, and that teenagers who skip school are, in fact, responsible for this crime. It is possible to strengthen this argument by referring to further evidence that teenagers who skip school commit crimes, and it is possible to weaken this argument with evidence that this is a mere coincidence.

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D) WOULD

THE PROPOSED SOLUTION SOLVE THE PROBLEM?

Sometimes an argument presents a problem and proposes a solution to the problem. But it isn't always certain that the proposed solution will, in fact, solve the problem. (In some cases, the proposed solution might even make the problem worse!) In this sort of case, the argument could be weakened by showing that the proposed solution does not, in fact, solve the problem that it is supposed to solve. This kind of problem is very close to a causal argument because it depends, effectively, on the factors that cause the problem in the first place. To respond to such a question does not require a thorough investigation into the causes: all we need to show is why the proposed solution might not work: GMAT CAT – Section 4: Verbal

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The number of crimes committed by adolescents in Los Angeles is highest during those hours when they should be in school (between 8:00 a.m. and 3:00 p.m. on weekdays). If we want to stop teenage crime, we should take action to ensure that teenagers do not skip school.

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Premise: Teenage crime is highest during school hours, when teenagers are absent from school. Conclusion: Teenage crime will be stopped by making sure that teenagers attend their classes.

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Some Critical Reasoning arguments look eerily similar to Problem Solving word problems. Historically, GMATs averaged 2 to 3 math-heavy Critical Reasoning questions per section.

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The problem presented in this argument is that of teenage crime, which happens mostly during school hours, by students who skip school. The author then proposes that we stop teenage crime by making sure that teenagers attend school. But do we know that this solution will stop crime? Because we don't know what is responsible for teenage crime, how do we know that making them go to school will stop it? The thinking goes: if teenagers are in school, they probably cannot at the same time commit crimes. But maybe, in the absence of opportunities to commit crimes during school hours, they will simply commit more crime after school, and the number of crimes may remain unchanged. Thus the proposed solution may not, in fact, solve the problem. We could weaken this argument by giving any evidence to show that the number of teenage crimes could – introducing an element of doubt – stay the same, even if teenagers are forced to attend their classes.

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E) EQUIVALENCE

OF DATA

(# = %)

A common type of argument is one that mixes real values and percentages or rates. Have a look at the following argument:

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Because of a recent crackdown on school absences, the number of crimes committed by teenagers during school hours (8:00 a.m.3:00 p.m. on weekdays) has dropped dramatically. It follows that a higher percentage of teenage crime is committed outside of school hours than during school hours.

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Flawed arguments don’t necessarily have false conclusions; an argument is considered flawed if readers are not provided with enough information to judge for themselves, even if the conclusion is accurate.

Step 11.1 Lesson

Premise: The number of crimes committed during school hours has dropped. Conclusion: The percentage of crimes committed is lower during school hours than outside of school hours.

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Once again, take careful notice of the different kinds of data presented. The conclusion states that the percentage of crimes during school hours is lower than the percentage outside of school hours. The premise, however, states only that the number of crimes during school hours has dropped. This does not necessarily imply a change in the percentage. If, for instance, the number of crimes outside school hours dropped as well, then the relative percentage of crimes committed during and outside of school hours might remain the same. We simply don't have the information required to draw any conclusion at all about the percentages of crimes committed during and outside of school hours.

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F) PARTICULAR

TO GENERAL

This sort of argument draws a conclusion about what is true for each of the members of a class of things, based on what is true for one specimen or member of that class. That is, it makes a generalization based on what is true in a single, or particular, case. In any such argument, it has been assumed that the generalization is valid, and that what is true of one member of the class is equally true of all of the other members of the class. Here is a subtle example of an argument that contains, among other things, a shift from the particular to the general: 01:05

GMAT CAT – Section 4: Verbal

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John must be allergic to strawberries. He suffered an extreme allergic reaction the other day after a meal of whipped cream and strawberries. John's doctor said that John's allergic reaction was certainly caused by something that John ate. John's mother certifies that he's not allergic to whipped cream. So, John must be allergic to strawberries.

Although only one assumption is tested per question, it’s good practice to identify as many as you can in each of these sample questions: the more you do, the easier it gets.

Premise: John suffered a bad allergic reaction the other day after eating whipped cream and strawberries. Premise: The doctor said that the allergic reaction was definitely due to something that John ate. Premise: We know that John is not allergic to whipped cream, Conclusion: So John must be allergic to strawberries.

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This argument relies on a couple of major assumptions. First, there is the causal assumption that it really was the strawberries that caused the allergic reaction and not something else. Even though we know that it wasn't the whipped cream that caused his reaction, there are still other possibilities: perhaps his reaction was due to something else that John ate during the day. We could therefore weaken this argument by citing some explanation for John's allergic reaction other than strawberries. But even if we know that it was the strawberries that caused his allergic reaction, there is still another major assumption in this argument. Note that the argument concludes that John is allergic to strawberries in general, which means all strawberries. But all we know from the premise is that John had an allergic reaction to these particular strawberries. Thus the argument generalizes, and assumes that if he's allergic to any one strawberry, then he's allergic to all of them. We could thereby weaken this argument in two ways: by showing that the particular strawberries that John ate are idiosyncratic in some way (perhaps a pesticide was used on the strawberries, or perhaps some chemical reaction occurred between the strawberries and the whipped cream that created a substance to which John is allergic), and that John's reaction to these strawberries may not imply that he's allergic to all strawberries.

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Step 11.1 Lesson

THE WRONG ANSWER FACTORY We have analyzed the different types of inferences contained in the reasoning of formal arguments, and suggested how to strengthen or weaken them. Equally important to scoring higher on this section is getting to know how wrong answer choices are made. You’ll soon see that Phineas has set up standardized mistakes to trick you and that the answer choices are not written randomly. The test taker's dilemma: Most people choose wrong answers for one of two reasons: 1. They ignore slight but significant differences between answer choices. 2. They miss the flaw in the argument. Let's return to Example 1: The conclusion above presupposes which of the following? Thus, we are looking for an assumption that must be true for the argument to work. Now, look back at the first argument: In years past, professional baseball players lifted weights less but were also injured less often during games. Obviously, the more an athlete lifts weights, the higher the likelihood of injury. Which part of the argument is the conclusion? What is the flaw in the author's reasoning? Answering these two questions before going to the answer choices can help you to predict the answer (or something close to the answer). Occasionally an argument will not be flawed, in which case you should go directly from the argument to the answer choices. Now let's look at the choices: (A) (B) (C) (D)

The increase in baseball injuries is due to a factor other than weightlifting. The activities of baseball players represent those of athletes as a group. Most baseball injuries result from too much weightlifting. There is no proven correlation between how much athletes lift weights and how likely they are to be affected by injury. (E) Weightlifting has always been common practice for professional athletes. How does Phineas design the wrong answer choices? As with the other sections, he constructs answer choices that look tempting but actually contain distorted or irrelevant information. In Critical Reasoning, the choices that include irrelevant information are outside the scope of the argument. Choice (E), for example, is outside the scope of the argument. Some choices are within the scope, but distort information in the passage or stretch logic too far. Choice (C), for example, is tempting, but the word "most" is a distortion. We do not know how many baseball players are injured because they lift weights too much, only that they lifted weight less in the past.

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THE MBA CENTER APPROACH

TO

CRITICAL REASONING QUESTIONS

Here is our method for coping with Critical Reasoning questions. Step 1: Read the question first. Reading the question tells you what type of information you are looking for in the argument. Sometimes it will be an assumption, sometimes a conclusion, an inference, or a weakness. The most common types of question are: - Which of the following can be most reasonably inferred from the information above? Translation: What is missing in the passage above? - Which of the following is an assumption made in the passage above? Translation: Find the answer that supports the logic of the conclusion. - Which of the following statements, if true, would be a valid objection to the conclusion drawn above? Translation: Choose the answer that weakens the conclusion of the passage above. Step 2: Read the argument. Each time you read an argument you should identify the premise(s), the conclusion, and the flaw (the assumption). Example: GMAT CAT – Section 4 :Verbal

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Increased competition among certain grocery stores has resulted in each store finding new methods of attracting customers. For example, Val-U-Mart is offering a deal in which every time a customer purchases an item at full retail price, he will receive a coupon entitling him to purchase the same item at half the retail price the next time he comes to the store. Therefore, Val-U-Mart’s profit will increase as customers are drawn back into the store.

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Premise : Increased competition among certain grocery stores has resulted in each store finding new methods of attracting customers. Premise : For example, Val-U-Mart is offering a deal in which every time a customer purchases an item at full retail price, he will receive a coupon entitling him to purchase the same item at half the retail price the next time he comes to the store. Conclusion: Therefore, Val-U-Mart’s profit will increase as customers are drawn back into the store. Assumption: Val-U-Mart will be able to make a profit offering products at half retail price.

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Some questions ask you to complete the passage: for these, the premise or conclusion required for completion will be located in the answer choices instead of the argument.

Step 11.1 Lesson

Step 3: Paraphrase the argument using your own words. The idea is to gain time and to be able to compare the reasoning in the argument with the answer choices. Phineas’ style is heavy, wordy, complex. The best way to understand the argument is to restate the main idea from the premises in the most simple manner using your own words.

DRILL 2 DIRECTIONS: PARAPHRASE

THE STATEMENTS BELOW.

1. Most airline passengers don’t pay attention when flight attendants give safety instructions before take-off. Unless airlines find a more effective means of communicating to their passengers, most passengers will not know what to do in case of an on-board emergency. Paraphrase: ______________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ 2. In an effort to reduce daily commuter traffic entering a certain city, the city government plans to raise the tolls on all major roads that have access to the city. The government plans to use part of the revenues generated by the tolls to modernize commuter rail systems. However, critics object that under this plan drivers will unfairly pay for a service that is beneficial only to those who ride trains. Paraphrase: _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________

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3. A rock-and-roll band recently won a lawsuit against a rap artist who had ‘sampled’ the rock band’s song, using some of the music from the song in one of his or her own. Subsequently, a law was passed requiring rap musicians wishing to 'sample' to pay royalties to the original artists. This will raise the cost of production for rap albums, and therefore discourage the music industry from signing rap acts. Paraphrase: _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ 4. A scientist planted two groups of plants under identical conditions of light, temperature, humidity, and moisture. Every day he would play sound effects of thunderstorms to one of the groups of plants and sounds of city traffic to the other. The group to which he played thunderstorms all died within a few weeks, but the other group thrived during the experiment. He therefore concluded that the sound of city traffic is more effective for helping plants grow than is the sound of thunderstorms. Paraphrase: _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ 5. In normal conditions, increased competition among businesses leads to lower prices. In midtown Manhattan, however, the prices of audiovisual equipment are, on average, higher than those in most other areas of America, despite the fact that there is a high concentration of stores specializing in audio-visual merchandise. Paraphrase: _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________

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Step 11.1 Lesson

Step 4: Predict the answer. Making a prediction before going to the answer choices saves you from confusion once you do start to compare answer choices. Remember, four answer choices are designed to test your concentration in the face of temptation. Take a moment between understanding the argument and evaluating the answer choices to form an idea of what you think the best answer choice should look like: it should be well-reasoned and strictly relevant to the text. Example: Director of airport security: Because of a recent increase in terrorist attacks, we have increased security measures at all terminals. We now require that all passengers show two forms of identification before boarding, and we x-ray and screen all carry-on luggage thoroughly. Which of the following, if true, most seriously weakens the viability of the airport’s plan? Make your predictions: 1. ______________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ or 2. ______________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ or 3. ______________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ Now take a look at the answer choices and compare them with your predictions. Did you guess right? If not, how close to the right answer were you? (A) Airport regulations had previously required passengers to show only one form of identification. (B) New government regulations state that all airport personnel must undergo a thorough screening process before they start work. (C) The rate of terrorist incidents has increased dramatically over the past several years. (D) Several recent terrorist incidents have resulted from explosives hidden in luggage stored underneath the plane. (E) The airport has never been victimized by a terrorist incident. (D) is the best answer.

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Step 5: Use Process of Error Identification to eliminate the wrong answers. The Process of Error Identification is the easiest way to find the “best answer.“ To narrow down the answer choices, you should identify:

If you are stuck on a question and must guess, always choose the plain and simple answer choice over the complicated one.

- Answer choices outside the scope of the argument - Answer choices that distort or exaggerate ideas from the argument Score Value: 600

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GMAT CAT – Section 4: Verbal

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Ambi Inc. and Robin Corp. manufacture bargain stereo equipment. Both companies use the same professional shipping service, and for both companies shipping costs account for eight percent of the total expenditures. Ambi Inc., in an effort to gain an advantage over Robin Corp., plans to begin to ship their merchandise themselves. Which of the following, if true, would most call into question the viability of the plan of Ambi Inc.? (A) Other shipping companies charge higher rates than the company employed by Ambi Inc. and Robin Corp. (B) The shipping company makes a profit of over 10 percent on its dealings with Ambi Inc., but over 12 percent on its dealings with Robin Corp. (C) The shipping company used by both companies offers special deals for bulk delivery. (D) Projections indicate that Ambi Inc.'s shipping costs under its new program would amount to eight percent of its total expenditure, in addition to a substantial initial cash outlay. (E) Robin Corp. ships materials farther than does Ambi Inc.

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Every word is important in a Critical Reasoning argument. There are no details which are unimportant. This is the principal difference between close critical reading and selective comprehensive reading on the GMAT.

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Step 11.1 Lesson

FIRE! We have seen that the answer choices and the arguments are written according to standardized types. In this part of the lesson, we will show you that each question type is standardized too and that there are 8 types of questions for GMAT Critical Reasoning arguments. Each question type has its own traps, and a specific strategy is required to ace each one of them.

A) DRAW

A

CONCLUSION

Some Critical Reasoning questions do not have a conclusion. For this type of question you are asked to supply a possible conclusion. The conclusion that you choose must closely and logically follow from the premises in the argument. Score Value: 510

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GMAT CAT – Section 4: Verbal

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A consumer’s advocacy group recently reported the results of a study concerning the deregulation of the airline industry. Deregulation has allowed the airlines greater flexibility in setting prices and selecting routes, and has allowed for more mergers between airlines. The report showed that prices have dropped on most flights without a decrease in flight availability or safety. At the same time airline profits are higher than ever. If the results of the study are correct, which of the following can be properly concluded about the effects of airline deregulation? (A) The airlines benefited from deregulation more than did the consumers. (B) Some airlines will soon go out of business because of decreased revenue from lower ticket prices. (C) The government will deregulate more industries following the success of airline deregulation. (D) Deregulation of airlines was financially successful both for the airlines and for the consumers. (E) Further decreases in ticket prices will start to erode the profits gained by airlines through deregulation.

Be wary of unjustified, illogical, or incorrect comparisons in the answer choices and choices that make predictions about the future. Test

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Paraphrase the premises: Deregulation in the airline industry was beneficial to both airlines and consumers, though we cannot say which group benefited more.

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Critical Reasoning

B) ASSUMPTION QUESTIONS Understanding assumptions is crucial to doing well on Critical Reasoning. Assumptions are unstated premises that are necessarily true for the argument to work. Questionable assumptions tend to make arguments weak, so finding the flaw in an argument is often the same thing as finding a questionable assumption. Score Value: 650

GMAT CAT – Section 4: Verbal

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Shortly before the elections in City C, many eligible voters polled stated they objected to the mayor's plans for the police force. Yet the mayor was elected by a 60 percent majority. So, at least 60 percent of the voters supported the mayor's plans for the police force.

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The conclusion of the argument above depends on which of the following assumptions? ! (A) People who object to a politician's position will not vote for that politician. ! (B) Some of the people in the poll have some involvement with the police force. ! (C) Everyone who voted for the mayor did so primarily because they didn’t agree with his plans for the police force. ! (D) Sixty percent of the voters elected the mayor because of his plans for the health care system. ! (E) Most of the people polled did not vote in the election.

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It is especially useful on assumption questions to try to predict the answer before going to the answer choices. Look for something in the conclusion that goes further-stretches logic a bit more-than the evidence justifies.

Premise 1:

Before the election many eligible voters stated they objected to the mayor’s plans for the police force. Premise 2: The mayor was elected by a sixty percent majority. Conclusion: Sixty percent of voters supported the mayor’s plans for the police force.

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Step 11.1 Lesson

C) STRENGTHEN

THE

ARGUMENT

Strengthen-the-argument questions accept as true the built-in, and more than likely flawed, assumption in the argument. For this question type, look for an answer choice that fills a gap in logic or provides further evidence to support the validity of the conclusion. Score Value: 590

GMAT CAT – Section 4: Verbal

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Students at a certain university must take the equivalent of two semesters of foreign language which can be done in a one-semester intensive class or two semesters paced normally. An academic investigative committee found that the students who take the intensive class tend to achieve a higher level of proficiency than do those in the two-semester class and therefore recommended that the university eliminate the two-semester class.

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Instituting the recommendation of the investigative committee would be most likely to result in improved foreign language proficiency of its students if which of the following were true?

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Necessary vs. Sufficient The best answer to an assumption question doesn’t have to be sufficient to justify the conclusion. It only has to be necessary for the conclusion to work.

! (A) The textbooks used in the intensive courses are not the same as those used in the two-semester courses. ! (B) Students who chose the intensive courses generally did so because they had some prior knowledge of the foreign language. ! (C) There are no significant differences in the quality of students taking the intensive courses versus those taking the twosemester courses. ! (D) An intensive course in a foreign language makes it more difficult for a student to learn vocabulary and practice speaking. ! (E) Students who take intensive mathematics courses tend to get better grades than do those who take regular-paced mathematics courses. Answer Time Time

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Premise 1:

Students can take a 1-semester intensive or 2-semester regular foreign language class. Premise 2: Students in the 1-semester intensive class learn more than do students in the 2-semester class. Conclusion: The university should eliminate the 2-semester class (to improve the foreign language proficiency of its students).

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Critical Reasoning

D) WEAKEN

THE

ARGUMENT

Weaken-the-argument questions are by far the most common question type in Critical Reasoning. For this type of question you must invalidate – find evidence that does not support – the conclusion. To ace this type of question, you must identify the assumption in the argument, the weak spot, and find an answer choice that does not restate, strengthen, or distort it. Score Value: 600

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GMAT CAT – Section 4: Verbal

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In 1991, produce growers began using a new, inexpensive pesticide, provoking many objections that they would damage both the environment and the produce they were growing. However, the fears have proven unfounded, as, through 1996, produce prices had dropped and no ill effects had been reported. Which of the following, if true, would be the strongest objection to the argument above? (A) Consumption of the produce declined from 1991 to 1993, but rose sharply from 1994 to 1996. (B) Several areas in which use of the pesticide was forbidden have also experienced a drop in produce prices. (C) The amount of produce grown in 1991 was larger than that of 1996. (D) The time since the beginning of the use of the pesticide has been too short to allow some of the predicted effects to occur. (E) Since 1992, new pesticides have been developed that scientists agree are relatively risk-free.

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Premise 1: Premise 2: Premise 3: Conclusion:

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Weaken-the-argument questions almost always have at least one answer choice that strengthens the argument. Likewise, strengthenthe-argument questions almost always have at least one answer choice that weakens the argument. In this case, (E) is a choice that comes close to strengthening the argument (it doesn't exactly strengthen it, but it supports the general idea that pesticides can be risk-free).

Growers began using cheap, new pesticide in 1991. Produce prices dropped. No ill effects were reported (through 1996). Fears that the produce and the environment would be damaged are unfounded.

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Step 11.1 Lesson

E) INFERENCE QUESTIONS Inference questions ask you to infer something from the passage other than an assumption or the conclusion. The correct answer will contain an inference that can be logically and safely drawn from the original argument. The best answer paraphrases words and ideas from the text and contains an inference just one step in logic away from the message of the text. Score Value: 650

GMAT CAT – Section 4: Verbal

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Being in debt does not necessarily restrict one's spending power. If it did, people in debt would be unable to make large purchases and would spend less money than people not in debt. In fact, when the spending habits of people in debt are compared with those of people who are not in debt, no such pattern emerges.

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If the statements above are all true, which of the following can be inferred? ! (A) Merchants make more money selling to people in debt than they do to people not in debt. ! (B) People who are in debt do not necessarily stay that way for prolonged periods of time. ! (C) If a graph were made of people's debts and their spending habits, those who are most in debt would be demonstrated as making the largest purchases. ! (D) Reliable comparisons between those in debt and those not in debt are not available. ! (E) Going into debt often does not deter people from going into greater debt.

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Conclusion ≠ inference. An inference is always true whereas a conclusion is not necessarily true.

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Note that this argument does not claim that people in debt spend more money or make larger purchases than those not in debt. It claims only that they don't spend less. Phineas will try to trick you into making hasty assumptions or distortions. Can you identify which choices do this? Premise 1:

If debts restricted spending powers, people in debt wouldn’t be able to make large purchases. Premise 2: People in debt do make large purchases. Conclusion: Debts don’t necessarily restrict spending power.

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Critical Reasoning

F) EXPLAIN

THE (APPARENT)

CONTRADICTION

For this question type, you will be given an argument with two statements that are apparently contradictory. Often the contradiction will be in the form of two trends that seem to oppose each other. In order to ace this type of question, clearly identify the apparent paradox. The best answer is the one that explains – provides a logical link for – how the two apparently paradoxical positions can be reconciled or both be true. Score Value: 490

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GMAT CAT – Section 4: Verbal

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Try to predict a possible answer before looking at the choices.

Studies show that more and more Americans are removing meat from their diets. Yet sales of meat increased in the United States last year. Which of the following, if true, could best explain the simultaneous decrease in the number of Americans who eat meat and increase in sales of meat? (A) Last year, Americans imported more meat than they had in the previous year. (B) Those Americans who ate meat consumed more per person than they had the previous year. (C) The number of Americans who had stopped eating meat during the previous year was smaller than the number of Americans who started eating meat last year. (D) The global meat industry grew in the previous year. (E) The studies all used large samples that were representative of the general population.

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If you find the answer you predicted, quickly scan the rest of the choices to make sure there is not something better (this is not necessary on math sections, but it is useful for all the verbal sections). All the answer choices are in competition for your attention.

Premise:

More Americans are removing meat from their diets (according to studies). Premise: Sales of meat increased in the United States. Conclusion (implied): There is a contradiction.

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G) COMPLETE

THE

PASSAGE

Some questions ask you to complete a passage. For these types, the question comes before the argument, and the end of the argument is usually broken off in mid-sentence. The answer choice that best completes the passage might provide a missing premise, state the conclusion, or connect the premises to the conclusion. Score Value: 680

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GMAT CAT – Section 4: Verbal

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Which of the following best completes the passage below? At a recent meeting of a company's top management, most of the managers present argued that since the black-and-white television market as a whole was rapidly shrinking, the company should reduce production levels for all models of black-and-white televisions. What must be shown, of course, in order for the company not to lose profits from hasty decision making, is that __________________________

Don't make associations based on your own knowledge that are not made in the passage. Color televisions and computers have nothing to do with this passage.

(A) the market for color televisions is growing at a rate faster than the market for black-and-white televisions is shrinking. (B) none of the black-and-white televisions the company currently sells match the technological standards of modern color televisions. (C) computer screens will eventually be capable of performing all functions normally performed by televisions. (D) none of the models of black-and-white televisions manufactured by the company are popular enough to sustain high profits at current production levels. (E) the company has the engineers and production equipment necessary to mass produce state-of-the-art color televisions.

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Premise: The black-and-white television market is shrinking. Conclusion (of the company management): We should reduce production levels of all models of black-and-white televisions.

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Critical Reasoning

H) "EXCEPT"

QUESTIONS.

An "Except" question differs from a strengthen/weaken question in that all the wrong answer choices satisfy the question's statement; only the correct answer choice does not. In other words, if a question says “all the following strengthen the conclusion EXCEPT,” then the correct answer choice simply fails to strengthen rather than actively weaken. These questions can also be phrased using “NOT” or “LEAST”. The best approach to an EXCEPT question is Process of Error Identification. Score Value: 550

GMAT CAT – Section 4: Verbal

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Books put on prominent display in bookstores, either in the store windows or near the cashiers, generally outsell the books on other shelves. A publishing company, disappointed by the poor sales of a new novel by a famous author, complained to a leading chain of bookstores that the novel would have been a bestseller had it been prominently displayed. . All of the following, if true, would support the publisher's claim EXCEPT:

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! (A) Many books which do not sell well on regular shelves become popular after they are put on prominent display. ! (B) People who shop in bookstores often do not have specific books in mind when they enter the store but buy books whose cover catches their eye. ! (C) Managers of bookstores only put books on prominent display that are already bestsellers. ! (D) Three of the author's recent books were bestsellers. ! (E) The new novel received favorable reviews in newspapers and on radio upon its release.

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I’ll figure it out later For strengthen- or weakenthe-argument questions which have “excepts” in them, mark a little “w” next to each choice that weakens, an “s” next to the choices that strengthen, and an “n” next to the choices that are neutral or have no effect. This way you don’t have to keep in mind exactly what you are looking for until you have evaluated each choice.

Premise: Premise: Premise:

Books on prominent display outsell other books. A novel by a famous author was not put on display. The novel sold at levels disappointing to its publishing company. Conclusion (of the publishing company): The novel would have been a bestseller had it been put on prominent display.

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Step 11.1 Lesson

SUMMARY -There are about 14 Critical Reasoning items on the GMAT CAT. - Each Critical Reasoning item consists of a short, usually flawed, argument, a question about the argument, and five answer choices. The section requires no outside knowledge. Each question can be answered solely on the basis of the information in the argument. - Each item is made of : -

An argument A premise or premises A conclusion An inference (not always) An assumption A question Five answer choices

- A premise is a piece of evidence, a conclusion is the main idea of the argument and an interpretation of the premises, and an inference is an unstated idea that follows logically from the reasoning of the premises. Most arguments contain an assumption that makes them logically unsound. - The wrong answer choices are not written randomly. Therefore the Process of Error Identification is the best way to find the “best answer.” - Use the MBA Center Five-Step Approach -

Step Step Step Step Step

1: 2: 3: 4: 5:

Read the question. Read the argument. Paraphrase the main idea using your own words. Predict the possible answer. Use Process of Error Identification to eliminate wrong answer choices.

- There are 8 question types. A specific technique is required to ace each one of them.

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* Draw a conclusion

* Inference

* Assumption

* Explain the (apparent) contradiction

* Strengthen the argument

* Complete the passage

* Weaken the argument

* EXCEPT questions

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Critical Reasoning

CRITICAL REASONING LESSON ANSWER KEY 1. 2-8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

B N/A D D A C D E B D C

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Critical Reasoning

HOMEWORK/PRACTICE TEST CRITICAL REASONING ANSWER GRID B !

C !

D !

E !

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Step 11.2 Homework

End

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GMAT CAT — Section 4: Verbal

TIME — 25 MINUTES 16 QUESTIONS Directions: In this section, each question follows a brief passage. Select the best answer of the choices given.

Directions

When finished reading directions click on the icon below

Dismiss Directions ➩

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Critical Reasoning

1. A very popular, though relatively recent, theory postulates that the extinction of the dinosaurs resulted from climate changes caused by three large meteors entering the Earth’s atmosphere near the end of the Mesozoic Age. Which of the following statements, if true, could be used in an argument against the theory? (A) The dinosaurs were cold-blooded, meaning their body temperature was regulated by external temperature. (B) Archaeologists have located several large craters, probably caused by falling meteors, that they have estimated were formed during the Mesozoic Age. (C) Comparisons between fossils found in different areas of the planet indicate that the dinosaurs all became extinct within a short time frame. (D) Scientists have estimated that numerous species of flora intrinsic to the biosystem in which the dinosaurs participated became extinct shortly before the time at which the meteors are supposed to have struck the Earth. (E) In existence throughout the Mesozoic age, and long beyond it, were prehistoric mammals, who were warm-blooded, meaning their body temperature remained constant regardless of external factors.

3. A beverage company recently hired a celebrity to introduce a new soft drink in radio and television advertisements. Sales of the new soft drink have exceeded all expectations, and the beverage company has therefore decided to hire celebrities to endorse all its older, well-known beverages. The company should therefore expect to see greatly increased profits in the future. The passage, in arguing that the company’s profits will rise greatly, assumes all of the following EXCEPT: (A) The costs involved in the media campaigns will be significantly less than the increase in sales due to celebrity endorsements. (B) Most of the customers buying the new soft drink did not stop buying other brands from the same company to do so. (C) Celebrity endorsements will be more effective than the advertising methods currently employed for the company’s better known beverages. (D) The sales of a well-known product can be increased by a celebrity’s endorsement. (E) All the older beverages sold by the company will be at least as popular as the new beverage once they are endorsed by celebrities.

2. Company K claims that although the wholesale price of its new product B is less than its manufacturing cost per unit, the price is appropriate because people who buy product B will also buy company K's expensive and highly profitable product A. This could be most clearly demonstrated by _________ . Which of the following best completes the passage? (A) showing that none of company K's competitors manufacture products similar to product B (B) the fact that sales of product A have been steadily rising for the last four years (C) examining the likelihood of customers who already buy product A to buy product B (D) by comparing the sales of product A in markets where product B is available and markets where product B is not available (E) measuring the market share of product A relative to its production costs in recent years.

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4. An athlete, in order to excel in a sport, must have a natural ability for that sport or spend a great deal of time practicing. Thus if you are a college student and your first priority is getting good grades, you should not do a sport unless you have a natural ability for that sport. The argument above assumes all of the following EXCEPT: (A) College students should not do sports unless they want to excel in their sport. (B) Time spent practicing a sport limits a college student’s ability to get good grades. (C) A college student cannot succeed in sports and get good grades. (D) Only college students who have a natural ability for a sport can get good grades and do well in their sport. (E) College students who spend a lot of time practicing a sport will not get good grades.

5. In an effort to combat sinking reading scores in its public schools, Harville decided to fund the hiring of afterschool tutors. However, in order to do this and stay within its budget, the town will not be able to begin a long-needed renovation of its park system, which the students use for their physical education classes and after-school sports leagues. Which of the following best expresses the conclusion of the passage? (A) Because of budgetary constraints, Harville will have to find a means of raising reading scores in its public schools that is less expensive than the hiring of after school tutors. (B) The quality of physical education in Harville will decline as a result of the new after-school tutoring system. (C) Harville considers good reading scores in its public schools a greater priority than the success of its school sports teams. (D) Harville will not be able to fund the hiring of after-school tutors and the renovation of its park system and keep within its budget. (E) Some students who used to participate in afterschool sports leagues in Harville will now take part in after-school tutoring.

Step 11.2 Homework

Questions 6-7 refer to the following: Senator #1: By taking people off welfare you are cutting off their only means to support themselves. Senator #2: By taking people off welfare, we are both providing them with incentive to get jobs and change their lives, and saving money for the federal government, enabling us to cut the deficit and improve the economy. This will reduce poverty overall.

6. Which of the following, if true, best supports the second senator’s argument? (A) There is a high unemployment rate. (B) The majority of families on welfare include families with children too young to work. (C) Most recipients only receive welfare for brief periods while they are between jobs. (D) Welfare amounts to a relatively small percentage of the federal budget. (E) Senator #2's plan is modeled on the welfare reduction plans of certain states that successfully reduced poverty in those states.

7. Which result of a serious reduction in welfare expenditures would best indicate that the second senator's reasoning was correct? (A) A sudden lowering of the unemployment rate (B) The initiation of programs by the federal government spurring businesses to hire former welfare recipients (C) A rise in the average salary for low-level, unskilled workers (D) A reduction in the number of public high school students earning their diplomas (E) A sharp rise in inflation

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Critical Reasoning

8. Excavations on the Island of Crete have revealed a palace, built in a labyrinthine style, dating back almost 3,000 years. Many point to this as evidence that there is an element of truth behind the Greek myth in which a warrior from Athens named Theseus goes to Crete and wanders a labyrinth until he kills the half-man, half-bull called the Minotaur. Which of the following, if true, most strongly supports the theory that there is an element of truth behind the myth? (A) Archaeologists have uncovered ruins from Athens that date back to roughly the same period. (B) The Minoan civilization, centered on Crete, is universally agreed to have been extremely advanced; excavations of the palace demonstrate that it may have had running water. (C) Archaeologists theorize that the palace was leveled by a natural disaster around 3,400 years ago. (D) Documents indicate that people from kingdoms outside Crete, including Athens, often had reason to go to Crete, which was the center of power in the region at that time. (E) In most versions of the myth, Theseus is said to have used a ball of thread to find his way through the labyrinth.

9. Most airline passengers don’t pay attention when flight attendants give safety instructions before takeoff. Unless airlines find a more effective means of communicating to their passengers, most passengers will not know what to do in case of an onboard emergency.

(E)

Most airline passengers, unless informed in advance of what do to in case of an emergency, are likely to panic should there be an actual emergency.

10. In a recent survey, Travel Company X found that 30% of its customers were not satisfied with the quality of service. Company X has lost many of its customers to Company Y recently and has therefore decided to increase its number of service representatives by 25 percent in an effort to regain customers lost to Company Y. Which of the following, if it were discovered, would make Company X’s plan most likely to fail to regain customers lost to Company Y? (A) The poor quality of service at Company X is due to the fact that its customer service representatives are poorly trained and lack experience. (B) Company X has always charged less for the same services than has Company Y. (C) Not all of Company X’s customers responded to the survey. (D) Company X has many loyal customers who are satisfied with its services. (E) Company X does most of its sales in package deals, including airfare and hotels, while Company Y does mostly “airfare only” sales.

Which of the following, if true, would most seriously weaken the conclusion drawn above? (A) Onboard emergencies are extremely rare, and because of technological improvements are likely to become even more rare. (B) Most of the passengers who do not pay attention are already familiar with airline safety procedures, which are standardized on all flights. (C) In presenting an airplane’s safety features to their passengers, flight attendants must follow a script written by high-level flight engineers. (D) In addition to the safety instructions given by flight attendants, a card with all necessary safety instructions is provided for each passenger.

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11. From 1950 to 1975, the average number of students graduating per year at a group of five associated universities increased by 40 percent. During the same period, the number of students graduating from these universities with honors degrees grew by only 20 percent. Which of the following statements about the period from 1950 to 1975 in these five universities is best supported by the statements above? (A) The criteria for selecting honors students became more rigorous. (B) The faculty-to-student ratio declined, allowing less time for advisors to encourage students to pursue honors degrees. (C) The increase in enrollment resulted from lower admissions standards. (D) Students at the end of the period were more career-oriented than those at the beginning. (E) The number of students graduating without honors increased by more than 40 percent.

12. A company that manufactures lawn mowers developed a new model for a lawn mower with safety features lacking in its earlier models still on the market. During the first year that the new model was sold, its sales lagged far behind the company’s older models. The company management thus concluded that safety was not the primary concern of its customers. Which of the following, if true, would most seriously weaken the conclusion of the company management in the passage above? (A) Other companies that manufacture lawn mowers developed similar safety features for models that then sold very well. (B) The safety features included in the new model did not result in a retail price higher than those of the company’s earlier models. (C) Many of the company’s lawn mowers are bought by the municipal parks commission and are used by professional gardeners to maintain the city's park system.

Step 11.2 Homework

(D) Lawn mower users generally find that they have the fewest accidents using older models all of whose safety features they are already familiar with. (E) A recent study on lawn mowers published in a consumers’ guide magazine reported that many accidents caused by lawn mowers are due to faulty safety equipment.

13. The introduction of plant or animal species to a region where the species do not exist naturally sometimes has disastrous effects on the environment of the region. Since countries X and Y are planning to eliminate all border controls for visitors traveling between the two countries, ecologists are worried that the environments of the two countries will be at great risk. Which of the following points, if true, provides the strongest evidence that the ecologists’ fear concerning the environments of countries X and Y is unfounded? (A) Both country X and country Y will continue to enforce their border controls for visitors whose country of origin is neither of the two countries. (B) Country X and country Y are part of a large desert region whose plant and animal species exist throughout the entire desert. (C) The elimination of border controls between countries X and Y will benefit the economies of both countries by increasing trade and promoting transnational businesses. (D) Government efforts to protect the environment in country X in the last decade have successfully resulted in the removal of a number of plant and animal species from the endangered species list. (E) The border controls between the two countries will be phased out gradually over a five-year period.

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Critical Reasoning

14. A sporting goods company found that the waterproof material it uses for manufacturing backpacks, ski bags, and tents has consistently resulted in low sales when used to manufacture rain jackets. Tests, however, have revealed that the material is not only waterproof, but also lighter and less expensive than the material used in more popular rain jackets.

(D) The less heavily-used ports are as convenient as ports that are centers of international trade for most private boat operators (E) Commercial boats are more likely to be involved in accidents than private boats.

Which of the following statements, if true, would best reconcile the test results above with the poor sales of the rain jackets?

16. Television news programs often announce the results of medical studies indicating that a certain type of food has been shown to be beneficial or harmful. Because the news programs generally focus on one finding relating to only one type of food, it is impossible for viewers not in the health profession to develop a coherent nutritional plan.

(A) The company sells most of its products to outof-state residents through mail-order catalogs. (B) The company’s sales of backpacks and ski bags have increased by an average annual rate of 15 percent over the last three years. (C) People who buy rain jackets most often choose a jacket based on its fashion appeal. (D) Some mountain climbers and hikers prefer material that is even lighter than that used by the company in its rain jackets. (E) The company has traditionally been more successful in selling footwear than rain jackets.

15. If the harbors around ports that are centers of international trade were restricted to commercial boats and only those private boats equipped with advanced communication devices, most private boats would be forced to use other ports that are less heavily used. Such a reduction in the amount of private boat traffic would lower the chances of collisions around the ports which are centers of international trade.

If all of the above statements are true, which of the following can be properly inferred? (A) Nutritional experts focus their research primarily on the effects of a small number of foods. (B) Television journalists are unable to relate specific new medical findings to broad health issues. (C) Viewers of television news programs rely on the programs for nutritional information. (D) Information relating to only one type of food is not useful to people who are not in the health profession. (E) Television news programs often distort scientific findings reported by nutritionists.

The conclusion drawn in the first sentence is dependent on which of the following assumptions? (A) Most private boats that use ports that are centers of international trade are not equipped with advanced communication devices. (B) Most of the less heavily used ports are unable to handle big, commercial boats. (C) The decline in the number of private boats used at ports that are centers of international trade would eventually result in a rise in the commercial boat traffic at these ports.

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Step 11.2 Homework

CRITICAL REASONING HOMEWORK/PRACTICE TEST ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

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Critical Reasoning EXPLANATIONS FOR CRITICAL REASONING HOMEWORK/PRACTICE TEST 1. (D) Premise: 3 large meteors entered the earth's atmosphere near the end of the Mesozoic era. Premise: The meteors caused climate changes. Conclusion: These climate changes caused the extinction of the dinosaurs. The conclusion asserts a causal relationship. We have to assume, first of all, that the dinosaurs became extinct at the end of the Mesozoic. Even then, though, the temporal relationship is not the same as a causal one. This is a weaken-the-argument question. It is necessary to find the answer choice which indicates that climate changes from meteors did not cause the extinction of the dinosaurs. (A) is irrelevant to the argument as it is stated; whether it is tangentially related to theories of the extinction of dinosaurs is irrelevant here. (B) and (C) strengthen the argument. (D) weakens the argument because it suggests an alternate explanation for the extinction of the dinosaurs – the flora which they needed became extinct before the meteors landed. Providing alternative explanations is a good way to weaken a causal argument. The prehistoric mammals of (E) are outside the scope of the argument.

2. (D) Premise: The wholesale price of product B is less than its manufacturing cost per unit. Premise: People who buy B will also buy the highly profitable A. Conclusion: Therefore product B is appropriately priced. The wholesale price of new product B is less than the manufacturing cost. What is supposed to keep B from losing money for Company K is that people who buy product B, according to the premise, will also buy the profitable product A. B, then, must lead to increased sales of A. The best way to verify this is to investigate whether sales of A increase in markets where B is available, which, if demonstrated to be true, would correlate purchases of the 2 products. (A) is wrong because K's competitors are outside the scope of the argument. So is the history of sales of A referred to in (B). (C) is close, but it reverses the relationship – it is necessary to find the likelihood of people who purchase A to buy B, not the other way around. (E) compares 2 details about product A that are not relevant to the argument. (D) explicitly states the proper method of investigating the potential profitability of B. © The MBA Center

3. (E) Premise: A celebrity introduced a new beverage product in advertisements. Premise: Sales of the new product exceeded all expectations. Premise: Celebrities will endorse all of the company's beverages. Conclusion: The company's profits will increase greatly. This is an argument by analogy: what worked with one product will supposedly work with others. The question asks for what is not assumed in the argument, so four of the answer choices will be assumptions that were made that, if true, strengthen the argument that the two situations are analogous. The wrong choices will indicate that, indeed, the celebrity endorsements will be profitable. (E) is not assumed, because it is not necessary that all the older beverages sell as well as the new one. The conclusion that the company's profits will rise can be true even if only some of the older beverages sell much better. The other choices are assumptions necessary to the argument; if any of them were false, the argument would break down.

4. (C) Premise: To excel in a sport, you must have a natural ability or spend a lot of time practicing. Conclusion: College students who want good grades should only do a sport if they have a natural ability. This question necessitates finding what is not assumed in the argument. (C) is not assumed, because, according to the argument, it is possible for a student to succeed in sports and get good grades (if the student has a natural ability for the sport and doesn't need to spend much time practicing). The other choices are assumptions that must be true for the argument to work. By the way, if you felt that (E) is untrue because you think a student can spend time practicing a sport and get good grades, you are basing your answer on your own knowledge and not on the passage. Stick to the premises and the logic; stay within the scope of the argument.

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5. (D) Conclusion: in order to fund after-school tutors and stay within its budget, Harville will not be able to begin a long-needed renovation of its park system. Premises: everything else Here you are looking for the conclusion. Remember that "find the conclusion" questions are not necessarily based on flawed arguments. Don’t waste your time looking for flaws or assumptions. (A) contradicts the premises – we expect that Harville will fund the tutors. (B) is a trap – it sounds good, but isn't necessarily true. Maybe Harville will find an inexpensive way to continue its physical educational classes and maintain the quality. (C) is the same – tempting, but goes too far. We don't know what the priorities of the town are, and, what's more, we don't know that the success of the sports teams is related to renovating the parks. (E) is wrong because there is no connection between the tutoring and sports teams in terms of participants. (D) is a good, clean paraphrase of the conclusion.

6 – 7. Premise: Taking people off welfare provides incentive to find jobs and change their lives. Premise: The federal government will save money Premise: The deficit will be cut and the economy improved. Conclusion: Poverty will be reduced overall. 6. (E) Remember to read the question first. It tells you to focus on senator #2's argument, a "Does the proposed solution solve the problem?" argument. The premises are really a series of predictions, and the conclusion is just a broader prediction. Something could go wrong in any of the steps, but keep in mind that the overall point of the plan is to reduce poverty. In (A), a high unemployment rate doesn't show that poverty will be reduced. In (B), the concept of children too young to work is outside the argument's scope. (C) and (D) weakens senator #2's argument. (E), the right answer, shows that the plan is based on similar plans that have worked, therefore adding credibility to the plan. 7. (A) Again, we're trying to show that senator #2's proposed plan will solve the problem. We can do this by showing that any one his predictions is valid. One of the premises was that people would have more incentive to find jobs. Therefore a sudden lowering of the unemployment rate, or (A), would demonstrate

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that at least part of his plan was working. (B) is a trap; it can be interpreted as a positive result of cutting back on welfare, but it is not a sign that the senator's reasoning is correct. Unskilled workers and their salaries, high school diplomas, and inflation, mentioned in (C), (D) and (E), respectively, are all outside the scope. 8. (D) Premise: A labyrinthine palace from 3000 years ago was found on Crete Conclusion: There is some truth to the myth of the Athenian Theseus going to Crete and killing the Minotaur after wandering the labyrinth. The conclusion asserts a link between the myth and the discovered palace. All we really know, though, is that the myth exists and the palace exists. We don't know whether they're related, i.e., whether the palace found was actually the palace used by Theseus, or even whether Theseus actually existed and went to Crete. Notice the conclusion says there is "some" truth behind the myth. We only need a choice that strengthens the relationship between the conclusion and the premise. (D) does this by pointing out that it was common for Athenians to travel to Crete, thereby supporting the possibility that someone went to Crete at this time from Athens, perhaps finding his way through the labyrinth in the palace. None of the other choices specifically relate to the myth.

9. (B) Premise: Most airline passengers don't pay attention during safety instructions. Conclusion: Most passengers will not know what to do in case of an emergency unless airlines find a better way to communicate safety instructions. This argument suggests a solution (better means of communication) for a supposed problem (most airline passengers don't pay attention during safety instructions). The premise, though, says nothing about emergencies. Maybe there's no problem at all and people already know what to do in case of an emergency. (B) asserts this and therefore weakens the argument. (A) does not weaken the argument, because the argument concerns what would happen if there were an emergency; the likelihood of there actually being an emergency is irrelevant. (C) is outside the scope; the people who write those annoying speeches are not part of the argument. (D) may sound good, but it's definitely not as good as (B). The argument says a more effective means of communication is necessary. The cards may not be effective at all (who reads them anyway)? (E) strengthens instead of weakens the argument. © The MBA Center

Critical Reasoning

10. (A) Premise: 30% of Travel Company X's employees were not happy with the service (according to a survey). Premise: Company X has lost many of its customers to Company Y recently. Premise: Company X will increase its number of service representatives. Conclusion: Company X will regain customers from Company Y. Does the proposed solution solve the problem? Look carefully at the premises. First of all there is a survey involved. That doesn't automatically invalidate the data, but if the survey did not use a representative sample, the conclusion would be invalid. The passage doesn't state why customers were unhappy with the service provided. Maybe there were not enough service representatives (in which case the plan might help); maybe there were already enough but they were incompetent, or ineffectual. (A) therefore is the right answer. Notice that (C) is a trap. A survey doesn't have to be filled out by everyone to be valid. Only choose answers about samples to weaken arguments when the choice argues that the sample was not representative.

11. (E) Premise: The number of students graduating from five associated universities increased 40% from 1950 to 1975. Premise: The number of students graduating from these universities with honors degrees grew by 20%. Conclusion: none This question could be viewed as a resolve-thecontradiction question, in which two statistics need to be resolved. The (apparent) contradiction is that the number of students graduating overall increased more than the number of students graduating with honors degrees. The inference is pretty straightforward; the number of students graduating without honors degrees must have increased by more than 40%. (E), then, must be correct. (A) is a possible explanation for the first premise, but it doesn't have to be true; the criteria could have stayed the same (or become even less rigorous) while the students got worse. (B), in fact, is another possible explanation for the first premise, but it also is not necessarily true. (C) is an explanation for the second premise, but (C) doesn't have to be true; the increase in enrollment (assuming enrollment – and not just the number of students graduating – increased) could be due to an increase in the number of applications. (D) is outside the scope – we cannot establish a connection between honors degrees (or the lack of honors degrees) and career orientation. © The MBA Center

12. (D) Premise: A new lawn mower model with new safety features was put on the market. Premise: In its first year of sales, the company's older models sold far better than the new one. Conclusion (of the company management): Safety is not the customers' main concern. The conclusion establishes a causal relationship between the premises. The management tries to explain why the new lawn mowers did not sell better. To weaken a causal argument, the easiest thing to do is to find another cause. (D) shows that even though the new lawn mowers have new safety features, customers consider them less safe (because they are unfamiliar with them). This helps explain why the sales are lower than their old models and weakens the conclusion that safety is not the customers’ primary concern.

13. (B) Premise: New plant or animal species can have bad effects on a region's environment. Premise: Countries X and Y are planning to eliminate border controls between the countries. Conclusion (of ecologists): The environments of the two countries are at great risk. The question asks which choice will weaken the ecologists' "fear," or conclusion. The correct choice will demonstrate that the environments of X and Y are not at risk. The threat to environments, according to the passage, is from new species. The argument assumes that species from X that don't exist in Y will be taken across the border (or vice versa). (B) proves the assumption wrong, saying that the two countries have the same environment and the same species; therefore there is no threat and the ecologists' fear is unfounded. (A) is outside the scope because the argument doesn't concern countries other than X and Y. (C) is outside the scope because, though the increased trade might be good for the countries, the ecologists are worried about the environment, not the economy. Ecologists might be happy to hear (D), but it does nothing to calm fears about the introduction of new species. (E) perhaps postpones the fear for a while, but it doesn't actually solve the problem.

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14. (C) Premise: A company manufactures backpacks, ski bags, and tents with a certain waterproof material. Premise: When the company uses this material for rain jackets, the jackets sell poorly. Premise: Tests show that the material is waterproof and lighter and less expensive than the material in more popular rain jackets. Conclusion (implied): The premises seem to contradict each other (the rain jackets should have sold better). This is a resolve-the-contradiction question. Why did the rain jackets, whose material tested well, not sell better? Look carefully. What did the company test? It tested the fact that the material is waterproof, light, and inexpensive. What determines how well rain jackets sell? There's no way to know! A choice which explains that the popularity of rain jackets is determined by something other than the material (or by an untested quality of the material) would solve the problem. (C) does this by suggesting that it is a jacket's fashion appeal, and not its material, that can determine its popularity. (A) is outside the scope – in-state, out-of-state – who cares? (B) focuses on backpacks and ski bags; it explains nothing about rain jackets. (D) is pretty close, but it has two problems. First, the word "some" is weak; "some" means one or more. Second, even if they prefer material lighter than that used by the company in its rain jackets, why should other rain jackets which are even heavier sell better? And as for (E), now really – "footwear"? That's way outside the scope.

15. (A) Note that the question is only about the first sentence. You should therefore ignore the second sentence. Premise: If harbors around ports that are centers of international trade were restricted to commercial boats and only those private boats equipped with advanced communication devices… Conclusion: then most private boats would be forced to use other ports that are less heavily trafficked.

Step 11.2 Homework

(B) is irrelevant, because big commercial boats can continue to use the busy ports. (C) is a prediction about the future that is not justified by the premises. (D) doesn't have to be true; the passage does not state the policy will be convenient for private boat operators. (E) refers only to the second sentence.

16. (C) Premise: TV news programs announce the results of medical studies about food. Premise: The programs usually focus on only one finding about one food. Conclusion: It is impossible for lay people to plan a good diet. Impossible? What ever happened to people reading, consulting doctors, learning from their parents, listening to the radio? Since the question says "If all of the above statements are true… ," it is not necessary to contradict the argument, even if you personally disagree with the conclusion. The only way this conclusion would follow logically from the premises is if people rely on TV news programs for information to plan their diets. If not, it would simply be wrong to conclude that it's impossible to plan a good diet. (C), then, is a proper inference. (A) distorts the argument. TV programs focus on one type of food – the passage states nothing about the focus of nutritionists. (B) goes too far by claiming that the journalists are "unable" to do something – just because they don't doesn't mean they can't. (D) also goes too far. Even after accepting the fact that viewers can't "develop a coherent nutritional plan," it should not be assumed that information concerning only one type of food is useless. This choice would have been correct had it said that the information is "of limited use." (E) is a distortion. We know that the programs report about one type of food item at a time. This doesn't mean they "distort scientific findings." Watch out for choices that might disparage professionals (even TV journalists)!

This argument goes from the particular to the general. Why should most private boats be forced to use other ports? The premise says that the busy ports will be restricted to commercial boats and private boats with advanced communication devices. Maybe most private boats have advanced communication devices. The conclusion is based on the assumption that most private boats don't have these devices. Therefore (A) is the answer.

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Step 12 Critical Reasoning Workshop

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Critical Reasoning EASY 1. Advanced Audio, a manufacturer of stereo components, is planning to expand its production in order to participate in the stereo sales boom that has occurred over the last two years. The company also plans to continue the heavy marketing campaign that it commenced several years ago. Which of the following, if true, best weakens the view that Advanced Audio can increase sales using the plan outlined above? (A) Advanced Audio's stereo components, with those of three other companies, accounted for over half of the industry's increase in sales last year. (B) Advanced Audio manufactures stereo parts for other companies in addition to those sold under its own name. (C) Although Advanced Audio lowered its retail price last year, its market share also fell. (D) Advanced Audio's products are among the most state-of-the-art in the industry, which makes them among the most expensive. (E) Advanced Audio's products are sold more in authorized dealerships than in discount stores. 2. A city's public transportation board has decided to cut costs by reducing the frequency of its bus service from an average of eight minutes to an average of ten minutes between buses. The board announced that it can do so without seriously reducing the quality of service. Which of the following statements, if true, would most strengthen the validity of the board's announcement? (A) The less frequent use of the buses will lower maintenance costs, resulting in savings that can be used for much-needed repairs of the city's pedestrian bridges. (B) At rush hour, congestion in the city slows bus service by thirty percent. (C) Because of a robust economy in the city, passenger patronage has increased substantially in recent years. (D) The public transportation board has recently gathered detailed data on the levels of ridership

on all bus lines, showing that some lines are used by many more riders than others. (E) The contract with the bus drivers union stipulates that the city not lay off any drivers because of reduced bus service. 3. A scientist planted two groups of plants under identical conditions of light, temperature, humidity, and moisture. Every day he would play sound effects of thunderstorms to one of the groups of plants and sounds of city traffic for the other. The group to which he played thunderstorms all died within a few weeks, but the other group thrived during the experiment. He therefore concluded that the sound of city traffic is more effective for helping plants grow than is the sound of thunderstorms. Which of the following, if true, would most seriously weaken the scientist's conclusion? (A) The scientist put different varieties of plants in each group. (B) The light affecting the plants changed according to the time of day. (C) The plants in the group for which he played city traffic sounds died several weeks after the experiment. (D) The plants were all purchased at the same time. (E) The plants in the group for which he played city traffic sounds required more water than the scientist actually gave them. 4. The town council recently voted to rename 11th Street "Shane O'Connor Street," after the famous poet and novelist who once lived there. Supporters of the plan argued that the change would promote community pride and togetherness. The council members' plan is based on the assumption that (A) Shane O'Connor's books are required reading in the town's public schools (B) Most of the residents of 11th Street favor the name change (C) There are no other famous writers who have lived on the street (D) Some of the residents of the town are proud of the fact that O'Connor once lived there (E) O'Connor mentioned the town numerous times in his work

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5. A popular Internet service provider changed its billing system, charging customers per each connection to the system rather than per total hours connected. According to company representatives, under the new system, customers will spend more time connected to the Internet while being billed the same or smaller amounts. Which of the following statements, if true, would most strengthen the conclusion of the company representatives? (A) Customers will connect to the service less frequently and spend more time connected to the service each time they do. (B) The change in the billing system will attract new customers resulting in increased profits for the company. (C) By spending more time connected to the Internet customers will be able to take advantage of services that previously would have been too expensive. (D) The popularity of other Internet service providers relies on their having billing systems similar to the one this compay is adopting. (E) The company's employees, all of whom have free unlimited Internet access, support the change in billing.

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7. In an effort to alleviate the problem of traffic congestion in City R, the municipal authorities authorized roadwork which would increase the number of lanes on several major highways. However, when the new highways were opened, the level of congestion actually increased. Which of the following, if true, best explains why the level of congestion did not decrease when the new highways were opened? (A) People drive faster on highways than on other types of roads. (B) Highways do not have traffic lights as other types of roads do. (C) The highway patrol police increased their efforts to catch drivers who were speeding. (D) A person's inclination to drive depends in part on his or her perception of space. (E) The new lanes enabled journey times for many trips to be substantially reduced.

6. A film critic: Since he moved from the South End to the North End of the city, Willy Marcus has totally rejected the lower-class subjects of his greatest films. He has only made films about the wealthy and elite. Therefore, in order to get back in touch with his roots, Marcus should move back to the South End before making more movies. If the film critic's conclusion above is accurate, which one of the following statements can be most reasonably inferred? (A) Most filmgoers prefer Marcus’s early films. (B) The lower-class subjects of Marcus’s films bear a relation to the South End. (C) The South End is populated by people with more money than those living in the North End. (D) Marcus’s films about upper-class society fail to make valuable insights about the society they portray. (E) Marcus comes from an impoverished background.

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Critical Reasoning MEDIUM 8. During a recent earthquake over half of a city's residential housing was destroyed. Many feared that there would be a great housing shortage and that many people would be homeless. However, just six weeks after the disaster, the rate of homelessness was virtually the same. Very few people had left the city either. In fact, the only things that changed were the addresses of those people whose homes had been destroyed and the rent they were paying, which was substantially higher for equivalent accommodation. Which one of the following can be inferred from the passage? (A) The quality of people's lives declined after the earthquake. (B) The new accommodation that people found was higher in quality than their old homes which had been destroyed. (C) Many other types of buildings apart from residences were also destroyed in the earthquake. (D) Increasing rents allow the market to quickly supply more housing when it is needed, such as after a major disaster like an earthquake. (E) After the earthquake many new laborers moved to the city in the hope of getting lucrative work for new construction. 9. The owners of gambling casinos are keen to attract inexperienced poker players because, on average, these people lose money to the casino, which increases the casino's profits. This is because the average inexperienced player does not have sufficient skill at the game to win. Which one of the following can be inferred from the above argument? (A) There is always an element of chance when playing poker. (B) The probability of winning a game of poker increases with experience. (C) Casinos make extremely large profits. (D) Inexperienced players lose more money than they expect to when playing poker at casinos. (E) All games played at casinos involve an element of risk.

10. In response to years of increasing congestion at airport X, the government decided to redistribute landing slots. Henceforth, all international flights arriving from continent A would be rerouted to nearby airport Y; all flights arriving from continent B would continue to land at airport X. Several airlines opposed this measure on the grounds that it would result in lost business. Which of the following, if true, justifies the airlines' conclusion? (A) The airlines' customers prefer less congested airports. (B) It takes five minutes more flying time to reach the second airport. (C) There are fewer runways, and thus less capacity, at airport Y. (D) Airport Y is located in a region with better transport links to the final destinations of many travelers from continent B. (E) Many customers traveling between continent A and continent B choose certain airlines because of the easy flight connections they offer at airport X. 11. The admissions officers at a certain university use standardized test scores as the main factor in deciding whether to admit an applicant. One year the average test scores of all applicants went up. The admissions officers concluded that the difficulty of the test had declined that year and raised the score required for admission. The admissions officers assumed which one of the following in reaching their conclusion? (A) Fewer applicants reached the standard required for admission. (B) The overall applicant population maintains a constant ability from year to year. (C) Less intelligence was required to score highly on the test this year. (D) The test is becoming less and less relevant to the admissions process. (E) Some questions on the test had become harder.

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12. It has often been hypothesized that global oil consumption, which increases every year, will deplete the supply of oil, with catastrophic results for the global economy. However, these claims never stand up to scrutiny, as the volume of oil in reserves around the world has remained constant. Which of the following, if true, best resolves the apparent paradox? (A) The actual annual consumption of oil is below that which many experts estimate. (B) The cost of operating oil refineries has steadily decreased over time. (C) The consumption of oil has greatly increased in the past 50 years. (D) It is the policy of all major oil producers to locate new reserves at a rate consistent with that at which old reserves are depleted. (E) The number of oil-producing countries has been steadily declining. 13. Kobayashi coffee has more caffeine than Marlowe Select coffee. But since Chula Vista coffee has more caffeine than Valentino coffee, it follows that Kobayashi coffee has more caffeine than Valentino coffee.

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14. In the past, companies in the paper production industry have always opposed restrictions on cutting down trees in forests because they perceived that this would impede their ability to earn profits. The government recently proposed to ban the cutting of trees in all national forests. The paper production companies were in favor of this ban. Many industry observers subsequently concluded that the paper production industry was no longer interested in protecting its ability to earn profits. Which one of the following is an assumption made by the industry observers? (A) The profits of paper production companies will not decrease after the ban comes into effect. (B) The companies concerned only manufacture paper products. (C) Maximizing profits is the only objective of the paper production companies. (D) The legislation will take effect immediately. (E) Paper production companies always act in their interest.

Any of the following, if introduced into the argument as an additional premise, makes the argument above logically correct EXCEPT (A) Marlowe Select coffee has more caffeine than Valentino coffee. (B) Marlowe Select coffee has more caffeine than Chula Vista coffee. (C) Marlowe Select and Chula Vista coffees have the same amount of caffeine. (D) Kobayashi and Chula Vista coffees have the same amount of caffeine. (E) Chula Vista coffee has more caffeine than Kobayashi coffee.

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Critical Reasoning

15. Japan has the highest rate of savings in the developed world. Research indicates that the average family savings of the middle 40 percent of the population declined by 9.9 percent from 1989 to 1996. At the same time, the average family savings of the richest 15 percent of the country increased by 12.7 percent. Statistics imply that this decline in savings is due to recession and inflation in the early 1990's and that there has been a significant redistribution of wealth from middle-class families to affluent families. Which of the conclusions below can be properly drawn from the information above? (A) Affluent families are less susceptible to economic downturns than are middle-class families, and maintain a high rate of savings under such conditions. (B) Average savings in Japan have declined by 9.9 percent from 1989 to 1996. (C) Middle-class families can sustain customary rates of saving even when prices rise and economic momentum slows. (D) A return to normal economic conditions will reverse the redistribution of wealth from affluent families to middle-class families. (E) Spending levels for affluent families declined from 1989 to 1996. 16. A town plans to turn the public hospital over to a private organization in order to maintain its financial viability. While no one questions the ability of the private organization to provide quality health care, such a change will make the hospital unaffordable for the town's low-income residents. If the above statements are all true, which of the following inferences can most reasonably be drawn?

(D) The hospital, under private ownership, will charge low-income residents more for health care than it did when it was publicly run. (E) The staff of the hospital will remain unchanged after the transition of the hospital to private ownership.

DIFFICULT 17. Which of the following best completes the passage? Critics of Country A's trade policy with Country Z contend that Country A's low tariffs are responsible for its large trade deficit with Country Z. Government officials, however, argue that there is a trade deficit with Country Z because low labor costs in Country Z allow its companies to manufacture goods cheaply. The officials also claim that economic competition from Country Z is responsible for better prices for Country A's consumers. Therefore, they say, the most logical way to lower the trade deficit without hurting Country A's consumers is to ________. (A) raise the tariffs on goods imported from Country Z (B) encourage businesses in Country A to reduce their labor costs (C) increase taxes on all goods not manufactured in Country A (D) improve the products manufactured by Country A's companies and market them heavily in Country A (E) subsidize all of Country A's companies that manage to maintain their prices at the level of the goods produced by Country Z

(A) State regulations require that government aid for medical costs in public hospitals be made available to all citizens on the basis of need. (B) The wealthier residents in the town have health-care plans that cover all their medical costs. (C) Without federal aid, most people cannot afford the high costs associated with specialized medical procedures.

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18. As the popularity of American professional sports and sports merchandise grows worldwide, the demand for paraphernalia - caps, jackets, etc. marketed with the logos of American sports teams will continue to grow as well. By necessity an increasing quantity of this merchandise will be manufactured. However, it is doubtful that this increase will provide new jobs for American factory workers. Which of the following, if true, would most strengthen the conclusion drawn above? (A) Competition among various U.S. manufacturers of sports team–related equipment insures that retail prices of this merchandise will stay low. (B) Professional sports teams in other countries are starting to model their marketing plans and production of merchandise on those of American sports teams. (C) Companies that manufacture merchandise relating to American sports teams recently established production plants in foreign countries in preparation for a popularity boom of their product on the foreign market. (D) Increased attendance at American professional sporting events has led to an increase in sales of sports merchandise at those events. (E) Past increases in demand for products related to American sports teams have led to increased popularity of sports retail equipment overall. 19. One argument of opponents of laws that require drivers and passengers of motorcycles to wear safety helmets is that not wearing a helmet endangers no one but the rider, and that it is a right of all citizens to have the option of putting themselves in danger as long as they do not endanger others. Therefore, critics conclude that helmet laws unnecessarily restrict riders' rights. Which of the following, if true, most seriously weakens the conclusion of the critics above?

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(C) Some motorcyclists have fought the law using the argument that not wearing a helmet is a tenet of their religious beliefs. (D) Automobile owners have had to pay higher insurance rates because of the need to pay for the injuries or deaths of motorcycle riders who were not wearing helmets. (E) Many automobile drivers and passengers have suffered injuries in collisions with motorcycles, the drivers of which were not wearing helmets. Questions 20 and 21: Scientist A: If carbon dioxide emissions continue to rise, this will lead to an increase in the concentration of carbon dioxide in the atmosphere. If there is an increase in the concentration of carbon dioxide in the atmosphere, more heat from the Sun will be trapped, and the temperature of the atmosphere will rise. Scientist B: That theory is incorrect because if the concentration of carbon dioxide in the atmosphere increases, the metabolism of plants which consume carbon dioxide and convert it into oxygen will increase. 20. Scientist B responds to Scientist A's argument by (A) accusing Scientist A of misrepresenting the facts (B) challenging Scientist A's ability to form a scientific hypothesis (C) showing that the circumstances which produce a certain effect in Scientist A's theory will also produce a second effect which will negate the first effect (D) showing that the concentration of carbon dioxide in the atmosphere is not the only factor that influences atmospheric temperatures (E) showing that the Earth's temperature will never change because it is naturally self-regulating

(A) Many motorcycle riders have suffered serious injury in accidents that occurred when they were not wearing helmets. (B) Proponents of the law liken helmets to seatbelts in automobiles, which most states require by law to be worn by automobile drivers.

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21. If Scientist B's objections are true, Scientist A's argument could still be valid if it could be shown that (A) plants can consume other atmospherewarming chemicals (B) the erosion of the Earth's ozone layer will have a warming effect on the Earth's atmosphere (C) scientist B lacks formal scientific qualifications (D) scientist A is an acknowledged expert in the field of global-warming research (E) the rate of increase of the amount of carbon dioxide in the atmosphere is greater than the rate of increase of carbon dioxide absorption by plants

23. What could the government do to lower demand and solve the problem of shortages in the health care system? (A) Reduce the amount of health care services offered to the population (B) Increase the number of new doctors trained each year (C) Impose a charge on citizens every time they use the health care system (D) Consolidate the provision of health care services into large medical centers rather than a greater number of small ones (E) Expand the range of treatments available under the national health care system

Questions 22 and 23 The government of a certain country decided to provide a system of national health care which was free at the point of use for citizens of the country. Before the creation of the system, all citizens had to pay for their health care out of their own pocket. After it was first created, the system worked well. After a generation, however, the demand placed on the system by the population increased dramatically and shortages started to occur even though the population and amount of health care services offered remained constant. 22. Which one of the following does most to explain the rise in demand on the national health care system? (A) As soon as a service is provided for free, the demand for it rises. (B) The quality of health care provided declined after the national system was created. (C) Private health care providers outside the national system increased the amount of business they did every year after the creation of the national health care system. (D) People’s propensity to use health care services is higher if they have never had to pay for such services. (E) Doctors’ salaries increased after the national health care system was created.

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CRITICAL REASONING WORKSHOP ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

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Step 13 Analytical Writing Assessment

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Step 13.1 Lesson

GENERAL OUTLINE

The Analytical Writing Assessment is a one-hour section, which takes place before you begin the two main test sections of the computer-adaptive GMAT. You are allowed 30 minutes for each of the two essays you are asked to write. For all test takers, but especially those from educational systems outside of North America, these essays are an opportunity to demonstrate proficiency in the standards of written English and abilities in academic writing. This lesson introduces the two types of Analytical Writing Assessment questions and shows you specific strategies for writing effectively about them.

THE FOLLOWING TOPICS WILL BE COVERED

IN

THIS LESSON:

Presentation of Analysis of an Issue and Analysis of an Argument Question Types The MBA Center Approach to Analytical Writing Assessment Questions Sample Analytical Writing Assessment Essays Brief Essay Writing Review

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READY… The Analytical Writing Assessment was added to the GMAT in October 1994, about 40 years after the first GMAT was given. It is scored independently of the multiple choice section, and a photocopy of the essays is sent to all the business schools that receive your score reports. The AWA consists of two 30-minute essays (not necessarily in this order):

1. ANALYSIS

OF AN ISSUE

You will be presented with a short, usually broad, and (somewhat) controversial topic. Your task is to analyze the topic and develop an argumentative position using examples in an essay of about 500 words. Though the test makers do not specify the length, our experience shows that short essays get poor scores.

2. ANALYSIS

OF AN

ARGUMENT

For this assignment you will be given a short argument to analyze. Phineas writes these by adapting a Critical Reasoning question; the result therefore looks eerily similar to a CR problem. Your task is NOT to agree or disagree with the author, but to evaluate and criticize the argument. Argument essays can be a bit shorter than Issue essays because they don't require detailed evidence.

AWA in a nutshell: Two 30-minute essays: 1) Analysis of an Argument 2) Analysis of an Issue

The major challenges of this exercise are timing, typing (for the CAT), and staying focused on the relatively short passages you read before the essay. Why would the GMAC introduce the AWA? The GMAC, remember, is made up of an assembly and a board consisting mostly of MBA admission officers. The admission officers requested the essays. Since the number of non-native English speakers applying to MBA programs has increased significantly in the last several years, the essays give the admission officers an extra opportunity to assess the verbal skills of their applicants. Some observers, more cynical than we might think, suggest that the admission officers suspect that some applicants pay their friends (or teachers) to write their application essays for them. The AWA provides a writing sample that the officers can be sure was actually written by the applicant. Do the schools really read these essays? Sometimes, yes. But no one expects them to be as clearly written as your application essays (which are undoubtedly prepared months in advance, leaving ample time to proofread and reflect), though a reasonably lucid and well-written response to the AWA questions can help your admission chances. What does the AWA test? It tests your ability to write a clear, wellorganized essay, with good grammar and relevant examples, on a vague, boring topic, early in the morning, in a short period of time.

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Your essay will be scored from 0 to 6. Your AWA score has nothing to do with your overall GMAT score. You could, in fact, get every multiple-choice question right and practically ignore the AWA, and score 800 on the GMAT and 0 on the AWA. Note, however, that you must write something on the AWA. Faliure to write essays will result in no reportable scores.

THE SCORING SYSTEM

6: 5: 4: 3: 2: 1: 0:

Outstanding Strong Adequate Limited Seriously flawed Fundamentally deficient Completely illegible, on a topic obviously unrelated to the question, or non-verbal response

Of course the essays are not graded by computers, even on the CAT. They are graded by official graders, who read piles of essays in intense grading sessions, devoting, on average, about two minutes per question. For a more detailed explanation of grading criteria, consult the Official Guide to GMAT Review or The GMAT Bulletin.

HERE

IS AN EXAMPLE OF EACH QUESTION TYPE:

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GMAT CAT Analytical Writing 1

Analysis of an Issue: “Some people claim that space exploration should not be funded by the government, arguing that it is too costly and provides little benefit for most of the population. Others disagree, claiming that fundamental scientific knowledge is valuable in and of itself, and that, additionally, knowledge gained through space exploration is often later used by industry and research scientists for purposes not foreseen by those who planned the exploration.” Analysis of an Issue questions often cover some of these subjects and topics: Personal achievement/Personal success; General business, United States; Issues of ethics and leadership in business and management; Topical issues involving Government and Business, United States.

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Which do you find more convincing, the argument that space exploration should not be funded by the government or the response to it? Explain your point of view using relevant examples, based on your experience, observations, or readings.

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Analytical Writing Assessment

GMAT CAT : Analytical Writing 2

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Analysis of an Argument: “It has become almost impossible to eat a balanced, healthy diet. Television news programs are constantly providing new, sometimes contradictory information about what is healthy and what is not. The average consumer cannot make informed decisions from this kind of scanty information and is generally overwhelmed upon entering increasingly larger supermarkets with more and more brands to choose from.”

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Discuss how logically convincing you find this argument. In explaining your point of view, be sure to analyze the line of reasoning and the use of evidence in the argument. Also discuss what, if anything, would make this argument more sound and persuasive, or would help you to better evaluate its conclusion. Answer Time Time

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Phineas often writes Analysis of Argument questions as if they came from sources like these: Speeches, by corporate spokespersons/government officials; Newspapers, Newsletters, Memorandums, Business proposals, and Trade publications.

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AIM… To prepare for the AWA, it is important to develop an organizational plan and to review some grammar rules and style techniques that can improve your score.

A) ANALYSIS

OF AN ISSUE

The graders are looking for several key elements in your essay: Development that explores the issue from different perspectives Organized support for your position with relevant examples Varied sentence structure Good command of grammar There are three key steps necessary before writing.

You have 30 minutes for each essay. Try allocating your time this way: 10 minutes (8-10) Brainstorm and organize 15 minutes (15 - 18) Write 5 minutes (2 - 5) Proofread for large errors

Step one:

Identify the issue. Properly identifying the issue is, of course, imperative. Pay close attention to the wording used in the question.

Step two:

Consider at least one reason for each side of the issue. The graders want to see that you understand the complexity of the argument.

Step three: Choose a position and list several supporting reasons. Let's try this with an example. 00:29

GMAT CAT : Analytical Writing 1 Analysis of an Issue:

“Some people claim that space exploration should not be funded by the government, arguing that it is too costly and provides little benefit for most of the population. Others disagree, claiming that fundamental scientific knowledge is valuable in and of itself, and that, additionally, knowledge gained through space exploration is often later used by industry and research scientists for purposes not foreseen by those who planned the exploration.” Which do you find more convincing, the argument that space exploration should not be funded by the government, or the response to it? Explain your point of view using relevant examples, based on your experience, observations, or readings.

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The issue will be clearer if you rephrase it as a yes/no question. In this case, you should think, "Should space exploration be funded by the government?" © The MBA Center

Analytical Writing Assessment

Step two:

Yes, because it is important for a country to advance scientifically and technologically. or No, because there are more pressing needs the government should address such as education and health care. (Of course, you can use other reasons.) Step three: The government should fund space exploration because … 1. space technology has practical, short-term benefits (communication satellites, weather forecasting, etc.) 2. it provides jobs for scientists and engineers 3. the knowledge gained is of philosophical and scientific interest, and can not be learned elsewhere or The government should not fund space exploration because … 1. the astronomical (ha ha) expenses could be used for more important things 2. a lot of the benefits go to private companies which ought to make the investment themselves 3. there is a danger to astronauts Because the instructions are always the same (even though the topics themselves change), you can develop a model essay in advance. Here is a model for Analysis of an Issue: The issue of (restatement of issue) is complex and controversial. While (reason for one point of view), some people argue that (reason for other point of view). Both perspectives are important, but, overall, the advantages of (your position) outweigh the drawbacks. (Your position) is important because (first reason). This is evident (support for first reason). Secondly, (second reason). This can be illustrated by (support for second reason). In addition, (third reason). For example, (support for third reason). Some people might object that (support for other position). However, this objection can be countered by (reason against objection). While the issue of (restatement of issue) must be considered carefully, the reasons of (brief restatement of reasons) provide convincing support that (your position) is appropriate.

B) ANALYSIS

OF AN

Use the template method to prepare your essays in advance. Test it. Try it out for yourself, changing it to suit your style.

ARGUMENT

The planning stage of the Argument essay differs from that of the Issue essay. There is less brainstorming and more analysis.

A

GOOD

ANALYSIS

OF AN

ARGUMENT

ESSAY SHOULD HAVE

– a development that identifies all the aspects of the argument (the conclusion and the premises) – an examination of the argument’s logic (the assumptions which connect the premises and the conclusion) – a discussion of what would strengthen the argument – varied sentence structure – a good command of grammar © The MBA Center

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In planning your essay before you begin writing, you should follow two key steps: Step one:

Identify the conclusion of the argument.

Step two:

Compare the conclusion with the evidence, listing any questionable assumptions.

Let's look at an example. GMAT CAT: Analytical Writing 1

“It has become almost impossible to eat a balanced, healthy diet. Television news programs are constantly providing new, sometimes contradictory information about what is healthy and what is not. The average consumer cannot make informed decisions from this kind of scanty information and is generally overwhelmed upon entering increasingly larger supermarkets with more and more brands to choose from.”

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Discuss how logically convincing you find this argument. In explaining your point of view, be sure to analyze the line of reasoning and the use of evidence in the argument. Also discuss what, if anything, would make this argument more sound and persuasive, or would help you to better evaluate its conclusion.

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The conclusion is the author's main point. If you aren't sure, try paraphrasing the argument: the author believes "X" because of "Y." "X" is the conclusion. Here, the author believes "it's impossible to eat a good diet" (conclusion) because "TV news programs keep announcing different things" (evidence) and "supermarkets have lots of different brands" (more evidence).

Step two:

What must be true for this argument to work? That is, what does the author assume? The author assumes… most people watch TV news programs most people rely on TV news programs for diet information most people shop in supermarkets the wide selection of brands makes it very difficult to find healthy food (You might have found some other assumptions or expressed these differently) Think about the assumptions above. If any of the above are false, the author's argument is weakened. If, for example, most people plan their diets based on recommendations from their doctors, the author's conclusion loses all of its validity. If the wider

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selection of brands makes it easier to find healthy food, and not harder, the argument is also weakened. Note: All arguments given to evaluate are seriously flawed.

MODEL

FOR

ANALYSIS

OF AN

ARGUMENT

You can, of course, modify this template or make your own. The argument presented is not convincing. The author concludes (conclusion) based on (evidence). There are several questionable assumptions, resulting in a logical gap between the premises and conclusion. A major assumption made in this argument is that (first assumption). This assumption may very well be wrong, as (why it may be wrong). The validity of the conclusion also depends on (second assumption), a key concept omitted in the argument. For if (opposite of second assumption) were true, it is likely that (opposite of conclusion). Finally, even if the two assumptions discussed above were true, the argument would be unconvincing because, without providing any evidence, it requires that (third assumption). In order to make the argument more persuasive, the author would have to demonstrate that the assumptions discussed above are, in fact, true. Thus, evidence supporting (first assumption), (second assumption), and (third assumption) would tighten the link between the premises and conclusion, making the reasoning more sound. Without any discussion of these ideas, however, it is impossible to evaluate the conclusion.

‘Argument’ questions might sound familiar, suspiciously familiar – very much like Critical Reasoning arguments, no? Ask yourself the same questions: What is the conclusion? and What are the flaws?

BRIEF ESSAY-WRITING REVIEW The following are some guidelines for effective writing. None of the following hints are related to the rules of grammar tested by GMAT Sentence Correction questions, and they are not included in the Grammar Review. However, all of the rules explained in the Grammar Review should also be adhered to for the AWA essay. The guidelines which follow are intended to help you improve your AWA essay but are by no means a comprehensive review of the rules for effective essay-writing.

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PUNCTUATION Here are a couple of important points to remember. – Avoid comma splices A common mistake is to link what should be two separate sentences with a comma (,). Here's an example: "Research into this disease is important, governments should support it." There are two ways to remedy this error: "Research into this disease is important and governments should support it," and "Research into this disease is important, and governments should." – Avoid most forms of punctuation, period. Commas and periods should be all that are necessary to the essay. Of course, if there is a rhetorical question included, it must be followed by a question mark. If you’re not sure about whether to punctuate or not to punctuate, don’t.

If you have been utilizing semicolons all your life and you are 100% certain that you've mastered the difficult art, go ahead and use them. Otherwise, pretend they don't exist. Many good essays are reduced in effectiveness by a proliferation of unnecessary semicolons (written by people who have semicolon cancer). – Colons can also be somewhat tricky. If you insist on using them, remember this: colons are abbreviated equal signs. What is on one side of them must be roughly equal to what is one the other side of them (within the sentence). – Parentheses, although are fun to play with, have no place in a short, formal essay, in which every sentence should be relevant and should contribute equally.

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SOME

ELEMENTS OF STYLE

Logical links For clarity in your essays, employ transitions to signify emphasis or contrast, or simply to provide the essay with a sense of fluidity. Here are some useful expressions. – Giving examples: … is demonstrated by… … is illustrated by … … is typified by … For example … One instance of this … … as in the case of … – Emphasis In fact … Obviously … It is clear that … Definitely … Pertinently … – Contrast Conversely … Regardless … On the contrary … While … is true, it can also be argued … Although … another viewpoint is that … Despite this situation … In contrast to … … is in opposition to … – Causal relationships Therefore … Thus … Consequently …

SENTENCE

Good ideas can easily be lost without logical links. Graders like ‘em because they make explicit the relationships among your ideas. So, link it up.

VARIETY

Diversify your phrasing. Avoid writing more than two sentences in a row of the same length. Avoid writing more than two sentences in a row that are patterned on the subject-verb-modifier formula. Avoid writing more than two sentences in a row that begin with the same word. (You see what we mean?) Don't:

Jake ran to the post office to mail his letter. Jake arrived at the post office at 5:05. Jake found the post office closed. Jake went to another post office not far away. Jake tried again to mail his letter. Jake found that post office closed too.

Do:

Jake ran to the post office to mail his letter. At 5:05 he arrived, found the post office closed, and decided to try again at a different post office. Jake went to another post office. It too was closed.

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VOCABULARY While use of formal language (specialized vocabulary used more in writing than in speech; such as specific business terms used in business documents) can improve your essay, it is more important to use language you know how to use. Try to strike a balance between sophisticated and showy. Most importantly, be specific. Avoid vague words. Before you write "people," think to yourself "What kind of people?" There's probably a more specific word you could use, whether it's "homeowners," "consumers," "students," "test takers," etc. Apply the same process for "things," "places," and other words that encompass broad categories. Here are some verbs that are generally overused and vague: – To do It is rare that the verb "to do" is necessary. In formal writing you can almost always replace it with a more specific verb. Instead of: "Governments need to do something about this problem," try "Governments need to remedy this problem." Instead of "College graduates do great work for the world," try "College graduates perform important actions in society." – To have "To have," of course, means "to possess, to own". Avoid phrases such as "The argument has three parts." There might be three parts in the argument, but does the argument possess those parts, the way you possess, for example, the new Madonna CD? Would you write "The argument owns three parts"? or "Three parts belong to the argument"? No, not unless you are writing metaphorically, and metaphorical writing should be avoided on the AWA. Try, "The argument is composed of three parts," or "The argument can be divided into three parts." VAGUE give show, point out get

SPECIFIC provide demonstrate, depict, illustrate receive, become

– Avoid the passive voice of verbs. Instead of "The discovery was made by scientists in 1934” … write "Scientists made the discovery in 1934 …" Instead of "The voters' opinions are demonstrated by the results of the survey," write "The results of the survey demonstrate the voters’ opinions." – Avoid colloquial words such as: really, pretty (as in “The example is pretty important”), and lots of. – Avoid contractions. – Never state in many words what you could just as effectively state in a few.

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FIRE! ANALYSIS

OF AN ISSUE

This is an example of a "2," or "seriously flawed" essay. Look for problems of content, style, grammar, and organization as you read this essay. Think about how it could be improved and compare your ideas to the critical comments that follow. Space exploration is definitely a good idea. Not just now, also for the future. There's already 5 billion people on the planet. We put people in a biosphere, why not in space? 5

The moon may turn out to be uninhabitable, but Mars is pretty similar to the atmosphere on earth. And the Russians, while having problems, have kept people in a space station for a long time. If we didn't fund space exploration, we 10 wouldn't have any of these things. It's important to learn about space. If Galileo didn't make a telescope, we would still think the earth went around the sun! Over the centuries we have learned a lot about space and science, 15 and now that we have the technology, we really should continue. There are lots of advantages for space research. Economic, scientific, even health advantages. Thank you. Content: Notice that the writer of this essay misses the point that the issue is government funding of space travel rather than space travel itself. The author makes basically one point: that space exploration will benefit humanity if it is judged possible for people to live in space, thus relieving the earth of its population problem. This point is valid, and the references to the world's overpopulation problem and the biosphere experiments would support it well if their relevance had been explained. A good essay would include at least one other benefit and also address some of the opposing arguments. Organization: There seems to be a vague attempt here to fit this essay into a introduction-body-conclusion format, but it crumbles. There is also no development of the author's main point: it is rather a stream-ofconsciousness ramble of somewhat related facts and ideas. Grammar: The essay is littered with mistakes. The problem is that not only are there grammatical errors, but also the errors interfere with the essay's intended (one guesses) meaning. For example, the sentence fragment that concludes the passage might actually contain a valid argument (that space research could produce benefits in various fields). Its unintelligibility, however, prevents its contributing to the essay. © The MBA Center

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Style: Note that this essay does contain an admirable variety of sentence lengths. Stylistic problems, though, pervade. The vocabulary is limited. Changing a few words to strengthen the transitions between the ideas (the "but" in line 6 would be more effective as a "however"; the "and" in line 7 could be a "furthermore"; etc.) would improve the style of the essay. Furthermore, too much colloquial language is used: "lots of," "we really should," etc. This is an example of a "4," or "adequate" essay. Again, look for problems of content, style, grammar, and organization as you read. Think about how it succeeds, how it could be improved, and compare your ideas to the critical comments that follow the essay.

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I am strongly in favor of space exploration and government funding thereof. I believe that it is an essential aspect of humanity that we are explorers, and that the money, though there is a great deal of it necessary, could not be better spent than on our journeys into the nether regions of our knowledge! What distinguishes humankind from the bestial elements of the earth? Our ability to think, to reason, and above all, to imagine, does. Humankind has been granted the gift of intelligence. What a shame it would be to waste it. The frontier of space is the last remaining border of our knowledge! It is there to be conquered. There are more mundane reasons, too, to explore space, like, for example, the short-term benefits. These include helping unemployment levels stay down by providing jobs to everyone associated with the space programs, and aiding meteorology by placing satellites in orbit around the earth. Moreso, however, it seems that is our responsibility to expand the limits of our knowledge! I know what you are going to say, that the money should be spent on social initiatives such as schools, feeding the poor, cleaning the environment. These are valid ways to spend money, but not as essential as stretching the possibilities for knowledge! Although government funding of the space program is a sensitive issue, I think it is clear that, if governments can afford to have humanity explore the universe, it is our responsibility to do so.

Content: This essay manages to focus on the issue of government funding and presents two sides of the argument, clearly choosing one side and acknowledging the other. The author's main point here, the quasi-mystical belief that space, as a final frontier, represents some sort of metaphysical barrier to be breached, is

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supported, though only slightly, by mention of the difference between human beings and other animals, and that there is a great deal of further exploration possible in space. The author laudably adds two other reasons for why space research is valuable, although the benefit of keeping people in work seems of only marginal relevance to the issue. Organization: This essay is fairly well-organized. The first paragraph states the author's position while referring to the main flaw in his or her position. A more detailed description of the opposing position would have strengthened this paragraph. Each ensuing paragraph has a clear individual focus, although the “knowledge” tirade somehow manages to show up everywhere (it shouldn't). Grammar: There are numerous minor grammatical mistakes in this essay, none of which interferes with its meaning. The “we,” for example, in line 3 does not have a grammatically correct antecedent, although it is obviously meant to refer to “humanity.” Style: The essay contains well-crafted transitions between ideas: "moreso," "however," "although," etc. The rhetoric, unfortunately, is a tad overblown. It is advisable to shy away from phrases such as "the nether regions of knowledge." The word choice is also occasionally suspect ("cleaning the environment"? Really.) Furthermore, the phrase "I know what you are going to say," is a poor attempt at a rhetorical device.

Flaubert did it, maybe you can too... but not on the AWA: Resist dramatic flourishes and focus on specifics – it is very easy to lose sight of the facts when you try to write dramatically.

This is an example of a "6," or "outstanding" essay. Notice its strengths and weaknesses and compare your ideas to the critical comments that follow the essay.

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The issue of government funding of space exploration is complex and controversial. The costs required to fund a major space program are enormous, and some might argue that the investment would be made more sensibly and productively in education, housing for the poor, or other programs with concrete social benefits. There are many long-term advantages to space exploration, however, that justify the high costs. Both perspectives on the issue are valid, but, overall, the advantages of government funding of space exploration outweigh the disadvantages. Space exploration and research are important because they offer practical technological advances. For example, weather satellites and communications technology would not have reached nearly their advanced stages were it not for the information acquired by space programs. Perhaps with continued research further advances in these or other fields will develop. Secondly, because scientists are certain of relatively little about the universe in comparison

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with, for example, human anatomy, space 25 exploration is a field wide open for scientific thought. Such research not only encourages intellectual thinking and new research, but also provides a format in which theoretical physicists can test abstract hypotheses. 30 Furthermore, the knowledge gained through exploration of space is of immense scientific and, potentially, philosophical interest, and could not be learned elsewhere! Continuing this research is the sole method by which the human 35 race can continue to learn about it's place in the universe. Naturally, the objections that can be raised about space exploration, particularly concerning its financial costs, are substantial. It is true that 40 money is badly needed elsewhere in society. However, it seems likely, though unfortunate, that there will never be a time that funds won't be required to improve the lot of the destitute. The time is right for governments to capitalize 45 on what public support there is for space exploration, and for space research programs to build on what progress has been made. While the funding of space exploration is an issue that must be considered carefully, the 50 scientific and technological advances that may be within the grasp of our research, compounded with the short-term benefits, provide ample support that governments should continue to support the space program. Content: Both sides of the issues are addressed. One is chosen. The author supports his or her position with three reasons: that space research has practical technological advances, that it encourages scientific thought, and that there are no other available methods by which this information will become available. The counterargument is acknowledged and, not dismissed, but refuted. Notice that the grounds for this refutation are perhaps not perfectly sound, but they are elucidated as thoroughly as possible considering the time constraints. Organization: First of all, note the structure of the first paragraph. The issue and its complexities are clearly identified. The author then presents the stance to be taken in the ensuing paragraphs. Grammar: The essay contains exactly one grammatical error. (Can you spot it?) Obviously, it doesn't affect the essay. Style: Note the preponderance of transitional or emphatic phrases employed: “however,” “For example,” “Secondly,” “not only … but also,” “furthermore,” “naturally,” etc. The essay thus reads fluidly and easily. Note also that the essay is not stylistically flawless – the phrase, “weather satellites and communications technology would not have

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reached nearly their advanced stages,” is slightly clumsy. (The sentence could have been written: “the tremendous progress in meteorological and communications technology might not have been achieved.”) An essay does not have to be perfect to be scored a 6!

ANALYSIS

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ARGUMENT

The following is an example of an essay that was scored a “2.” Look for problems of content, organization, grammar, and style. Think about how it could be improved and compare your own analysis to the comments that follow. This argument isn’t really convincing. It may be true and it may be false, but the “author” doesn’t really give so much information. What do supermarkets have to do with this? What if 5 you eat in restaurants or shop in others kinds of stores? One could then still have a good diet. The author also fails to mention exercise. Even if you don’t eat that well, if you exercise a lot you might still be in good health. The author 10 talks about TV (I don’t watch TV) but he should also mention radio and newspapers and if a news program gives contradictory information, it maybe isn’t there fault. Maybe it is the doctors, not the journalists, who keep changing 15 they’re mind. The point about their being lots of different brands is a good one. What with all the hassles of modern life, who has the time to study each brand and decides what’s healthy and what’s 20 not. And all the fast food restaurants. Everywhere you go there’s a McDonald's or Burger King. How can you have a very healthy, good diet under these circumstances? If the author discussed other kinds of places 25 where you get food, and talked about doctors not just TV, he would have a pretty good point. As it stands, I disagree with the argument. Content: The essay fails to stay focused on dissecting the argument. The issue of exercise is not presented in the argument; neither is the issue of whose fault it is for the misleading health information on television news programs. They are therefore irrelevant. Another salient error is the author's inclusion of his or her opinion of the argument. This is never appropriate. There are some positive points in this essay. Note the references, incoherent though they are, to flaws in the argument – specifically, the assumption that all consumers receive information from television, and the assumption that everyone purchases food from supermarkets. Another positive point is the author's inclusion, in the final paragraph, of a proposal to strengthen this argument. © The MBA Center

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Organization: As in the case of the previous “2” essay, here there are hints of a introduction-body-conclusion format, but hints just aren't good enough. The individual paragraphs show no coherence. Grammar: There are many grammatical errors. Among the most salient are the conflation of “their,” “they're” and “there,” and repeated pronoun errors. Style: The essay is a mess stylistically. The preponderance of rhetorical questions lends this piece an absurdist quality. Notice the parentheses. (You shouldn't use parentheses.) The use of the firstperson pronoun should be avoided. In this instance what could have been a sound critique of the argument, the observation that not everyone watches television, is obscured by the style. The word choice is poor. Note that the phrase “give so much information,” should be “provide enough information.” There are also a strange set of unnecessary quotations marks around the word “author.” The following is an essay that was scored a “4.” Notice its relative strengths and weaknesses. How would you improve it?

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“It has become almost impossible” to eat a balanced diet states the author, yet without providing ample backup. There are some sound ideas presented here. Unfortunately they are marred by a lack of rationality and a tendency to overstate the case. The writer doesn't give enough solid examples or provide enough reasons why this is so. One of the author's biggest points is that the size of supermarkets prevent consumers from being able to locate healthful food. While this may be true to an extent, this line of reasoning, in order to justify the author's viewpoint, needs strengthening; this could be accomplished by, for example, citing specific food types and the brands of that ilk that are available. Another way to bolster this argument might be to show statistics including where people shopped and what they buy. Although the authors' second point, about how the television news media people don't know what they are talking about half the time, makes sense, again, it would be productive to include specific examples. This could be done through mentioning key individuals who propagate the myths of health that permeate society, or by showing that television influences our lives. Again, statistics showing how many people watch television and exactly for what they use it for would support the author's argument.

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Analytical Writing Assessment

What the author mainly fails to do in this piece of writing, though, is restrict their commentary to those to whom it actually 35 applies: people who shop in the supermarkets and watch so much TV that they get all their information there. If the passage had stayed focused on them instead of generalizing, it would have been successful. As it stands, it fails 40 to convince me that “it is impossible too eat a balanced, healthy diet.” Content: This essay successfully identifies the flaws in the argument and offers solutions which could strengthen the argument. The proposed solutions in the main body of the essay, however, are not the most direct methods to strengthen the argument. Only in the concluding passage does the author include the clearest remedy, re-focusing the argument on those who actually receive their nutrition information from television and shop only in supermarkets. Organization: The essay presents an overall view of the argument in the introductory paragraph, and then proceeds to break down the features of the argument paragraph by paragraph. Grammar: There are several minor grammatical or spelling errors, none of which interfere with the author's intended meaning. Style: There are numerous stylistic problems here. First of all, the author's prejudices repeatedly color his or her analysis. The phrase “the television news media don't know what they're talking about half the time,” could contribute more effectively to the essay were it to read “the television news media indiscriminately disseminate the latest health findings,” or was written in another way with less opinion, and more objectivity. The word choice is occasionally poor. Instead of “biggest” (line 9), use “most important” or “major” (the points are all the same size). Also, note the semicolon in line 14. It is actually used correctly, but is unnecessary since there is no need to connect those two sentences, which would be fine independent of one another. This is an example of an essay that was scored a “6.” Look for a successful analysis of the argument, and the use of style, grammar, and organization. Why was this essay given the top score? The author's conclusion that it's almost impossible to eat a balanced, healthy diet, depends heavily on two principles: misleading information provided by television news 5 programs, and the increasingly wide selection of brands available at supermarkets. That these points are the main factors contributing to the average diet is disputable, and consequently, so © The MBA Center

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is the author's position. The argument rests on 10 numerous questionable assumptions and vague, incomplete evidence. The premise concerning the new, “sometimes contradictory” information provided on TV news programs may be valid. This evidence is only 15 relevant, however, if it is true that average consumers watch television news programs, and, moreover, use the information to plan their diets. Clearly, if people are unaware of the information provided, the contradictions in the 20 information won't affect their eating habits. Even if it is accepted that consumers watch news programs, the premise of the author's argument is flawed, as it rests on the assumption that viewers actually rely on these 25 programs to determine their diets. It is likely that people use other, readily available, sources of information, such as nutritionists, doctors, literature, for this purpose. The conclusion that it is “almost impossible” to eat a healthy diet is 30 therefore completely unfounded. The author's second premise, pertaining to supermarkets, is debatable, and thus also results in questionable assumptions. The author does not explicate the assertion that there is a 35 correlation between having many brands to choose from and the impossibility of dieting healthily. Presumably, the intended contention is that consumers, upon entering the markets, are overwhelmed by the sheer volume, and 40 consequently are unable to make sound, informed choices. This is certainly an unfounded assumption. It is, in fact, arguable that the greater choice makes it easier to find healthy brands. The author fails to mention that in this 45 wide selection of brands comprises many healthy food choices. It is entirely possible that government regulations ensure a high quality of food despite the large number of brands. The author's statement about supermarkets, 50 furthermore, is only relevant to an analysis of people who shop in supermarkets. Consequently, yet another weakness in the argument is the failure to account for alternative sources of food products, such as specialized health food stores, 55 local markets, which may supply only healthy food. The argument would be more persuasive if it addressed some of these questionable assumptions. A validation of the stated 60 conclusion necessitates evidence that the majority of consumers shop in supermarkets and use no source of nutritional information other than television news programs. Additionally, the author should demonstrate that the diverse 65 selection of brands includes largely unhealthy products. Another method by which the

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argument could be strengthened would be a limiting of conclusion to refer to people who shop in supermarkets and rely on television for 70 diet information. Content: The essay analyzes the argument fairly thoroughly, pinpointing the premises and the conclusion, and the flawed logic. It offers several options by which the author could strengthen the argument, including the most direct method – limiting the conclusion to consumers who only shop in supermarkets and base their purchasing decisions on information provided by the television news. Organization: Notice the systematic analysis of the argument. Each paragraph focuses on a specific aspect of the argument, and each contains an individual introduction and conclusion. Grammar: There are several small grammatical errors. For instance note that line 28 needs an “and” between “doctors” and “literature.” Style: The style is acceptable, but not flawless. There are some awkward phrases, such as “A validation of the stated conclusion necessitates evidence…” (line 59). Notice the effectiveness of the transitional and emphatic phrases, such as “consequently,” “however,” “therefore,” “clearly,” “furthermore,” etc.

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FAMOUS LAST WORDS Be sure you have read and understood both the essay-writing review in this chapter and the Grammar Review in this book, preferably before you have written any practice essays. Prepare and memorize a template. All AWA essay topics can be addressed using one of the templates which are included in this chapter. When you take your exam, spend a few moments preparing some notes or an outline. Don't indulge in stream of consciousness writing. Abstract poetry might be a hit in Lit. classes and at cocktail parties, but on the GMAT it won't fly. Try to leave a minute or two to proofread, just to make certain you haven't made any egregious errors.

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Analytical Writing Assessment – Homework

ANALYSIS OF AN ISSUE TIME - 30 MINUTES

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Directions: Analyze the issue presented below and develop your position. There is no “correct” point of view. In presenting your position, you should consider different perspectives. Read the issue stated below and the instructions that follow. You may make any notes in the empty space on the page that will help you plan your essay.

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ESSAY 1 Some educators argue that children who demonstrate particular aptitude for learning when they are young should be placed in special programs where they are given the opportunity to advance more rapidly than they might in normal classes. Many child psychologists, however, have publicly stated they do not support special programs for gifted children. They claim that separating children by aptitude at an early age is unfair to those in the slower classes, some of whom might also thrive in a more challenging environment. Which do you find more convincing, the argument of the educators or that of the child psychologists? Explain your point of view using relevant examples, based on your experience, observations, or readings.

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Analytical Writing Assessment – Homework End

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ANALYSIS OF AN ARGUMENT TIME - 30 MINUTES Directions: Analyze the argument presented below. You should not develop your own position on the issue. Rather, you may consider any assumptions made in the argument, the ways in which the evidence is used, how the argument’s conclusion might be strengthened, or any logical flaws you observe. Read the argument and instructions that follow. You may make any notes in the empty space on the page that will help you plan your essay.

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ESSAY 2 Over the last five years, newspaper sales in Region X have declined by over 10%, while sales of weekly news periodicals have increased slightly. This demonstrates that more and more people in the region have less time to read a newspaper every day, and prefer to read a once-weekly summation of world events. Discuss how logically convincing you find this argument. In explaining your point of view, be sure to analyze the line of reasoning and the use of evidence in the argument. Also discuss what, if anything, would make this argument more sound and persuasive or would help you better evaluate its conclusion.

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Step 14 Analytical Writing Assessment Workshop

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Analytical Writing Assessment

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Analytical Writing Assessment – Workshop

ANALYSIS OF AN ISSUE TIME-30 MINUTES Directions: Analyze the issue presented below and develop your position. There is no “correct” point of view. In presenting your position, you should consider different perspectives. Read the issue stated below and the instructions that follow.

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ESSAY 1

“ I don’t think being well-rounded is particularly important; I would rather see people with a cutting edge on them.” Discuss the extent to which you agree or disagree with the opinion expressed above. Support your point of view with reasons and/or examples from your own experience, observations, or reading.

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Analytial Writing Assessment – Workshop End

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ANALYSIS OF AN ARGUMENT TIME - 30 MINUTES Directions: Analyze the argument presented below. You should not develop your own position on the issue. Rather, you may consider any assumptions made in the argument, the ways in which the evidence is used, how the argument’s conclusion might be strengthened, or any logical flaws you observe. Read the argument and instructions that follow.

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ESSAY 2

“ The country of Aviar could best solve its current trade deficit problem by lowering the price of parrots, its primary export. If Aviar pursued this course of action, it would be able to compete more successfully for markets with other parrotexporting countries. Sales of Aviar’s parrots abroad would increase- an increase which would dramatically reduce Aviar’s trade deficit.” Discuss how logically convincing you find this argument. In explaining your point of view, be sure to analyze the line of reasoning and the use of evidence in the argument. Also discuss what, if anything, would make this argument more sound and persuasive, or would help you better evaluate its conclusion.

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Step 15 Reading Comprehension

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Step 15.1 Lesson

GENERAL OUTLINE

Slightly more than one-third of the questions in the Verbal Section of the GMAT CAT are Reading Comprehension questions. These questions test your ability to understand and analyze information presented in written form. This lesson introduces the most common Reading Comprehension question types and provides strategies and specific reading theories for answering each one of them. In addition, in this lesson you will learn reading techniques that will help you improve your reading efficiency and comprehension.

THE FOLLOWING TOPICS WILL BE COVERED

IN

THIS LESSON:

The MBA Center Reading Theories for Reading Comprehension Passages The Three Kinds of Reading Comprehension Answer Choices The Four Groups of Reading Comprehension Question Types The MBA Center Approach to Reading Comprehension Four Drills in Reading Comprehension

KEY TERMS Passage: Reading Comprehension passages are generally between 250 and 450 words in length and relate to a variety of subjects, including literature, philosophy, law, the social sciences, and the physical sciences. Trigger words: Words in a passage which identify the conclusion, idea transitions, changes in points of view, evidence of authorial opinion, and introductions to examples. Scope: This concept describes what is relevant or irrelevant in a Reading Comprehension passage. Any information, ideas, or assumptions not directly related to what is stated or implied in a passage are considered irrelevant and therefore out of scope. Understanding scope improves your ability to answer Reading Comprehension questions quickly and accurately.

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READY… The Reading Comprehension passages and questions are part of the Verbal Section of the GMAT CAT. The questions appear randomly during the Verbal Section in groups of 5 to 7. There are between 14 and 18 Reading Comprehension questions in the section divided among 4 passages (one of which is experimental) of varying lengths. The Reading Comprehension questions are the only ones on the CAT that are not adaptive. This means that once you are given a passage to read you can expect a set of 5 to 7 questions that will not vary in score value. Because the questions on the Reading Comprehension passages are not adaptive, you will not see them at the beginning of the Verbal Section, since the first 7 questions or so of either section determine your testing level. In short, because this section is not scored adaptively, lower and higher numerical score values are not assigned to each question, although there is still a range of difficulty from easy to difficult for any set of questions. The types of passages you will find address business, science, or social science topics. In the interest of test-fairness, so that one student will not have an advantage over another, the 4 passages you see should each cover one of the three subject areas listed above. The length of the passages ranges from 250 to 450 words written according to a dense, academic style, what we call GMAT-style. Reading the passages and answering the questions on the CAT test is no easy task: staring at the monitor, not making notations on the monitor, and using the mouse to scroll up and down are all disadvantages of computerization. The passages and questions in Reading Comprehension require a strange combination of speed, critical reasoning, and less-than-complete understanding. Because the CAT does not allow you to look ahead at different passages or questions before responding to them, an awareness of your strengths and weaknesses regarding subject topics, reading, and vocabulary skills will help you invest your time more effectively in two ways. One, you can spend more time on subjects you grasp well and, two, you can use the MBA Center strategy and guessing tips to answer questions about passages you find particularly confusing or difficult.

On the GMAT CAT, the passages you are given come from magazines, newspapers, books, and academic journals. Phineas rewrites them in his incomparable style to make them difficult to understand.

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DIRECTIONS If you click on the Help Button on your screen the day of the test, the following directions will appear. Learn them now and save yourself the time and trouble on the day of the exam. GMAT CAT – Section 4 : Verbal End

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Directions: This set of questions are based on your understanding of a passage. Select the best answer following the passage on the basis of what is stated or implied in the passage.

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As usual, the directions don't provide a great deal of information. Just remember that you get points from the questions, not from the passages.

THE GOOD NEWS No outside knowledge of business, science, or social sciences is required for this section. You are being tested on your ability to understand a text, not on general knowledge. Any familiarity you do have with a particular subject and vocabulary is a natural advantage for you in this section.

THE BAD NEWS

Identify the main idea of a passage first. Many questions refer to it directly or indirectly, and it holds together the network of supporting ideas which run through every passage

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The Reading Comprehension passages are written in a dense, long-winded, and confusing manner. You are rarely given a complete enough presentation of a topic to grasp it fully. Nor are you given enough time.

WHAT

ABOUT

VOCABULARY?

GMAT-style is not an easy style to read and understand within the short amount of time you are given. The grammatical structure of the sentences is varied and complex and makes the ideas presented difficult to understand, especially under the pressure of testing conditions. For vocabulary and for grammar, you can only increase your understanding with more and consistent practice. Nevertheless, you do not need to understand every single word in a sentence or paragraph in order to answer a question correctly. You can guess the meaning of most words by using context clues to help you.

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Reading Comprehension

THE CHALLENGE The main challenge in Reading Comprehension is time: to understand just enough of each passage to answer the set of questions in the very limited time allowed. Most students use their time to read each passage and each question for full comprehension. This is a normal reading habit, but it has no place and no time in this section – there are better uses of your time. Since you score points only from correct answers and not from your reading technique (no one will know how you read each passage), this lesson is focused on reading passages with efficient but less than full comprehension, while still being able to answer the most questions in the time given.

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There are basically two structures used for Reading Comprehension passages: descriptive and argumentative.

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Step 15.1 Lesson

AIM… 1. GMAT READING THEORIES THE MAKING OF A READING COMPREHENSION PASSAGE Although Reading Comprehension passages represent a variety of subjects (business, science, and social sciences), they are all constructed in similar ways. Each passage is an adaptation of a full-length article which is shortened and rewritten to conform to GMAT conventions. Remember: standardized test = standardized content. In the rewritten GMAT passage: Transitions and expositions are minimized to make the passages more difficult to comprehend quickly. The four most common types of idea development are: refutation, illustration, explanation, reconciliation.

Most of the important terms and concepts are not defined and require you to derive their meaning from context in order to answer the questions. The opinion, tone, or argumentative position of the author is only suggested, rarely stated, in each passage, so your ability to infer meaning or information is very important. The result is a passage containing the following features: - A main idea at the beginning of the passage - A theme by paragraph

Don’t try to remember every single detail. You do need to remember the location of details in the passage (in roughly the middle third of a passage) for quick reference when asked a detail question.

- 1 to 2 key concepts - Some examples and details - Some quotations from authorities on a given subject - A few undefined phrases, terms, or concepts - In argumentative passages, 2 or 3 competing theories. With such a model, Phineas will use his standard question types and set some traps in the answer choices. Descriptive and argumentative passages are most often structured in the following ways: Descriptive passages 1. 2. 3. 4.

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A main idea is presented Supporting ideas Supporting details Conclusion (not necessary)

Argumentative passages 1. A problem is presented 2. First position on the problem 3. Second position on the problem 4. Return to the first position, or a third position is presented

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Reading Comprehension

2. READING GMAT PASSAGES Key 1: Look for the main idea. Ignore the facts. Imagine that you’re playing a memory game and someone shows you a satellite photo of Southern California, taken from space. You have a short time to look at the photo and then it is removed from view. You are then asked to make a list of the identifiable objects which you were able to recognize before the photo was removed. What will you remember? The largest objects which stand out in the photo, like baseball diamonds, the Pacific coast line, or perhaps a large government building will stick in your memory. You wouldn’t try to list the houses, cars, or trees (the little details) because they are less significant. There is little chance that you would have the memory to list every single object in the image. The same technique applies to Reading Comprehension passages, which are full of details, examples, facts, secondary ideas, and varieties of tone and style – but should be reduced to one main idea. The reason is simple: if you try to remember every single detail, you will not understand the main idea or purpose of the passage. You’ll remember specifics but miss the general sense of the passage, which is what counts. Key 2: Do not read a passage entirely. In these passages, the key sentences which carry the main idea from one location to another, are usually at the beginning of each paragraph. The first few sentences of the first paragraph usually give you the main idea of the passage, and the first few sentences of the following paragraphs restate the idea as it was developed in the passage. An exception is the last two or three sentences of the final paragraph which contain the conclusion of the passage. Do not skip these last sentences: they state the results of the line of reasoning which has been developed throughout the passage, the line of reasoning you should follow from beginning to end, tracing the progression of just the main idea. Key 3: Identify the trigger words. Once you have a good, but less than complete, idea of the content of the passage, it’s time to identify trigger words which give you clues to shifts in points of view and take you directly to the overall meaning, or primary purpose, of the passage. Triggers words introducing: New ideas

Contrasts

In fact Similarly For example Besides Still Therefore For instance

But Although However Not only...but also Some...others Yet Conversely In contrast to Either...or/Neither...nor

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Step 15.1 Lesson

DRILL 1 The passage which follows the original below has been condensed to approximately one-third of its complete length to highlight only key sentences. After reading the condensed passage, answer the questions which follow.

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The world’s longest fence is the 3,307 miles of unbroken wire mesh that comprise the "Dog Fence," which runs from off the eastern coast of Australia, near Brisbane, to the center of the continent's southern coast, ending at a remote village called Yacka. Parts of it almost a hundred years old, the fence is in place to protect what has become the world's second-largest sheep population and a wool industry that earns Australia the equivalent of five billion U.S. dollars per year. Employment opportunities generated by the wool industry and maintained by its success provide at least two jobs for every one hundred sheep and are viewed as critical to a country in which over 10% of the stable population is registered for unemployment benefits. The fence protects the sheep from dingoes, Australian wild dogs, cousins to coyotes and jackals. Dingoes are indigenous to the Outback regions, have never been effectively domesticated, and hunt in packs like coyotes. Voracious carnivores, dingoes have been the enemy of Australian ranchers almost since the first European settlers arrived, and, despite the "Dog Fence," still manage to cause several millions of dollars’ worth of damage to the industry each year. Efforts over the last 50 years to control dingo populations – they are rapid breeders – have been unsuccessful. That the fence is necessary to the industry is demonstrated by the fact that when damage occurs, such as when 1992 rains caused flooding that destroyed parts of the fence in many areas, the punishment inflicted by the dingoes becomes exponentially worse. The 1992 flood was one of the most severe in Australian history and the government provided disaster relief for thousands of inhabitants, many of them sheepranchers, in the areas hardest hit by the rains. The “Dog Fence," though, has stirred controversy and protests from conservationists, most of which are based around the notion that animal migration, which the fence severely restricts for many species, is an essential component of the ecology. Conservationists have long been in conflict with sheep ranchers who devote a large portion of their annual revenues to retain lobbyists and attorneys to protect their commercial interests. Some environmentalists warn that the landscape has become overgrazed inside of the fence. They argue that there is overcompetition among species for the scarce and diminishing nutriments available inside the fence. This is partly due to another development © The MBA Center

Reading Comprehension

50 which is a problem itself: The kangaroo population inside the fence, consisting of red and gray kangaroos and wallabies, has exploded, as the large marsupials, natural prey for dingoes, have had no enemies to keep their population in check. The most 55 recent government estimates point to a kangaroo population increase of over 50% from 1973 to 1991. The kangaroos now also threaten the sheep population, competing with it for water and grass. Ranchers have noted a corresponding decrease in 60 wool quality from sheep which are undernourished as a consequence of this competition. As a result the Australian government has had to cull 3,000 kangaroos per year from the environment. Obviously, another solution to this problem should be found.

CONDENSED

PASSAGE

The world’s longest fence is the 3,307 miles of unbroken wire mesh that comprise the "Dog Fence," which runs from off the eastern coast of Australia, near Brisbane, to the center of the continent's southern coast, ending at a remote village called Yacka .................. …………………………………………………… …………………………………………………… …………………………………………………… …………………………………………………… The fence is in place to protect the wool industry and what has become the world's second largest sheep population. The fence protects the sheep from dingoes, Australian wild dogs, cousins to coyotes and jackals…………… …………………………………………………… …………………………………………………… That the fence is necessary to the industry is demonstrated by the fact that when damage occurs, such as when 1992 rains caused flooding that destroyed parts of the fence in many areas, the punishment inflicted by the dingoes becomes exponentially worse. …………………………………………………… The "Dog Fence," though, has stirred controversy and protests from conservationists, most of which are based around the notion that animal migration, which the fence severely restricts for many species, is an essential component of the ecology………… …………………………………………………….. …………………………………………………….. The kangaroo population inside the fence, consisting of red and gray kangaroos and wallabies, has exploded, as the large marsupials, natural prey for dingoes, have had no enemies to keep their population in check. The kangaroos now also threaten the sheep population, competing with it for water and grass ……………………………………………….. Obviously, another solution to this problem should be found. © The MBA Center

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2. According to the passage, the erection of the "Dog Fence" has contributed to all the following developments EXCEPT

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! (A) highlight the unreliability of the "Dog Fence". ! (B) convince the reader of the necessity of the wool trade to Australia's economy. ! (C) give an example of how the "Dog Fence" manages to protect the flocks of sheep. ! (D) demonstrate the potential damage to the wool industry prevented by the "Dog Fence". ! (E) underline the savage nature of the dingo.

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3. The author of the passage probably mentions the 1992 flood damage in order to

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! (A) a population boom among wallabies. ! (B) the success of the Australian wool industry. ! (C) areas where the high concentration of sheep and kangaroos has caused overgrazing. ! (D) several million dollars worth of damage to the Australian wool industry. ! (E) protests from environmentalists concerning Australia's treatment of its wildlife.

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! (A) the problem of overpopulation of large marsupials afflicting certain areas of eastern Australia. ! (B) the conflict between environmentalists and ranchers over sheep-grazing areas. ! (C) the challenges the "Dog Fence" places on animal migration. ! (D) the role of economics in determining human manipulation of an ecological system. ! (E) the positive and negative effects of the "Dog Fence."

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GMAT CAT – Section 4 : Verbal

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4. According to the passage, the Australian government has had to keep the kangaroo population in check because ! ! ! ! !

(A) (B) (C) (D) (E)

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overgrazing has damaged the soil in southeastern Australia. they have caused damage to the "Dog Fence". the rate at which the species is reproducing has accelerated. there are now more kangaroos than sheep. large marsupials use important resources necessary to the wool industry.

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5. The passage provides support for which of the following statements?

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! (A) The gradual removal of the kangaroo population to another region of Australia where there are fresh grazing areas. ! (B) The construction of another fence separating the sheep from the large marsupials. ! (C) A dismantling of the fence in order to allow the dingoes to prey on the kangaroos. ! (D) The use of pesticides to eradicate the dingo population. ! (E) A cessation of the Australian wool industry.

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6. Which of the following solutions to the problem, if feasible, would the author of the passage most likely support?

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! (A) The "Dog Fence" has led to a steady deterioration of Australia's environment. ! (B) Before the "Dog Fence" was built the dingoes preyed on kangaroos. ! (C) Floods prevented Australia's wool industry from turning a profit in 1992. ! (D) Uncontrolled overgrazing could endanger Australia's wildlife. ! (E) The "Dog Fence" was originally built by Australian ranchers to prevent the flocks of sheep from leaving a certain area. Test

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Step 15.1 Lesson

DRILL 2 For the passage below you have between two and three minutes to get an overview. Then determine the main idea, the main terms and concepts, the contrasts or new ideas through trigger words, and identify the location of details.

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The politically charged atmosphere of Europe in the 1930’s drastically affected the production of art, particularly in Germany and Russia, where government intervention with artistic works not only limited what was considered socially acceptable, but also prompted many artists themselves to suddenly demonstrate greater interest in politics than they had previously. The result of this interaction was a generation of European painters and sculptors who, out of either necessity or impulse, became implicated in the historical and political fabric of their time. In Germany, some artists responded to the rise in power of the Nazi Party with unmitigated pessimism. Raoul Hynckes’ 1934 “The Sponge of Bitterness” depicts a rotting skull and an exposed human brain sitting amidst symbols of Nazi power, perfectly conveying the despair felt by many Germans. Other artists were swayed by the Nazi cause. Emil Nolde joined the Nazi party in the 1920’s, but was castigated in the 1930’s and had his work displayed in the Munich “Degenerative Art” exhibition which publicly announced to the population exactly which artists were not considered exemplary. Nolde was not allowed to continue to paint, although he continued to do so in secret. Otto Dix took another tack, retreating to the country and painting innocuous, and bland, landscapes, eschewing his more daring work of the previous decade. Some artists banned from working simply fled; many of those unable to were eventually sent to concentration camps. Restrictions and stigmatizations were simultaneously occurring in Russia, where any art not falling under the category “realism” had become unacceptable, and any artists practicing unacceptable work put themselves at risk. The abstract painter Malevitch’s rather creative response to this was to antedate his works to make it appear that he wasn’t countering Communist dogma. Artists were summarily forced to create work for the propaganda machines being produced by the dominant political parties of both countries. These pictures, unswervingly heroic, are generally regarded as absurdly pompous and vacuous. They are unfortunately matched by much of the art of protest produced elsewhere in Europe in the 1930’s, which to the modern viewer usually appears, frankly, singleminded.

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2. STANDARDIZED TESTS = STANDARDIZED MISTAKES At this point, you must be familiar with our techniques and the famous Wrong Answer Factory, the production line of seemingly right answer choices that trick the average test taker. Does the Wrong Answer Factory apply here? Let’s have a look at question 1 of the ”Dog Fence” passage.

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GMAT CAT – Section 4 : Verbal

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The passage is primarily concerned with (A) the problem of overpopulation of large marsupials afflicting certain areas of eastern Australia (B) the conflict between environmentalists and ranchers over sheep-grazing areas (C) the challenges the "Dog Fence" places on animal migration (D) the role of economics in determining human manipulation of an ecological system (E) the positive and negative effects of the "Dog Fence"

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Use of Scope Understanding scope helps you recognize answer choices that add additional information which is neither stated nor implied in the text, or information which distorts the truth or actual ideas expressed in the text.

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If you look closely at the answer choices, you’ll notice that there are three types: – Totally wrong answers. This type of answer introduces new information that is neither stated nor implied in the passage. This type of answer choice is easy to spot and eliminate because its contents don’t relate to what you’ve read in the passage. This is the case with answers (B) and (D), which are completely unrelated to the passage.

The answers to primary purpose/main idea questions are often found in the opening sentence. Ask yourself, “Is this the topic that remains the focus for the entire passage?”, and doublecheck the passage to make sure.

– Almost right answers. This type of answer has some information directly from the passage and some information which is completely irrelevant. The elements of truth it does have are greatly distorted. Read every word of every answer choice carefully checking for zero-distortion. Distortion is apparent in choices (A) and (C) which are related in some way to the passage, and mentioned as potential dangers of the “Dog Fence” but do not constitute the main concern of this passage. -The Best Answer. Here (E) is the best answer because it is not out of scope, does not distort the meaning, and does include the main concern of the passage: evaluating the advantages (1st paragraph) and the disadvantages (2nd paragraph) of the “Dog Fence.”

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Sometimes understanding just the main idea of a passage is enough to determine the answer to detail questions without returning to the text.

Don’t approach the questions as enemies. Many students fear questions and consider them as enemies. But, questions can be used to your advantage because many of them give you clues on where to find information in the passage.

Step 15.1 Lesson

3. SCOPE In order to make best use of the Process of Error Identification and the principles of the Wrong Answer Factory, scope should be understood. Anything outside the contents of the passage is outside its limits, or scope. The scope of the passage begins with its opening words and ends with its final sentence: this describes the region you are tested on. No outside knowledge of the subjects you’ll read about is presumed, and this should tell you something: you are expected to stick closely to the text itself, not to your personal experiences, to answer these questions. The four answer choices which must be written to distract you from the one best answer are written with distorting scope in mind. Therefore, do not read outside the text (even the inferences required are based closely on the text) and know that four of five answer choices will have distortions of some kind. Understanding the scope of the passage (what is relevant to it and what is not) helps you interpret the answer choices to eliminate all that is neither stated nor implied, all that cannot be safely inferred from a passage. Let’s look a question from the “Dog Fence” passage.

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The author of the passage probably mentions the 1992 flood damage in order to (A) highlight the unreliability of the "Dog Fence" (B) convince the reader of the necessity of the wool trade to Australia's economy (C) give an example of how the "Dog Fence" manages to protect the flocks of sheep (D) demonstrate the potential damage to the wool industry prevented by the "Dog Fence" (E) underline the savage nature of the dingo

You need to go back to the passage for inference questions. This is one reason why it’s not worth reading the passage carefully the first time.

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If you look at the last sentence of the first paragraph, you can infer that the event in 1992 indicates that the “Dog Fence” protects sheep from dingoes and is therefore necessary to the wool industry, which needs sheep alive and kicking. Let’s go to the answer choices: Choice (A) is contrary to the example and distorts the truth. Phineas is PC. Avoid any answer choices that are politically incorrect or could be perceived as offensive to any minority group.

Choice (B) is completely out of the scope. The author tries to convince us of the necessity of the sheep to the wool industry, not the necessity of the wool industry to the economy. This is certainly true, but not directly relevant to the example. Choice (C) seems very close to the truth and is a trick. You should wonder, “Do they really give an example? Where is the example?” Of course there is no example. Choice (C) should be avoided.

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Choice (E) is certainly true in the absolute, but is not relevant to the primary purpose of the passage. Choice (D) is definitely the best answer to the question. The author mentions the 1992 flood example to show that without the Dog Fence, sheep would be lost, which means fewer resources for the wool industry.

4. QUESTION

TYPES

Up to now we’ve been discussing general information and showing you general strategies. The existence of standardized types of questions has been hinted at, and we now arrive at a pivotal moment in this lesson: your introduction to the four groups of questions which accompany RC texts. In each group, every type of question requires a specific approach combined with our general strategy. THE 4 STANDARDIZED GROUPS: A) GENERAL QUESTIONS These questions ask you for general information on the passage. They are written in a number of ways. The four most common look like these: What is the primary purpose of this passage? What is the passage’s main idea? What is the author’s tone or attitude? Which of the following best describes the structure of the passage? Here is the approach for general questions: Step Step Step Step Step

1: 2: 3: 4: 5:

Get an overview of the passage. Determine the general idea of the passage. Use scope to eliminate the wrong answers. Eliminate answer choices that are too vague. Eliminate answer choices that distort the truth.

B) SPECIFIC QUESTIONS This type of question asks you to identify a specific detail or example in the passage and find the best statement of its meaning from the answer choices. Specific questions can be phrased like these: According to the passage, which of the following is true? The example of....in line 17 is included to demonstrate... Information in the passage suggests that which of the following... The author uses the term...in line 37 most probably in order to... Here is how to approach specific questions: Step Step Step Step Step

1: Return to the passage if necessary. 2: Determine the information required. 3: Use scope to eliminate the wrong answers. 4: Eliminate the answers referring to the wrong part of the passage. 5: Eliminate the answer choices that rephrase information from the text but from irrelevant parts of the passage. Step 6: Make sure the right answer rephrases (that is, rewrites detail information from the passage in slightly different words) the correct information as it appears in the passage. © The MBA Center

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C) INFERENCE QUESTIONS This type of question asks you to make logical deductions based on the information or argument in the passage. Inference questions are difficult because they require a precise and thoughtful understanding of the passage. They are often phrased like these: Which of the following can be inferred from the passage… The author mentions...(lines 31-33) most likely in order to...? Which of the following can most reasonably be concluded on the basis of information in the passage? The passage suggests that the author believes which of the following? Here is how to approach inference questions: Step 1: Analyze and understand the logic of the question before going back to the passage. Step 2: Return to the passage to search for information, such as author’s point of view. Step 3: Eliminate answers that violate logic or common sense. Step 4: Eliminate answers that distort logic or common sense. Step 5: Use scope to eliminate remaining answer choices. D) LOGIC-BASED QUESTIONS In recent years, the test makers have introduced new question types which come directly from the Critical Reasoning section. These are logic-based questions, and you can now find strengthen, weaken, except, or assumption questions mixed in with the other more common types of questions in the Reading Comprehension section. Logic-based questions ask you to evaluate a short argument based on something in the passage in terms of the rules of logic, not in terms of your reading skills. To ace this type of question, use the strategies in the Critical Reasoning lesson in this book. Look closely at the AIM section for specific approaches to answering logic-based questions. These are some of the most common forms of logic-based questions: Which of the following, if true, would most strengthen/weaken the author’s assertion about...? Which of the following would most logically be the topic of the paragraph immediately following this passage? Which of the following hypothetical situations best exemplifies x noted in y location (lines 1-3)?

5. THE MBA CENTER

APPROACH

Step 1: Get an overview of the passage using our reading theories. Step 2: Determine the type of passage, the main idea, the structure, the author’s attitude, and the location of details. Step 3: On general questions a rapid overview of the passage is enough to answer correctly. Step 4: On detail or specific questions, go back to the passage to get precise information (the line number is often contained in the question). Step 5: Use scope to eliminate wrong answer choices.

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FIRE! Now you are ready for some practice questions…

DRILL 3

DIRECTIONS: This exercise contains one passage followed by questions on its content. Select the best response to each question based on your understanding of the content of the passage.

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In the early-twentieth century, influenza was responsible for the deaths of millions of people worldwide. In the spring of 1918, a pandemic of influenza believed to have begun in the United States spread quickly around the world killing more than 21 million people before it ended in 1919. The pandemic of 1918–1919 is possibly the single most deadly trauma ever survived by the human species. Dubbed the Spanish flu—since Spain did not participate in World War I, it was able to detail the widespread illness of its population free of domestic wartime censorship laws—this strain of influenza was soon known to the rest of the world. After an initial wave in the United States in the spring of 1918, Spanish flu reappeared in a second, more intense outbreak in August which struck hundreds of millions of people. With no vaccine, doctors were unable to effectively treat patients or immunize the general public, and hundreds of thousands of patients died before winter arrived. Young adults in particular were among the victims in abnormally large numbers. After a mild third wave struck, the pandemic subsided in spring of 1919. By the time the pandemic finally ended, more than 550,000 Americans had died, ten times the number of American fatalities from World War I. From the United States, the disease spread quickly, leaving virtually no part of the world untouched. Regions which had never before known influenza were particularly susceptible. For example, during the last two months of 1918, 7,542 deaths were recorded in Western Samoa, out of a total population of 38,302. While the global mortality figure is estimated to be in excess of 21 million, historians and demographers have determined scores of unreported deaths in Latin America, Africa, and Asia that increased the actual mortality figure by several million. It is still unknown why Spanish flu proved to be more lethal than other strains of influenza, or where it originated. Medical researchers now know that permanent immunity to influenza is impossible, regardless of previous exposure, and that vaccines are ineffective due to the virus’ brief incubation period and its rapidity of contagion.

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Step 15.1 Lesson

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GMAT CAT – Section 4 : Verbal

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The primary purpose of the passage is to (A) (B) (C) (D) (E)

evaluate the efficacy of disease prevention measures define the mortality assessment of a pandemic compare the similarities of a disease and a pandemic investigate the reasons for deaths by infectious diseases chronicle the history of a specific disease

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According to the passage, the pandemic of 1918 - 1919 was responsible for all of the following EXCEPT (A) the deaths of young adults in higher amounts than earlier contagions (B) the development of a permanent vaccine for viral diseases (C) more American fatalities than from World War I (D) a record level of fatalities compared to previous welldocumented pandemics (E) arriving first in the United States and then moving on to other parts of the world

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The author of the passage most likely mentions the Americans killed in World War I in order to

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! (A) censorship laws during wartime did not affect the country of Spain which suffered greatly from the influenza pandemic ! (B) influenza afflicted Spanish citizens before it afflicted citizens of other countries ! (C) the origin of influenza was discovered in 1919 to be from a small region in Spain ! (D) a prominent immunological researcher from Spain was the first to classify the properties of the disease ! (E) morbidity figures for Spain during 1918 - 1919 were higher than anywhere else in the world

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According to the passage, influenza became known as Spanish flu because

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! (A) identify a weakness in the virulence of a contagious disease ! (B) estimate the percentage difference between American mortality rates and worldwide mortality rates ! (C) accentuate the significance of the number of deaths in the United States resulting from Spanish flu ! (D) provide data to support a previously established assumption ! (E) analyze the sociological impact of influenza on American soldiers

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GMAT CAT – Section 4 : Verbal

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Which of the following can be properly inferred from the passage?

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! (A) Spanish flu led medical researchers to a permanent vaccine for the disease. ! (B) Remote regions of the world have natural defenses against viral outbreaks. ! (C) Self-immunity to influenza increased since 1919 as an adaptive response to an environmental threat. ! (D) Human populations anywhere on earth can expect reoccurrence of influenza and the possibility of widespread contagion. ! (E) Prescription remedies are effective against the short incubation period of influenza. Answer Time Time

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In the last paragraph, the author is primarily concerned with

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! (A) correcting suppositional errors made by historians and demographers in their mortality assessments ! (B) rebutting claims made by medical researchers about a known cure for influenza ! (C) offering evidence to explain why the pandemic of 1918 - 1919 was so deadly ! (D) interpreting previously undiscovered mortality records from Latin America, Africa, and Asia ! (E) summarizing the characteristics of influenza presented earlier in the passage and offering updated information

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Reading Comprehension

DRILL 4

DIRECTIONS: This exercise contains one passage followed by questions on its content. Select the best response to each question based on your understanding of the content of the passage. In order to develop a theory to explain galaxy formation, physicists have focused their efforts on neutrinos, weakly interacting elementary particles that are abundant in the universe. By 5 establishing the average mass weights of neutrinos, researchers hope to find the missing piece of the galaxy formation puzzle. There are currently two approaches to measure the mass weights of neutrinos. 10 The first approach is based upon the idea of neutrino oscillation, which hypothesizes that neutrinos change their state unpredictably during transmission in space. Using neutrino sources from particle accelerators, reactors, the Sun, 15 and Earth’s atmosphere, physicists have captured, observed, and measured neutrino oscillation in an attempt to resolve the mystery of the apparent shortage of neutrinos traveling from the Sun to Earth. While early results were not conclusive enough to 20 gather widespread acceptance of neutrino oscillation theory, a recent test at the Super-Kamionkande laboratory in Japan has provided the most verifiable statistical evidence to date to support neutrino oscillation. Originating from cosmic rays 25 transmitted from outer space, neutrinos were detected by photodetectors as they struck Earth’s atmosphere. High-energy electrons, or muons, emitted from the impact indicated that neutrino oscillation occurs during every several hundred miles 30 of travel. After evaluating thousands of muon emissions, physicists were able to approximate an average mass weight for neutrinos. Though more such tests must be performed before theorists can cite a definitive body 35 of evidence, neutrino oscillation theory has become widely accepted. The second approach to measure neutrino mass weights proposes the use of sophisticated satellite technology to make cosmological measurements of 40 selected groups of neutrinos. The theory behind this approach argues that since the universe is full of neutrinos, their combined mass should be more than sufficient to influence galaxy formation. Those in favor of this approach intend to combine the most 45 accurate cosmological maps of galaxies with those of the cosmic microwave background in order to draw inferences about the mass weights of neutrinos above a minimum level of 1eV. However, unlike neutrino oscillation researchers, proponents of cosmological 50 measurements have yet to amass the data that would support their theory of neutrino participation in the formation of galaxies.

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Step 15.1 Lesson

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In the passage, the author is primarily interested in (A) describing an improved method for research which could invalidate an established theory (B) proposing an alternative to a failed research experiment (C) analyzing the invalidity of data provided by a new scientific test (D) engaging in a debate about an accepted theory (E) presenting a theory and explaining two scientific procedures to verify that theory

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The author of the passage would be most likely to agree with which of the following statements about the cosmological measurement approach? (A) It is the only possible method to measure the mass of neutrinos. (B) It is not inferential enough to provide a statistical theory for the mass weights of neutrinos. (C) Its test results have been confirmed, and neutrino research has been halted. (D) For lack of data, it has yet to provide verifiable evidence to support its claims. (E) It is not a possible method to measure the mass weights of neutrinos, although improved methods have been based on its results.

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It can be inferred from the passage that cosmological measurements taken from galaxy and cosmic microwave background maps would be more useful to scientists if which of the following were true?

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! (A) It provides an explanation for the abundance of neutrinos in transmission from the Sun to the Earth. ! (B) It indicates that lighter neutrinos are more influential than heavier neutrinos in galaxy formation. ! (C) It provides an explanantion for the lack of neutrinos in transmission from the Sun to Earth. ! (D) It is the only theory to propose an approach to measure the mass weights of neutrinos. ! (E) It explains neutrino oscillations at various times in the formation of galaxies.

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According to the passage, which of the following is true of the theory of neutrino oscillation?

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! (A) The maps indicated neutrino mass weights below 1eV. ! (B) The maps were currently available to prove or disprove the claims that neutrino mass weights above 1eV could be determined from them. ! (C) The maps had far less specificity in reporting neutrino mass differentiation. ! (D) The maps had indicated that heavier neutrinos reached Earth’s atmosphere from the Sun. ! (E) The maps had been available for more than ten years, so recent results could be compared with those from twenty years ago.

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It can be inferred from the two approaches to neutrino measurement that (A) Different methods of testing have different methods of interpretation which cannot be unified. (B) More investment in satellite-imagery research must be authorized before full-scale cosmological measurements can be performed. (C) Fewer photodetectors were used in prior research with the same results as the Super-Kamionkande experiment. (D) Accurate and verifiable measurements of neutrino mass weights must be performed before theories proposing a relationship between neutrinos and galaxy formation can be confirmed. (E) Similar neutrino experiments performed in the 1950’s made use of measurement techniques which should be in use in experiments today. Test

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Which of the following statements about verifiable statistical evidence is supported by information in the passage? (A) A higher percentage of lighter neutrinos were found to oscillate than were heavier neutrinos. (B) Outcomes from the photodetector experiment were sorted in three ways, which resulted in confusion about their authenticity. (C) A significant percentage of outcomes did not confirm neutrino oscillation. (D) Muon emissions from the photodetector experiment were evaluated thousands of times, most likely in order to insure the accuracy of the test results. (E) By the 1950’s, unambiguous evidence existed to prove neutrino oscillation.

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IV. WHAT

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DON'T WANT TO READ THE PASSAGE AT ALL?

Generally, completely ignoring the passage is ill-advised. Some questions, however, can be answered without reading the passage by using just critical reasoning abilities. The question below is an extrapolation of this idea, not an actual Reading Comprehension question. Try this one. GMAT CAT – Section 4 : Verbal

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It can be inferred from the passage that which of the following would be one major difference in behavior between Manager X, who uses intuition to reach his decisions, and Manager Y, who uses only formal decision analysis?

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! (A) Manager X analyzes first and then acts; Manager Y does not. ! (B) Manager X checks possible solutions to a problem by systematic analysis; Manager Y does not. ! (C) Manager X takes action in order to arrive at the solution to a problem; Manager Y does not. ! (D) Manager Y draws on years of hands-on experience in creating a solution to a problem; Manager X does not. ! (E) Manager Y depends on day-to-day tactical maneuvering; Manager X does not.

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Step 15.1 Lesson

SUMMARY - There are from 14 to 18 questions covering 4 passages in the Reading Comprehension section of the GMAT CAT. - The Reading Comprehension questions are all worth the same number of points, and this section is not adaptive. - The Reading Comprehension passages are on the following subjects: Science, Social Sciences, and Business. No outside knowledge is required. You are simply asked to answer the questions based on what is stated or implied. - The main difficulty of this exercise is time, and your challenge is to spend the bulk of your time understanding the passage and as little time as possible reading the passage. - The questions focus on only one third of the information in the passage; the most important thing is to get the main idea in a twoto three-minute overview. - Remember that you earn points by answering the questions – not by reading the passage. - The most efficient tool you have to select the “best answer” is scope. Understanding the scope of the passage will help you decide if an answer choice adds information not originally in passage or if an answer choice distorts information using a trick. - There are four types of questions tested in Reading Comprehension that are highly predictable. You have to anticipate these questions when you read the passage. The four types of questions are: -

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Reading Comprehension

ANSWER KEYS DRILL 1 1. 2. 3. 4. 5. 6.

E D D E B A

DRILL 2 7. E 8. D

DRILL 3 9. E 10. B 11. C 12. A 13. D 14. E

DRILL 4 15. 16. 17. 18. 19. 20.

E D B C D D

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HOMEWORK/PRACTICE TEST READING COMPREHENSION ANSWER GRID B !

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Step 15.2 Homework

End

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Reading Comprehension – Homework

18 QUESTIONS 25 MINUTES Directions: This section consists of passages followed by questions on their content. Select the best response to each question based on your understanding of the content of the passage.

Directions

When finished reading directions click on the icon below

Dismiss Directions ➩

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Many of New York City’s post-1890 laws governing tenement houses passed as a direct result of the campaign of Jacob Riis, a Danish-born writer and photographer. Riis’ work, published in the New York Tribune and the Evening Sun, affected the way the entire populace of New York City, at least the literate populace, viewed victims of poverty. Previously, many newspaper readers had assumed that the poor were so by choice and the unhygienic conditions in which they lived resulted from moral failure rather than economic reality. Slums had been viewed as either places to be shunned or, patronizingly, as exotic locales where intellectuals and tourists could “slum” for the day before returning to their highrent neighborhoods and rhapsodizing on the enviable happiness of the simple lives of the poverty-stricken. Riis changed the popular outlook by sympathetically portraying the urban poor in his writings and photographs, and, furthermore, calling attention to the squalor and danger of tenement habitation. Among the hazards Riis depicted were structural deficiencies, which regularly caused the actual collapse of parts of buildings, and conducivity to fires. Both of these problems resulted from construction with an emphasis on haste and using cheap materials. The subjects of Riis’ work were also subject to disease, often produced by a negligible water supply and close proximity to unsanitary activities such as animal slaughtering and bone-boiling, and easily spread by the incredibly overcrowded conditions. Riis was also responsible for exposing the differences between single tenements and what were known as “double-deckers,” which were tenements consisting of two dwellings, front and rear, in which all the problems afflicting tenement life were greatly multiplied. A survey of an area in lower Manhattan Riis cited in the 1890’s gave the mortality rate at nearly 30 per thousand for those living in single buildings and over 60 for those in tenements with two structures, and an equally drastic divergence in the infant mortality rate: about 100 for the former, double that for the latter. Eventually, Riis took a more active role, arguing for and actually supervising the demolition of many of the culpable tenement houses, and publicly supporting the licensing and rent control of all lower-class housing.

1. Which of the following best represents the main theme of the passage? (A) Housing conditions in New York in the 1890’s spurred reforms governing the construction of new buildings. (B) Until Jacob Riis, no journalist had made an attempt to adequately capture slum life for a newspaper’s readership. (C) Jacob Riis was a tireless social reformer and champion of the rights of the downtrodden. (D) Jacob Riis was among the first to postulate that “double-decker” housing was exponentially more hazardous than single-building dwellings. (E) The activities of Jacob Riis awakened many New Yorkers to the horrendous living conditions of the city’s poor. 2. The passage suggests which of the following about the “intellectuals and tourists” mentioned in line 14? (A) Their appreciation of the slums was based on the contentment of its denizens. (B) Their attitude toward the poor was not predicated on a thorough examination of factual or empirical evidence. (C) Regular visits produced in them an intense familiarity with the poor sections of New York. (D) They envied the living conditions of the poor. (E) They were fully aware of the hazardous circumstances in which poor people lived and considered these conditions reasons for the happiness of those living in the slums.

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3. From the information given in the passage, which of the following can most likely be inferred about Jacob Riis? (A) His photographs of New York’s poor are of particular historical interest. (B) He was responsible for the prosecution of landlords caught violating laws concerning tenement ownership. (C) His campaign to open the eyes of New Yorkers to the horrors of slum life was spurred by his immigrant background. (D) He developed a close relationship with many New Yorkers who lived in squalid conditions. (E) After establishing a foundation of support among newspaper readers, he began to become active politically, furthering the cause of housing reform. 4. Which of the following is NOT mentioned in the passage as a hazard of tenement houses of which Riis made the general populace aware? (A) The likelihood of fires (B) The possibility of disease being spread due to residents’ inability to maintain normal levels of hygienic care, resulting from the small amount of water available (C) The unsanitary proximity to disease-ridden animal carcasses (D) The high rate of crime resulting from incredible overcrowding (E) The high rate of accidents caused by buildings constructed from inappropriate materials

Step 15.2 Homework

5. Which of the following best describes the structure of the second paragraph of the passage? (A) A description of the methods used to promote social reform, and some reasons those changes were necessary (B) A close analysis of a political problem and its development (C) A tribute to a social reformer, followed by a systematic appraisal of a social phenomenon (D) A portrayal of the use of popular media for political purposes, followed by the results of such actions (E) A depiction of contrasting views of a social problem, one held by the general populace, the other by an individual crusader 6. The author’s claim that Jacob Riis was directly responsible for the reformation of New York’s housing laws would be most effectively strengthened if the author (A) related the dates and provisions of the laws to Riis’ campaign (B) described the arguments for and against the passing of each law (C) provided more statistics concerning the hazards of tenement living (D) explained in greater detail how readers of Riis’ work responded to their newfound sense of the dangers of tenement dwelling (E) gave specific examples of poor people living in New York tenements in the 1890s who were unable to relocate due to financial or social constraints

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Primatologists did not know of the existence of the bonobo, a species of great ape, until 1928, when researchers noticed that the primate long known as the pygmy chimp was actually its own species. The discovery of this close relative to man and the ensuing study of its behavior have forced scientists to rethink some of their traditional beliefs about male-female relationships in great ape species. Violent acts committed by males have been witnessed in many ape species, such as infanticide by male gorillas, rape by male orangutans if their courtship is rebuffed by females, and bloody territorial wars among rival chimpanzee populations. Recent research, however, shows that males do not partake in any of these types of behavior in bonobo society. The reason for the relative tranquillity in bonobo populations, according to scientists, is that the punishment of transgressors, the keeping of peace, and the setting of behavioral limits are enforced by females. Females will sound a distress signal if, for example, a male tries to hoard fruit at a feeding site and prevent others from approaching. Males can sometimes dominate females, but only those who rank lower than them and a female just as easily dominates a lowerranked male. This is in contrast to chimpanzee populations in which all females are subordinate to even the lowest ranked males. Bonobo females, who are powerful enough to resist even the strongest alpha male, are thus able to ensure that aggressive misbehavior, either in sexual or nonsexual settings, is not permitted. Even male-male aggression is limited, though only indirectly due to the vigilance of females. Violent contests between males secure breeding rights in most ape species, but as a dominant male bonobo cannot force an unwilling female to become a mating partner, there is little to be gained by such contests. Scientists are uncertain how such femaleenforced pacifism evolved, but the key may lie in the bonobo food supply. Bonobos are adapted to both a diet of leaves and stems, plentiful on jungle floors, and meat and ripe fruit, not always easily come by. Unlike chimpanzee communities, for example, which split up into foraging parties of varying sizes to find meat and fruit, bonobo societies are able to form more or less permanent groups, providing the chance for females to build alliances, ensuring that males don’t abuse their greater size. While female alliances were not unknown in primate species before behavioral studies of the bonobo, the absence of male domination and the female enforcement of

55 societal rules are unusual among primates and unique among great apes.

7. The primary purpose of this passage is to (A) present two conflicting theories about malefemale relations in great apes (B) dispute early evidence that male great apes often engage in violent behavior (C) explain the origin of bonobo behavior (D) discuss the unusual nature of male-female relations in bonobo society (E) portray bonobo group behavior as more socially advanced than that of other great apes 8. The author implies that male-male violent contests are limited in bonobo society because (A) alpha males can sometimes be dominated by females in non-sexual settings (B) female alliances ensure that transgressors are punished (C) female distress signals will alert other members of the population (D) there is a plentiful food supply allowing for stable group living (E) the winner would be unable to secure breeding rights and thus has no motivation 9. According to the passage, chimpanzees differ from bonobos in that (A) female chimpanzees are always subordinate to males while male bonobos are always subordinate to females (B) male chimpanzees forage in small groups and bonobos forage individually (C) chimpanzees compete violently for both territorial and mating rights, while bonobos compete only for territorial rights (D) bonobo females use distress signals whereas chimpanzee females do not (E) females can outrank males among bonobos but not among chimpanzees

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Step 15.2 Homework The following text was written in 1997.

10. The author mentions gorilla infanticide in line 11 in order to (A) contrast behavior of other great apes with the relative tranquillity of bonobos (B) emphasize that gorillas are unusually violent for a great ape species (C) demonstrate that except in the case of the bonobo, infanticide is common in most ape species (D) suggest that some female gorillas cannot properly care for their young (E) make a comparison between gorillas and orangutans

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15 11. Which of the following situations most closely parallels the primatologists’ discovery of the bonobo species described in lines 1-5? 20 (A) A judge makes a ruling making a certain action legal for the first time. (B) A team of astronomers devises a new method to measure the velocity of comets. (C) Archeologists discover artifacts from a previously unknown city. (D) A doctor finds that what was previously considered a variant of a common disease is actually a separate disease. (E) A stamp collector realizes that one of his more unusual stamps is a worthless counterfeit. 12. The third paragraph, in relation to the rest of the text, could most accurately be described as (A) a discussion of the consequences of ideas expressed in the second paragraph (B) a counter-theory to a theory put forth in the first two paragraphs (C) a theoretical model which explains data from the second paragraph (D) a proposed explanation for observations made in the first two paragraphs (E) a reiteration of themes expressed earlier in the passage

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With less than two years remaining before the introduction of the new European common currency, dubbed the “euro,” businesses and governments of the European Community are preparing for sweeping changes in the way that business will be conducted both nationally and internationally among the member states. During the three-year transition period, scheduled to last from 1999 to mid-2002, the euro will coexist with national currencies; afterwards, the national currencies will be phased out, leaving the euro as the single European currency. The transition to the common currency will be a difficult one, not only due to its high cost to governments (which will have to print millions of new banknotes) and to businesses (which will need to completely revise their accounting practices and cash handling systems) but also because many businesses will find that they cannot compete in the new, more open, European market. This openness, however, will be a boon for many business and particularly for consumers, who will benefit from a wider choice of products and services. Additionally, the new single currency will allow both businesses and individual consumers to save billions of dollars annually in transaction costs that are associated with the current multi-currency system. One factor that has been largely ignored by businesses and governments alike is the way that consumers will react to this switch to the common currency, which will be imposed on them largely without their input and, in many cases, without their even understanding the reasons for this change. People may be resistant to accept the euro for several reasons: an attachment to their national currency as a symbol of their homeland, the potential mistrust of a currency which is not controlled by their own national bank, or a feeling of complete disorientation when faced with the conversion to a new standard. When the French supermarket chain E. Leclerc decided, as an experiment, to print several million dollars worth of “euro” bills for use in its stores, it discovered that the majority of consumers were simply confused by the new currency and preferred paying with bank cards.

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Reading Comprehension

16. It can be inferred from the passage that the author believes which of the following statements?

13. The passage is primarily concerned with (A) the difficulties of changing from one currency to another (B) the three-year process of conversion to the euro (C) the importance of a national currency for consumer confidence (D) why the euro will be good for European business (E) the advantages and problems of the conversion to the euro 14. The word "boon" used in line 21 is most accurately described by which of the following? (A) (B) (C) (D) (E)

help challenge mild difficulty advantage necessity

(A) The three-year transition period currently scheduled for the conversion to the euro should be considerably lengthened. (B) The conversion to a single currency will have some effect on competitive pressures on the European common market. (C) Many companies for whom the commission on currency transactions is a substantial part of their income will no longer be profitable after the introduction of the euro. (D) If people educated themselves about the euro before its introduction in 1999, the transition period would be made substantially easier. (E) The number of new businesses that will be created after the introduction of the euro will be greater than the number of businesses that will be forced to cease their operations because of the introduction of the euro.

15. It can be inferred from the second paragraph that

17. Which of the following is NOT cited as a drawback to the conversion to the euro?

(A) having a currency controlled by a national bank gives some consumers a sense of security (B) consumers often prefer paying with bank cards than with cash (C) many consumers do not yet know about the conversion to the euro in 1999 (D) The euro should not be introduced without a concurrent public information campaign (E) The introduction of the euro will entail less national sovereignty for the member states of the European Union

(A) The need for businesses to substantially modify their accounting systems (B) The difficulties that European consumers may have in adapting to the new currency (C) The cost of printing and minting new euro bills and coins (D) The fact that bank cards will have to be adapted to operate with the new currency (E) The fact that many companies may have trouble surviving greater international competition 18. The author’s attitude or tone in regard to the process of converting to the common currency is best described as one of (A) (B) (C) (D) (E)

wholehearted support moderate criticism objective analysis indifference mild distaste

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READING COMPREHENSION HOMEWORK/PRACTICE TEST ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

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Reading Comprehension EXPLANATIONS FOR READING COMPREHENSION HOMEWORK/PRACTICE TEST PASSAGE 1 The first sentence gives you an idea that this social science passage is about the campaign of Jacob Riis and its effect on government tenement housing laws. The rest of the first paragraph then discusses how Riis' work affected people's views on the poor. Paragraph 2: Remember to pay attention to first and last sentences. What did Riis do? He “changed the popular outlook.” How? “By sympathetically portraying the urban poor in his writings and photographs.” The rest of the paragraph is details on the poor conditions of tenements. The last, short paragraph briefly alludes to Riis' later activities. That's enough to get out of a first read in 2 minutes. On to the questions.

1. (E) The first question is a general one. The key word is “main” theme. The whole passage talks about Riis, so (A), which doesn't even mention Riis, is out. (B) is a sweeping generalization about the entire history of journalism – there's no support in the passage for such a strong statement. (C) might sound pretty good, but it's too general – GMAT passages never have such broad themes, and what's more, who's to say that Riis was tireless? (D) on the other hand, is far too specific. While Riis did expose the dangers of “double decker” housing, this choice is a detail mentioned in only one paragraph. (E) covers all the paragraphs. The word “activities” is broad enough to refer to his photographs, journalism, and political or social activities, while “the horrendous living conditions of the city's poor” is specific enough to stay in the scope of the passage. (Compare that to the broad language in (C): “the rights of the downtrodden.”)

2. (B) A question that gives you a line number is great, but make sure you read a couple lines below and above the line cited to find the answer. Then try to predict the answer before going to the choices. The word “patronizingly,” a distinctly negative word, tells us that the author probably doesn't approve of the intellectuals' attitudes. And because most of the passage is about how Riis opened people's eyes to the terrible living conditions of the poor, we can conclude © The MBA Center

that the intellectuals' opinions that the lives of the poor were “enviable” is probably inaccurate, according to the author. Thus the closest answer is (B), which basically says that their attitudes were not based on fact. (A) and (D) look at the intellectuals' point of view, not the author's (remember, the question asks about what the passage suggests). (C) misses the point that the intellectuals' visits were superficial. (E), besides not being suggested by the passage, could be considered offensive to the poor and would never be credited by the GMAC.

3. (E) It is possible to infer (E) from the first sentence of the passage and the last paragraph, which mention Riis's effect on the cause of housing reform. (B) is a detail that we cannot infer – it is mere speculation; landlords violating laws are not mentioned (if you search the passage for “landlord” you come up empty). (C) is also pure speculation. The fact that Riis himself was an immigrant does not tell us that his background provided his motivation. (D) is also a wild guess. Just because the passage says that his photographs and newspaper articles sympathetically portrayed the poor doesn't mean he was close friends with those people. (A) is pretty close, but his photographs are just mentioned briefly as, together with his writings, having “changed the popular outlook.” It goes too far to then infer that they are of particular historical interest.

4. (D) Crime is never mentioned in the passage. Remember to go back to paragraph 2, which focused on the details of housing conditions.

5. (A) For an organization question like this, go back to the paragraph, read the first sentence, then quickly skim the details. Predict an answer before looking at the choices. In this paragraph, we see that “Riis changed the popular outlook” by doing some things. Then there are details about housing conditions. So the right answer should say something about bringing about change and why this was necessary. (A) is the closest. (B) is wrong because there is not a political problem or a “development.” (C) is wrong because this is not a “tribute.” Watch out for making judgments about the author or the subject – you may admire Riis, but that doesn't make this passage a tribute to him. (D) is wrong because the paragraph doesn't talk about results. (E) is wrong because there are no contrasting views.

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6. (A) This is basically a Critical Reasoning question stuck into the Reading Comprehension section. The claim in choice (A), made in the first sentence, is not strongly backed up in the passage, primarily because, in order to establish a link between Riis and the reformation of housing laws, we need to know what the laws say and when they were passed. Then we would be better able to assess whether they are related to Riis's efforts. (C), (D), and (E) are not related to laws, and so can't be right. (B) is not right because even if we knew the arguments for and against the passing of the laws, it is likely that we still wouldn't know whether it was Riis's efforts that sparked the debate or affected the outcome.

PASSAGE 2 The broad topic of this passage is the bonobo, a species of great ape, but GMAT passages always have more specific topics. In this case, the first paragraph leads us into the topic which is then clearly stated in the first sentence of the second paragraph. The topic is the female-enforced pacifism in bonobo populations. The first sentence of each paragraph reveals the structure. The first paragraph is a scientific discovery (that bonobos are their own species), followed by some observations. The second paragraph describes the mechanism of bonobo tranquillity, and the third suggests an explanation for the mechanism.

7. (D) The unusual nature of male-female relations in bonobo society is discussed throughout the first passage. (A) does not even mention bonobos, and there are no “conflicting theories” in the passage. (B) is wrong because the author did not write the passage to “dispute” something. (C) is a typical wrong answer to a primary purpose question, as it relates to only one paragraph (the third). (E) is a value judgment that is not justified by the passage (even if one happens to agree with it).

8. (E) You should remember to go back to the second paragraph for this, as that is where the author discusses the details of female-enforced pacifism. The right answer is a paraphrase of the last sentence. (A) is a distortion of a detail from another part of the paragraph. (B) is a true statement, according to the passage, but does not specifically relate to male-male

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aggression. (D) simply comes from the third paragraph. With detail and inference questions, you usually need to locate the part of the passage that is referred to – don't guess based on what just seems right.

9. (E) The answer to this question is in paragraph 2. Note that the passage uses the words “this is in contrast to.” Comparisons in GMAT passages almost always show up in the questions and are therefore important to note when you skim the passage. You don't have to remember the details of the comparison the first time, just note that there is one and where it is in the passage. (A) goes too far – male bonobos are not always subordinate to females. (B) is tempting, but the passage does not state that bonobos forage individually, only that they don't “split into foraging parties of varying sizes.” (C) is outside the scope. (D) is incorrect because the passage does not state whether chimpanzee females use distress signals.

10. (A) This is a logic question. Why does the author mention gorilla infanticide? Go back to the line numbers and remember to read a little bit before and after the lines the question asks about. The line before (8) states that violent acts are committed in many ape species. The sentence afterwards states that bonobo males are an exception. Therefore the motivation behind the mention of gorilla infanticide is to compare violent acts in most great ape species with the tranquil behavior of bonobos, or (A). (B) is a distortion--gorillas are not unusually violent among great apes, but typically violent. (C) is also a distortion. The passage only mentions that gorillas commit infanticide. It says nothing about other ape species committing infanticide. (D) is a value judgment with no basis in the passage. (E) doesn't mention bonobos, the focus of the entire passage, including this comparison.

11. (D) Here it is necessary to draw a parallel between the situation in the passage and a hypothetical one in the answer choices. Go back to the lines to which the questions refer. The primatologists discover that what they had thought was a kind of chimpanzee (a pygmy chimp) was actually its own species. (D) is the same idea but with doctors and a disease substituted for primatologists and bonobos. (A) is wrong because a ruling is arbitrary – it is not a discovery. There is no new method in the passage, making (B) wrong. The primatologists did not discover remains (or artifacts), © The MBA Center

Reading Comprehension

nor were bonobos previously unknown. (E) sounds like a value judgment – are bonobos “worthless counterfeits”? One way to tackle this type of question is to take the choices and substitute in appropriate words from the passage. In this case, using “primatologists” and “species,” (D) emerges as correct because “Primatologists find that what was previously considered a variant of a common species is actually a separate species,” describes exactly the discovery in lines 1-5.

12. (D) The first sentence of the paragraph gives it away: “the key may lie in…” The “may” indicates a proposed explanation. It is definitely not a discussion of the consequences of ideas from the second paragraph, so eliminate (B); rather, it is a possible explanation, or a discussion of the causes. There is no “theoretical model” in paragraph 3, nor is there any “data” in paragraph 2. These terms are too precise: out goes (C). (E) might sound tempting, but remember that the question asks how the paragraph could “most accurately” be described. A reiteration is not enough, because there is an attempt to explain bonobo behavior, even if the explanation isn't very thorough or clear.

PASSAGE 3 As usual, you can quickly identify the broad topic: the “euro.” Also as usual, the passage has a more specific focus, though in this passage it is a bit difficult to spot. Look for key words and phrases to make some order out of the passage, such as, in paragraph 1, “transition period,” “afterwards,” “difficult one, not only due to … but also because,” “however,” “additionally.” This shows the structure and content. The paragraph is about the introduction of the euro, the transition period, some possible results, why the introduction of the euro will be difficult, and why it might also be beneficial (“however”). In paragraph 2, some key words are “one factor,” “largely ignored,” “resistant… for several reasons,” and “an experiment.” These indicate more problems with the euro and a critical attitude on the part of the author.

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13. (E) The passage discusses both benefits and problems of the conversion to the euro, so (E) is the best choice. (A) does not mention the euro, and the passage does not only focus on difficulties. (B) is too narrow. The passage is not just focused on the 3 year conversion process. (C) is a small detail, not the primary purpose, and it does not mention the euro. (D) ignores the benefits of the euro, and it ignores the consumer (the passage is not only focused on businesses).

14. (D) You don't have to know the meaning of the word “boon” – you can figure out the answer from the passage. “This openness… will be a boon… for consumers, who will benefit…” Before looking at the answer choices, you should have your own word in mind (based on the idea of benefiting). The closest choice to the words “who will benefit” is (D), “advantage.” (A) is perhaps tempting, but “help” and “advantage” are not the same. The consumers will benefit, but we don't know whether the euro will help them do anything. None of the other choices are positive, and so they cannot be right.

15. (A) Note that the word “some” makes the choice more attractive, as it is generally easier to defend or infer a statement about “some” things than about “most” things or “all” things. The right answer refers specifically to the line in the passage “the potential mistrust of a currency not controlled by their own national bank…” Choice (B) is a distortion of the last sentence. People preferred bank cards in this case because they were confused by the new currency, not because they don't like cash. (C) is an exaggeration, or distortion. People may not fully understand the euro, but that doesn't mean they don't know about it. The “concurrent public information campaign” in (D) might sound like a good idea, but that doesn't mean it can be inferred that the author deems it necessary. This choice is a typical trap. Generally, in Reading Comprehension stay away from choices that make an inference about what policy the author thinks should be followed. (E) just isn't mentioned in the paragraph.

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Step 15.2 Homework

16. (B) This is a hard question because it provides no clue of where to find the answer in the passage. The word “some” in (B) makes it a more attractive choice (cf. explanation quest. 15). In the first paragraph, the author writes “many businesses will find that they cannot compete in the new, more open European market.” This is quite similar to (B). (A) is a distortion. We cannot guess whether or not the author thinks that the conversion period should be lengthened (at least not on the GMAT, which is very picky about staying within the scope). (C) is a prediction that isn't justified – companies might become less profitable; nowhere in the passage is it asserted that they won't be profitable at all. (D) is a statement that sounds true, but it is uncertain whether the author believes the transition would be made “substantially” easier. Moreover, the author seems to be sympathetic with the consumer, and this choice sounds judgmental, and many of the reasons the author cites for difficulties people will face probably wouldn't change even if people educated themselves about the euro. (E) is too specific. Who would make such a precise prediction about the future? Not a GMAT author.

17. (D) Problems with bank cards are just not mentioned – the only thing said about bank cards is that some people used them instead of paying with cash because they were confused by the euro. There is no indication that bank cards will have to be adapted.

18. (B) The author certainly does not have an attitude of “wholehearted support,” as most of the passage addresses problems with the transition to the euro. (C), “Objective analysis,” might sound tempting, but the second paragraph is clearly negative, as is part of the first. The choice of words, such as “imposed on them largely without their input” indicate that the author is critical. “Indifference,” in (D), is wrong for the same reason. “Mild distaste” is negative, but what does “distaste” mean?

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Step 16 Reading Comprehension Workshop

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Reading Comprehension – Workshop End

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TIME – 25 MINUTES 18 QUESTIONS Directions: This section consists of passages followed by questions on their content. Select the best response to each question based on your understanding of the content of the passage.

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The avant-garde movement of the 1950’s, including the generation of poets and writers that came to be known as the "Beats," was a movement that, in general, avoided specific political commentary in favor of an emphasis on intense self-expression. So it would seem ironic that from this movement emerged one of the most uncompromising and strident nationalistic voices of African-American literature. Yet this contradiction and others are precisely what contributed to the development of the original vision of Afrocentric radicalism expressed in the work of Amiri Baraka. That the Beats influenced Baraka is indisputable. Baraka recognized that their experiments in form and structure and their deviations from what had been the widely accepted subjects for poems placed them outside the cultural mainstream and denoted a critique of the traditional depictions of American society as inherently humanitarian and just. He saw in their technique the possibility of creating a new rhetoric that helped enable him to reject the common course of African-American poets who, in attempts to chronicle the experience of an oppressed group, had nonetheless utilized traditional poetic expression. Using the technical model of the Beats, Baraka established his own poetic dialectic, one which allowed him to demonstrate his repudiation of the notion that African-American writing can express the main concerns of the African-American experience while simultaneously attempting to establish a complicity between a marginalized poet and a mainstream readership. 1. The primary purpose of the passage is to

(A) explain how Baraka manipulated the traditions of western poetry in order to create a new form that would express his revolutionary ideas (B) demonstrate that, despite his ambivalent relationship toward his literary forebears, Baraka was firmly enmeshed in a tradition (C) depict the influence of the Beat movement on mainstream American culture and how that, in turn, affected African-American poetry (D) discuss the inherent contradictions in the position of an African-American poet (E) underline how, despite superficial dissimilarities,

the Beat movement influenced the writings of Baraka 2. According to the passage, a contradiction of Beat poetry is that (A) while it attempted to maintain a distance from politics, its experimental form and content expressed a dissatisfaction with the norms of American society (B) although it was a mainstream movement, it enabled African-American writers to find a suitable voice (C) it influenced writers of diverse ethnic origins although its practitioners were mostly white (D) it strove to re-create poetic form while adhering to literary tradition (E) it managed a widespread appeal despite content that had been previously considered unsuitable for poetry 3. The passage provides information to answer which of the following questions? (A) How did Baraka’s poetic technique diverge from traditional approaches? (B) How did Baraka reconcile his Afrocentric inclinations with his immersion in a movement dominated by white poets? (C) How can an outspoken voice such as Amiri Baraka be considered, if only tangentially, associated with an ostensibly apolitical movement? (D) What forces contributed to Amiri Baraka’s decision to eschew the traditions of AfricanAmerican poetry? (E) How did the writings of Amiri Baraka differ from those of contemporaries in the Beat movement of the 1950’s?

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4. The tone of the passage suggests that the author most likely has what attitude toward Baraka’s predecessors in African-American poetry? (A) Their failure to establish a literary form distinct from that of mainstream American poetry limited their ability to create an idiom relevant to revolutionary African-American politics (B) They successfully documented the AfricanAmerican experience in a poetic form accessible to readers of various backgrounds. (C) They wanted to impose the standards of traditional poetic forms on all practitioners of poetry. (D) They were marginalized by a mainstream literary public that failed to accept experiments in poetic content. (E) They altered the course of American poetry. 5. It can be inferred from the passage that Baraka (A) believed African-Americans should assimilate with American society (B) considered poetry the most effective vehicle for self-expression (C) rejected the influence of his white counterparts in the avant-garde (D) desired to create a poetic form with appeal to all readers regardless of their ethnic background (E) thought traditional Western literary forms inadequate for expressing radical AfricanAmerican attitudes 6. The author uses the word "complicity" (line # 34) in order to (A) question African-American poets’ commitment to their community (B) emphasize the revolutionary aspect of Baraka’s work (C) demonstrate the direct correlation between Baraka and the Beats (D) critique the ability of traditional poetic form to represent the African-American experience (E) suggest that African-American poets conspired to appeal to the mainstream literary public

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For the past five years, the United States government has spent over $2 billion per year to fund the Human Genome Project (HGP), whose goal is to create a comprehensive "map" of every human gene. The supporters of the HGP justify this expenditure by pointing out the numerous successes that genetic research has had in detecting and curing many serious diseases. Martingale’s Syndrome is, in their view, a case in point. Genetic researchers have discovered that this debilitating disease is caused by a point mutation of a gene on the X chromosome, which leads to the deformation of nerve cells in the brain. Since the early 1990’s those who might be carriers of the defective gene, but who do not suffer from the disease, could have themselves tested in order to avoid unknowingly passing the bad gene to a child and risking that the child will contract the disease. Recently, scientists have even been able to cure Martingale’s Syndrome by injecting a "good" copy of the gene into the fetus while it is still in the womb. Bolstered by their success against such diseases, scientists speculate that a substantial number of human illnesses have a genetic basis, and that once a complete genetic map is created, they will be able to cure most of them by this same method of genetic manipulation. Certain critics, however, have appropriately begun to question whether committing such a large percentage of the U.S. research budget to the HGP is the best thing to do. While admitting the usefulness of mapping the human genome in order to detect and correct genetic anomalies, these critics have pointed out that there are many other factors involved in genetically-based diseases aside from the defective genes themselves, and that too much focus on mapping genes could prevent us from finding potentially more useful ways of treating such diseases. Often, the most significant factor in contracting a genetically-based disease is not the defective gene, but the other factors that control whether the gene is active or inactive. If the gene is activated by any of a number of factors, ranging from hormonal to environmental factors, the disease will manifest itself; if the gene remains inactive, the disease will not. There may even be some genes which are defective in all humans, but which have been only activated in certain people. In such a case, the discovery of the factors which control the activation of this gene would be a much more promising avenue of research than the investigation of the gene itself.

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7. This passage is primarily concerned with (A) the value of genetic research (B) the potential benefits of the HGP relative to the money and time that it requires (C) the number of diseases that might potentially be cured by genetic manipulation (D) what kinds of factors determine whether genes are active or inactive (E) the soundness of the theoretical basis of the HGP 8. The critics of the HGP call into question (A) whether the U.S. government should fund the HGP (B) whether or not the scientists who advocate funding the HGP are acting in the best interests of scientific research (C) whether a cure for Martingale’s Syndrome would have been found without genetic research (D) whether the HGP is important enough to justify increased taxes (E) whether some of the money and research effort spent on the HGP would be better spent on other kinds of research 9. It can be inferred that the critics of the HGP believe which of the following? (A) More money should be spent investigating diseases that are not genetically based. (B) Mapping genes may not be the most useful way to fight genetically-based diseases. (C) Environmental factors play a significant role in causing Martingale’s Syndrome. (D) Even with a complete genetic map, we may still not understand how to battle infectious diseases. (E) Many genetically-based diseases cannot be cured by genetic manipulation.

10. Which of the following can be inferred from the passage? (A) Most diseases will one day be curable by genetic manipulation. (B) The effects of a defective gene can be counteracted by a good copy of the same gene. (C) With half of its current budget, the HGP could still be completed in 5 years. (D) The reasons that the budget for the HGP is so high are essentially political and not scientific. (E) A complete genetic map is the most useful tool we can create to help detect and cure genetically based diseases. 11. According to the passage, which of the following is true of Martingale’s Syndrome? (A) Scientists have known about the disease only since the early 1990’s. (B) Scientists have known that the disease was due to a point mutation on the X chromosome only since the early 1990’s. (C) Some people who carry the defective gene which causes this disease do not suffer from any of its symptoms. (D) The discovery of the cause of Martingale’s Syndrome was one of the results of the HGP. (E) Martingale’s Syndrome is usually fatal. 12. It can be inferred that the author’s attitude toward the critics of the HGP is one of (A) (B) (C) (D) (E)

general agreement amusement mild impatience general disagreement objective indifference

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13. It can be inferred from the passage that the author

Linguists currently classify the more than 5000 different languages of the world into 11 great language "families," for each of which, it is supposed, there was at one time an original language which gave birth to the other languages in the family. This classification system, with its 11 original languages, was decided upon only in the 1970’s, by using methods drawn from the biological sciences. Biologists can determine the familial relationships among animals by analyzing the similarities in their genetic structures; the more similar the genetic structures, the more closely related are the species, and the more recently they "branched off" from their common ancestor. Similarly, by comparing the structures of several languages, linguists have been able to determine the familial relationships between them. Of particular importance to linguists in the 70’s were analyses of the grammatical structures of these languages, for phonetic similarities alone were considered to be too unreliable to count as proof of a common origin. In the last few years we have been witness to a new effort to find a single original mother language. This ambitious project aims to push the analysis back one step further, and to show that the basic tongues of the "great families" are all derived from one most original language. Since the information about the grammatical structures of these ancient languages is scarce and vague, the attempt to show their interrelations is being carried out mostly on the basis of phonetic similarities between certain very basic words, such as "mother," father," "water," and "eye". While the single mother language may well have existed, this scientific methodology leaves many unanswered questions, particularly as to the reliability of these data. First, because of the mixing of peoples and cultures, one group of people can easily adopt a foreign word for use in their own language. Thus a similar word might appear in two languages, without being the result of any familial relation. Secondly, given the limited range of human sounds, and the evolution of sound patterns in human speech, by random chance alone a substantial number of words will sound identical in different languages.

(A) disagrees with the analogy between linguistics and biology (B) thinks that there is no single mother language (C) is one of the linguists of the 1970’s who helped create the 11-family classification (D) thinks that a single mother language is possible (E) doubts the validity of the 11-family classification scheme 14. If the analogy between the biological method cited in the passage and the method used in linguistics is a valid one, it can be inferred that (A) any two languages in the same family will sound more similar than any two languages not in the same family (B) the languages that split off more recently from the mother language will be more similar to it than those which split off earlier (C) just as new species are created from time to time, so are new languages (D) since biologists have discovered that all plant and animal life came from a common origin, all human languages must have a common origin as well (E) linguists, just like biologists, often neglect the impact of their own observation on their object of study 15. The advocates of the single mother language hypothesis assume which of the following? (A) Languages develop and change according to the same fundamental principles as do animal species. (B) The basic languages of all of the “great families” branched off of the single mother language at approximately the same time. (C) Phonetic similarities alone can, in some cases, be sufficient to determine the existence of a relationship between two languages. (D) It is impossible to analyze the grammar of the original languages of the “great families.” (E) Linguistics is not as similar to biology as earlier linguists believed.

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16. The author’s attitude toward the single mother language hypothesis can best be described as (A) (B) (C) (D) (E)

tentative acceptance mild surprise objective criticism simple denial indignation

17. It can be inferred that the linguists who classify all the world’s languages into 11 "great families" (A) assume that basic words like “mother” and “eye” are more stable over time and are subject to fewer phonetic changes than are words for more abstract concepts (B) can reconstruct the grammars of the mother languages of the 11 “great families” (C) believe that nobody ever actually spoke the original languages of the “great families” (D) believe that linguistic research should be conducted just like biological research (E) do not find the methods of those who advocate the single language hypothesis to be sound 18. According to the passage, why do the linguists who advocate the single mother language hypothesis rely primarily on phonetic data to determine the relations between languages? (A) The phonetic analysis of words like "mother" and "eye" provide themselves sufficient data to establish clear relationships between languages. (B) For the languages that are being compared by these linguists, there are not enough data of other kinds upon which their analysis could be based. (C) Phonetic data fit more closely with the biological model than do other kinds of data. (D) Phonetic data can be classified and compared much more easily than other kinds of data. (E) There are no other kinds of data which establish relations with as much certainty as do phonetic data.

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READING COMPREHENSION WORKSHOP ANSWER KEY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

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III. APPENDICES

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Appendix 1 Before the GMAT

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Before the GMAT

BEFORE THE GMAT

You're counting down to the GMAT. Before panicking or canceling your test appointment, or deciding that this test is just too hard and you're going to try professional sports instead of business school, step back and get a little perspective.

THE LAST WEEK Before taking the GMAT, you should be thoroughly familiar with the test. You should know the timing and the structure of the test, including the six multiple-choice question types and the two essay types. DO NOT CRAM! The GMAT is not suited to intense, last-minute study sessions. There is not a great deal to memorize for the test; while it is (arguably) inadvisable to cram for any test, you are more likely to succeed on a university history test, for example, than on the GMAT, after staying up all night studying. You can do well on the history test by memorizing all the facts in the appropriate chapters of the appropriate books. You cannot know in advance exactly what questions you will see on the GMAT. The only way to be make significant progress is to learn techniques and to use the practice examples, with some time lapse between the lessons and the practice tests. You must build your GMAT instincts, so that by test-day you react quickly when you see, for example, a faulty comparison in a Sentence Correction question. If you have followed the suggested study plan in Chapter 2, your GMAT instincts are probably pretty sharp by now. With one week to go, you should do a little self-assessment. Ask yourself which parts of the test are hardest for you. Do some light review. Go back through the lessons, skimming the text, focusing on the key concepts (the margin notes and chapter summaries should make this easy). Review some questions you worked through already. As you re-do questions and check the answers, ask yourself certain questions: If you got the question right, did you get it right for the right reason? If you got the question wrong, was there a simple mistake that you can avoid the next time? Was there a clue in the question indicating that there might be traps in the choices? For Problem Solving questions, did you look for answers to eliminate before calculating? For Data Sufficiency questions, did you look for shortcuts, such as setting up equations and comparing the number of variables and the number of equations? For Critical Reasoning, did you try to identify flaws in the argument and predict the answer? For Sentence Correction, did you compare the choices, looking for patterns, instead of treating each choice like an individual problem? For Reading Comprehension, did you get a quick overview of the passage instead of trying to memorize every detail? For any question type, did you look for traps and use Process of Error Identification? If the answer to any of these questions is "no," you need to review some basic techniques. But don't solve a ton of new questions. Answering a large number of questions without analyzing your work will not help a great deal. Don't feel that you have to have memorized every word in this book. You can work a little on bringing your weaknesses up to par in the last week, but don't forget about your strengths. Remember that solid approaches to every question type are more valuable than highly specific strategies that may only apply to one or two questions (or none at all) on the day of the test.

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Appendix 1

THE LAST TWO DAYS With two days left before the GMAT, it is more important to get into a good mind-frame than to learn test-taking techniques. Stop taking tests. Try to get at least two consecutive nights of good sleep. Minimize stress, especially from non-GMAT-related activities. Avoid scheduling important meetings or business-related deadlines just before or just after the exam. If you are able to take a half-day or even a full day off from work or school, do so. The actual GMAT testing time for the CAT is three and a half hours, and including the tutorial, the paperwork, etc. you will likely be at the test center for four and a half hours or more. The test is tiring and stressful, especially when you know that this time, the score actually counts. What you do the two days before the exam can affect your endurance and performance. You might continue doing a few practice examples, but don't spend more than about twenty minutes at a time on questions. The best last-minute preparation is relaxation. You might want to see a movie, go out for dinner, or just watch TV the night before the exam. Make sure you know exactly where your testing center is. Do not wait until the morning of the test to get directions. Remember to bring at least two forms of identification, including a recent photograph, and your admission ticket (there will not be any scalpers outside the test-site selling extra tickets). Bring several pens or pencils (even for the CAT). Bring a watch. You have the option of seeing the time remaining on the computer screen, but some people feel more comfortable using an old-fashioned wristwatch. Do not bring a calculator; the proctor will just tell you to put it away. Bring a bottle of water or juice and a snack, and a newspaper or some light reading in case you have to sit around before the exam begins.

THE MORNING

OF THE

TEST

Wake up with plenty of time before you are supposed to arrive at the test center. Eat a reasonable breakfast. Try to do some activity that gets your brain into gear, such as reading the newspaper. Do a few GMAT problems (not to learn new tricks, just to get warmed up). Do a short mental review. Think through some of the main techniques that you've practiced, focusing on what you're good at. At this point, forget completely about the question types that give you headaches. Think about some kind of celebratory or relaxing activity for when the exam is over. ("Boy, when this is over I'm going to buy myself that Harley I've been eyeing!") Do not think about your score or interviews with business school admission officers--you can worry about these things later. Most of all, stay calm. Remember that you are prepared! A lot of other test takers are in a panic because they don't know what they're getting into. You have seen all major question types. You know how the test writer thinks. You will surprise yourself during the test by remembering how to solve problems that in the beginning of your preparation which might have seemed nearly impossible.

THE TEST ITSELF On the CAT, the first few questions count more than the others. Go a little slower on these questions. Overall, you have nearly two minutes per question--just over two minutes for each math question, a little bit under two minutes for each verbal question. The questions always start out at medium difficulty. The difficulty level will change throughout the test. It is pretty difficult to guess the difficulty level of questions during the test, especially for verbal questions. Whether you think you're looking at an easy or a hard question, look out for traps. If you're convinced that you've seen several very difficult questions in a row, and then you think you have a very easy question, you probably missed one of Phineas's traps, i.e., the "easy" question only appears easy. The difficulty level doesn't jump a great deal from question to question, though the change is more significant at the beginning and becomes gradually less significant as the test progresses.

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Don't obsess about time. You don't need to advance exactly every 2.02 minutes on math questions or every 1.82 minutes on verbal questions. You do, however, sometimes have to guess and count your losses. Don't get stubborn! Never take more than three minutes or more to answer one question. Any extra time devoted to one question means less time available for later questions. If you find the clock on the screen distracting, you can turn it off by clicking on the clock icon. You can bring it back and hide it again as often as you like. (Whee!) Take the test actively. Try to predict answers on Critical Reasoning and Reading Comprehension questions. Look for shortcuts on math questions. Scan and compare on Sentence Correction questions. Remember that you are in control. You can get an unofficial score immediately after the exam. You can also cancel your score immediately after the test. The catch is that if you want to cancel your score, you must do so before seeing your score. In fact, if you cancel your score, you (and the MBA programs) will never have any idea how you performed. Of course, once you find out your score, you will never have the option to cancel it. You will not be able to retake the exam during the same calendar month, whether you cancel or accept your score. Good Luck!

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Appendix 2 MBA Admissions

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MBA Admissions

MBA ADMISSIONS The MBA has never been more popular. Applications to business schools worldwide are up over 50 percent from twenty years ago. Americans pioneered the degree in the 1920’s, but today MBA programs are as global as Coca-Cola, and almost as well marketed. Over 160,000 students (130,000 from the U.S., 20,000 from Europe, and 10,000 from Asia) on three continents sought MBAs in 1998. Popularity, however, is only part of the MBA story. As a mark of distinction in the intensely competitive world of business, the MBA is coming into its own. The blue-chips, the best of the best, employers like HewlettPackard, Coca-Cola, and Merill Lynch, have a special fondness for the MBA. Every year their recruiters sweep MBA graduates off their feet and into lucrative positions in marketing, finance, consulting, and technical management. No other business degree can set you apart or take you farther than the MBA. MBA programs continue to evolve and adapt to the demands of employers. Global business, in fact, has a very strong influence on what you’ll learn and what you’ll do in business school. No matter how many billions employers have sitting in the bank, they feel they pay a lot for their MBA recruits and aren’t shy about telling schools what they like, what they don’t, and what they need. As businesses everywhere and of every size strive to be the next Dell or Disney, scooping up profits and making markets the world over, they want people to help them do it: MBA people with international skills, experiences, languages, and perspectives. So, when businesses talk, business schools listen, and what’s being talked about now is wanting more and more from MBA graduates: more experience (3 to 5 years), more specialized training (information technology), more international exposure (an enormous competitive advantage), and more dynamism (the entrepreneurial model is the plat du jour). Between MBA programs and MBA employers is an understanding that curricula must be continuously improved to stay relevant and competitive. Competition improves the breed, and no one takes this more seriously than business schools and businesses do. Quality schools make curriculum changes yearly now which mirror the changes in the business world at large that we all read about in the Wall Street Journal – like the shift from heavy manufacturing to marketing and entertainment services. So, business schools and employers have a nice cozy relationship but where does that leave you? The more applications schools receive each year, the more choices they have to fill each year’s MBA class, their pride and joy. Your research then must be thorough and discriminating; your thinking, clear and long-term; and your decisions prudent and well-informed. The competition for MBAs is fierce – Stanford accepts less then one-fifth of those who apply – and expectations run high, but you have more choices than ever before too. The two-year MBA program used to be the only game in town, particularly in the United States, but things have changed. At many of the over 1,500 MBA programs worldwide, one-year and eighteen-month programs are springing up like Burger King franchises to better serve an increasingly diverse student body; a student body made up of more international students, students in their 30’s and 40’s, female students, and executives.

1. THE

DECISION TO PURSUE AN

MBA

None of these guys did badly after getting their MBA: Donald Trump (Wharton) Warren Buffet (Columbia) Alan Greenspan (New York University) Tatsuro Toyoda (New York University) Robert Lutz (Berkeley)

It’s a big decision to pursue an MBA and not an easy one to make. The potential rewards are fantastic, but before you get there you’ve got to think about things like interrupting your present career, a substantial debt load, loss of salary, relocation, and significant commitments of both time and energy, to not only getting in but also to staying in the school you covet. It’s no secret that higher pay (between 60- and 90-thousand U.S. for graduates from quality © The MBA Center

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Average job offers before graduation Stanford: 3.28 Harvard: 3.11 Wharton: 2.97 Columbia: 2.66 Indiana: 2.37 Darden: 2.07

Appendix 2

schools) and job placement (quality schools place between 85 percent and 95 percent of their graduates within three months of graduation, and graduates from the top Business Schools get an average of three job offers before graduation) are universal advantages to an MBA, but the motives for pursuing the degree are as diverse as the applicant pool. See if you recognize yourself in one of the profiles below.

THE MBA

AS CAREER-ENHANCER

If you’re here you’ve had several years of work experience and are thinking about bettering your chances in your present company for promotion and salary hikes in the future by going back now for an MBA. You’ll improve your specialized business and technical skills in a year or two, widen the range of opportunities, and increase the level of responsibilities offered you in your company when you return. No doubt you’re ambitious too, and though you want to elevate your level of career achievement, pursuing an MBA is a personal objective as well as a professional one.

THE MBA

AS PROFESSIONAL CERTIFICATE

In some professions, such as finance, consulting, and operations management, the MBA has become not just suggested for those who wish to reach senior management status, but necessary to get to the fabled corridors of power. Like a professor who must have a doctorate as the minimum requirement for tenure, the lower- or middle-manager in these professions needs an MBA even to be considered for higher posts, greater responsibility, brighter glory. It’s extremely competitive for you if you’re here: even at your present level of accomplishment, to move up and broaden your horizons you’ve got to distinuguish yourself from ambitious colleagues with the same ideas. Which means that in this case especially, the quality, reputation, and availability of the latest, most up-to-date management theories and methods are very important. Current emphases in quality U.S. programs are on self-direction, selfassesment, teamwork or group work, and ethics in business. These are the qualities judged essential for leadership at the senior level, and schools and businesses have worked very closely together to turn these qualities into active subjects in quality programs. Do some reading about any schools you have in mind – look for evidence of close links between the school and businesses. You want a school that’s as close to the market you want to be in as possible – it can only benefit you in the end. One other thing: do some checking around your company about tuition reimbursement, a great way to go if you can get it.

THE MBA

AS CATALYST FOR CAREER CHANGE

If you’re here, chances are you want to make a break from your current employer. Engineers, for instance, often find themselves trapped by work which is purely technical and want to make a career change. In many cases their company won’t sponsor them for an MBA – because they like engineers just the way they are – so these engineers, and many others from different fields like them, choose to go for an MBA both to quit their present job and enlarge their possibilities for future jobs. How will MBA programs go about their business of broadening you? By sharing with you a general management education, with opportunities for specialization, and valuable hard skills, such as quantitative analysis, in keeping with the most recent methodologies, employer demands, and requests from general business. The MBA is a worthy tool for positioning – placing yourself in the best path for the best job possible after graduation. If you

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read The Economist and watch Business Today on CNN but feel generally out of touch with the prevailing environment in management, then you’ve stumbled upon the MBA at the right time in your life – a quality, contemporary MBA will diversify, indeed enrich, your prospects far better than TV can.

THE MBA

AS TRAINING GROUND FOR ENTREPRENEURS

Business school admissions people love to have present or future entrepreneurs in their classrooms. They love that these dynamic, stimulating, and creative folks are also wise enough to see the value in having a formal business education whatever their entrepreneurial experience or success so far. Schools now like enterprising ideals so much that they’ve introduced elements of entrepreneirship into their programs, emphasizing characteristics such as vision, action, and originality. Entrepreneurs like MBA programs for skills in marketing and knowledge in finance – a practical education to go along with their audacity. Corporate recruiters like very much the entrepreneurial model, set of skills, and way of thinking; you might have heard many of them think of themselves as management entrepreneurs now. Whether you’re an entrepreneur now or want to find out if you’ve got what it takes to be one, do your research--you don’t have to look far for a quality program with a curriculum stressing entrepreneurial values. Even the most independent entrepreneur can benefit from an MBA in three ways: one, networking possibilites with other students; two, networking possibilities through the alumni organization; and three, connections in the business world through the program’s contacts. And one more item, data from ten or even fifteen years ago shows that a sizeable number of MBA graduates did not end up in Fortune 500 companies – they ended up running small businesses instead.

THE MBA

AS A PLACE TO GO

Three other types of MBA applicants we’ll roll into one here. What all three of them have in common is only that they’re going for an MBA for none of the reasons outlined above. They’re miscellaneous but they consistently show up in the statistics derived from the applicant pool. Who are these citizens and what do they want? Let’s take a look. A very small number of actual MBA students pursue the degree principally as an academic challenge. These are the perpetual students – if you’ve been around any college or university campus for long, you’ve seen or heard of them. To these students, the immediate professional reasons or benefits of the diploma are lost, but the test of one’s higher intellectual capabilities is not – yep, you guessed it, they want the degree for the degree itself. If this is your path in life, all the best....but, remember that the MBA is a dedicated (and expensive) professional degree, and is rigorous enough to make it difficult for even the hardiest professional student to justify. The small piece of advice above applies to this next group as well. If you’re here, you belong to an even smaller, even more rare type than the perpetual student above – but some characteristics are shared. Who are we talking about now? The younger student with little or no professional experience but with excellent academic credentials who applies for business school admission. Admissions officers advise all those in this category to think very carefully – and to research very thoroughly – before applying for an MBA program. Further, business schools and employers know precisely who they want in their program or their organization, so in all except rare cases does the talented student or intellectual who is not a professional, or who has no definite plans to be one, gain admission or remain commited to an MBA program. The third type of applicant is growing in number every year. If you’re here you’ve had between seven and ten years of work experience and want an MBA © The MBA Center

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What are your motivations? According to the Association of MBAs, people pursue an MBA for the following reasons: -Learning -Internationalizing their career -Changing jobs -Wanting a higher salary

Rankings If you want to know more about ranking, the following magazines publish rankings. They are: U.S. News and World report (U.S. MBAs), Business Week (U.S. MBAs), Capital (U.S. and European MBAs)

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to take a break from, or quit entirely, your present career. You not only want the academic challenge and environment of business school, you also have personal motives – often to reevaluate what you’re doing and to make a change. There are quite a few reasons admissions officers cite for why applicants in this category become excellent MBA students: they’re self-sufficient and believe in change; they have strong clear ideas about who they are and what they want to change in their life, education, and career the next time around; their maturity and unique perspective are appreciated in the classroom; they’ve taken a huge step toward what is expected of top executives and managers today, continuous learning.

2. CHOOSING

THE RIGHT SCHOOL

Rankings are not the only method for choosing a business school. Using rankings to choose your MBA school isn’t even recommended – if that’s all you’re doing for research. Use rankings as a guide only, to what’s out there, to how different schools are judged relative to the the national market, and to how different schools are judged relative to regional markets. (United States only) Magazines are only one small factor in a decision which is an important and highly personal one. Choosing the right school for you should be an individual decision which follows from close, thoughtful evaluation, and from thorough investigation. To do it right means expense of time, of energy, of motivation, of frustration – of searching your soul – to arrive at the first basic requirement of admissions: knowing what you want. After thinking it through personally, think about it methodically – it is a life-changing decision and an enormous financial investment. Business schools expect, and implicitly require, investigation from their applicants; they realize, they have lots of experience realizing, that it’s a difficult decision to make. So ask all the questions you want of any school you’re considering – by phone, by fax, by e-mail – and don’t hesitate, they expect you to. Consult any sources of information you feel will help you but give yourself time to thoroughly evaluate all the factors involved, such as reputation, location, job placement, curriculum, and networking. Only you know: neither rankings, nor advice from colleagues, friends, professors, or mentors can choose the right school for you.

REPUTATION The reputation of a school is determined both by word of mouth and by official rankings put together by independent researchers. There are a variety of sources for rankings in American and European publications. The rankings can tell you one thing for sure about reputation: there’s a strong correlation between the reputation of a school and the average starting salaries of that school’s graduates. However, the rankings offer a perspective but not the whole picture of what’s really going on and thought about in the world of business schools – so use them as a guide, not for answers. Everybody wants to go to the big schools, because they’re the best, right? and because everybody – any employer on Earth – knows their reputation. While this may be true, a school should suit the applicant well, especially at the graduate level, in all ways, not only reputation. Reputation can be used, true, but you must decide where you’re headed and in what field and where before you consider how a school’s reputation might of benefit to you. Not every reputation, for example, need be global for it to be good. Excellent schools exist both in America and in Europe with solid, local reputations; these are regional schools, like Babson in the U.S., which are not well-known nationally or internationally yet have unquestionable reputations within their scope and close ties to businesses in their area. So ask yourself the hard questions and keep in mind what industry and in what location you’d prefer to end up in – many, © The MBA Center

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many lesser-known schools can provide quality and specialization. Two more things to bear in mind. One, the quality and the reputation of a school are judged by its facilities, its faculty, and its student body. Two, as the correlation mentioned above implies, reputation is of considerable interest to employers when recruiting, so remember that your MBA and the reputation of the school it came from will follow you wherever you go in your career.

LOCATION With the exception of the top, brand-name, Platinum American Express card programs, the location of a school can make difference both to you personally and to your potential employers somewhere down the line after graduation. Smaller programs don’t carry much weight far from their regions, but they often have valuable ties to local industries. Ask yourself: will the location affect the quality of my business school experience? and will it affect my employability after graduation? (Get yourself the answers too.) Think about long-term plans as well – where do you want to settle, and is the school there or will it allow you to get there? Take into consideration personal as well as practical concerns. Urban, rural, or suburban enviroment? Do you like snow, rain, heat, the colors of the fall? Keep in mind pragmatic issues like the time and costs involved in commuting and travel – do you want to commute?, do you want to travel? This is the time to consider your personal preferences in things like geography, population, weather, economy (regular or extra-lucrative?) – you’ll spend time and a lot of money wherever you go, so make sure it’s where you want to be.

PLACEMENT An MBA program’s job placement record and practices should be of concern to you. More than likely you’re not going to business school to be left unemployed and drifting after you’re done. Statistics on placement are easily available either from the schools themselves or from the shelf-loads of MBA information guides. See the bookstore or library nearest you, but call, fax, or email the schools first for as much free information as you can get. Looking over these figures, wherever they are from, keep in mind that not just statistics are important; it is whether they tell you what you want to know. Average starting salary statistics, for instance, are only a place to start: you’ll want to find out whether recruiters prefer school experience or previous work experience when determining your salary. Look for placement services such as a career library, career counseling, career fairs, a job bank, off-site recruiting, and referrral services for résumés to employers. Read closely for the kinds of jobs found by a given school – jobs are usually listed by type of employer (manufacturing, services, banking, etc.) and by functional area (finance, marketing, consulting, etc.). Pay attention also to alumni accomplishments, they speak to the reputation and soundness of the school. Your career is a long-term project, so consider not just your first job offer but also where it might lead you.

CURRICULUM The curriculum is the heart of the program. You’ll sit over coffee talking management theory you learned by it, and the prestigious faculty earn their bread and butter by teaching it. In American schools the curriculum is under constant supervision and change, constantly responding to the needs of general business and the marketplace. In this endeavor, the most advanced schools are tightly linked to businesses and employers trying to hone their curriculum to its best, most cutting edge. This link between schools, businesses, and recruiters is © The MBA Center

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something you should be very aware of, for the results of it are found in nearly every quality-school curriculum. Simply put, MBA directors now work to supply what their business connections tell them they need – schools no longer are, or want to be, insulated from the active and very real global business environment. Schools feed businesses their polished graduates, and businesses give schools their always-evolving assessment and their suggestions for improvement of the strengths and weaknesses of a particular curriculum. Information-sharing, it is sometimes called. Teaching methods have changed in innovative programs. Their focus has switched from a teaching model (you learn what we know) to a learning model (you learn how to learn) after feedback from everyone involved – students, teachers, and employers. Satisfaction among all three has been very high. The learning environment is relevant for you in two ways. First, recruiting officers from potential employers are very opinionated about – they know exactly which – environments they prefer, so know that your learning environment can affect how you’re employed in the end. In addition, the learning environment of the school you choose should be suitable for your own personal needs, ends, and personality; it should be in character both with you and what type of job you want. In programs that interest you, learn all you can about recent or on-going curriculum improvements. Quality schools have made the student and how the student learns their number 1 objective, so you should realize that advertised faculty-to-student ratios don’t tell the complete and unabridged story of a school’s learning environment. Look for curricula which highlight studentteacher relationships, this is one of the improvements schools pride themselves on – closing the gap between teachers and students. For example, there are some two-year programs in which students see the same teachers for an entire year. You may not want to get that close, but be aware of this changing emphasis. Last, ask your target schools for the results of student exit-surveys from the previous year’s graduating class. These can tell you a great deal if you go through the trouble to get them and they are often published in some form by the school.

NETWORKING Networking is to business schools as makeup is to Ivana Trump: something they are very, very serious about. Not long ago networking was heard as a term tossed about by a few eager business school graduates; now it is much more than a buzzword, it is a b-school way of life. Networking is a genuine element of today’s MBA programs and a very commited purpose for their directors. Look over almost any brochure published by almost any school, and you will see the word littered throughout the pages. What does it mean then? Networking means building relationships among students, faculty, alumni, and the community; it is a very large part of the MBA experience and can be very advantageous for you – think of jobs, advice, partnerships – in the long run. Think of it as neccessary and worthwhile whether you like it, or are good at it, or not. Also seriously consider the network of the school – is it established?, well-organized? Some schools are known for excellence in networking, such as Thunderbird in Arizona, and others are not. In choosing a school with an appropriate (for the type of job you want), effective, and diverse network you can tremendously improve your long-term business and employment prospects. If you’ve read your Fortune and Forbes, you know that many a successful partnership originated in business school – Duty Free Shops, HewlettPackard, et al...

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QUALITY

OF

LIFE

How do you want to live once at the school of your choice? Quality of life is part of this picture too, though right now 10,000 other things probably seem more important. Classroom experience is not the only one of importance in school; your personal experience has its place too – particularly for full-time students. So, quality of life or personal experience should be meditated upon before choosing any of your target schools. The question is, what else does the school and/or its surrounding area have that interests you personally? Activities, community or cultural involvement, accomodations, sports, weather, cost of living, and city size are all features to keep in mind. Whatever emphasis or importance you place on quality of life, consider that business school is one to two years of your life, is more than likely in a new city if not a new country, and affects yourself, your family, friends, and others of significance to you.

3. EVALUATING

YOUR CHANCES OF ACCEPTANCE

The admissions application and process is the school’s way of getting to know you. Don’t assume that your undergraduate grades or your undergraduate school aren’t good enough – you don’t know. Know that admissions officers are regular folk who work all year round looking at scores of applications – they’re professionals who know their job, and what they like to see and they stress that they evaluate each applicant as an individual, not a set of numbers. They use all the tools at their disposal – letters of recommendation, essays, interviews – to get to know you as personally as they can. Applicants for the MBA are a diverse and competitive group: you can’t control your competition; however, you can control every aspect of your presentation of yourself to admissions officers. Everything required of you in the admissions process is your chance to present yourself in the manner you’d like to be seen – it’s your ballgame until your admissions packet hits their doorstep, so play the best game possible. Prospective students are sized up by admissions officers in four ways: one, according to intellectual, or academic, ability (scores and grades); two, by looking at professional work experience (emphasizing the international) to estimate professional potential; three, by judging the presentation of the applicant (how were the essays, interviews, and recommendations?); and four, by the personality, or personal qualities, of the applicant (what kind of personality is there evidence of?). The order of evaluation and the order of importance of these criteria vary from school to school. The process of admissions for your MBA is a time to put your best work forward the first time you apply – it’s first- impression time, and your golden opportunity to show these overstressed creatures exactly the picture of yourself you want them to see. Beyond that there is no secret ‘right way’ or formula to get into business school – not unless your family owns a very large corporation. If that’s not the case, then knowing yourself, the program you want, what you want from your MBA education, and submitting a compelling admissions application is your best approach.

INTELLECTUAL

ABILITY

We’ve mentioned this before, but it is important and applies here as well: the MBA is a professional degree, and a difficult and demanding task, which requires high intellectual stamina and acuity. The way admissions officers see this demonstrated is by looking at your transcripts and so forth to see if you have a solid history of accomplishment in the classroom. This is the part where © The MBA Center

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your grades and scores come into play. Business schools want leaders, yes, but they also want students who can keep up in the classroom – and you’ll have some tough classrooms. Your undergraduate records help them to gauge your intellectual aptitudes, your ability to study well at the graduate level. Some of you already have graduate degrees of one sort or another, okay, this part isn’t a challenge for you. But the scores, your GMAT, TOEFL, or both, are important for everybody. Of course the GMAT is the one they chiefly care about, and it is used to appraise your basic academic skills and to allow comparison – a nice, neat quantitative comparison – between competing applicants. The basic skills judged are: math skills, primarily quantitative problem solving abilities; and verbal skills, understanding and interpreting written material and basic writing skills. Schools report a definite correlation between GMAT scores and class performance during the first year of courses. Your test scores are used to some extent by nearly every school and they’re not the only criteria looked at, but they do give schools a sense of: can you study at the graduate level?

PROFESSIONAL

POTENTIAL

You might ask yourself this question: who knew Donald Trump would end up owning some casinos in Atlantic City? If you hazarded the guess, Wharton, his business school, well maybe you’re right. What admissions officers would love to do is to encourage the next Trump or Warren Buffet: what they’re looking for from you is evidence of leadership – leadership is the stuff MBA gradautes are made of. In this area, professional work experience – the quality of it, what miracles you’ve performed while doing it, how much of it you’ve had – are the most important of three factors; the other two are letters of recommendation and personal essays. For quality, or the most selective schools, full-time professional work experience is essential – they have plenty of applicants with part-time experience, but very few of them become candidates. Admissions officers say there is no more effective way of demonstrating your leadership potential as a manager than by the fact of career success – it gets them very excited about you. Show them your good side. For the most favorable sketch of yourself, demonstrate clearly the successes you’ve had in your career – don’t be shy. Also, tell them what contributions you’ll make to your MBA class because of your success, and how you’ll make them. It comes down to clearly presenting both your record of resposibility and leadership from the past and your plan for resposibility and leadership in the future.

PERSONAL

QUALITIES

Everyone knows that personality can take you a long, long way in life – look how far it has taken Lee Iacocca. You just can’t keep a guy like that down. That’s what these competitive schools want to see: something to show them that you can take the blows, learn a lesson or two, and come back for more. We’re talking about leadership, and business schools prize it as traders do bonus checks, that is, highly – and very seriously. Why? Schools want MBA candidates who are fit for responsibility, the sworn responsibilty of managing people and entire organizations. They know from educating legions of CEO’s, COO’s, CFO’s, and risk-takers like Trump and Lawrence Ellison that leadership is fundamental for success in business. In addition to a personality worthy of command, schools like to find in you such personal qualities as communication skills, initiative, and motivation. These are individual qualities, and they take their forms in each applicant in very different ways. In presenting your own personal variety of ingenuity, leadership, initiative, motivation, determination, creativity, and the like, it’s solely up to you

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to think of examples which show you at your best and demonstrate the principle involved. Individual qualities are what set you apart from your competitors (nothing you can do about them anyway). Therefore, your presentation of self – who you are, what you’ve done and why, and what you want – makes as much difference in distinguishing you from another applicant as your actual qualities do. Admissions officers don’t know you any better than they know the other thousand like you who apply. They’ll work to surmise what they can of you from letters of recommendation, your current professional position, and any evidence of your personal interests – but in this case those are the sketches, not the finished self-portrait. So use the tools you’re given, the personal essays and the interview, to showcase your character and yourself. In the application process, presentation is king.

4. FINANCING

YOUR

MBA

Did someone say they were handing out free MBA’s here? Not this year, pal, you must not be from around here. Here, wherever you are and wherever you’re going, an MBA will set you back a tidy sum. The amount varies from school to school, country to country of course, but expect to pay from $10,000 to $35,000 per year. What the MBA really is, at these prices, is an investment with expected returns somewhere off in the long-term future. It may grieve you, but probably won’t surprise you, to learn that the bill for tuition isn’t everything you’ll be putting on your tab once in school. Think about accomodations, transportation, personal expenses, and the odd textbook here and there to keep the bookstores happy and prosperous. These non-tuition (indirect) costs are typicaly just over one-half of the tuition (direct) costs; Harvard, for example, has tuition costs of around $21,000 and non-tuition costs of about $13,500. If you add up those two figures (you’re the MBA-hopefuls, you’ve probably already done it), you can see the wisdom in figuring the total cost per year for each school under consideration: tuition, room and board, books, computer, travel... Any, or a combination of all of the following four methods could be used to pay for your MBA.

FINANCIAL AID Financial aid in one form or another is by far the most common way of financing an MBA in the United States. If you’re an international student planning to study in the U.S., however, very little financial aid is available to you; on top of that, you must prove you have sufficient funds to cover the entire cost of the program before you can be admitted to the program in question. International students find their MBA money from: their government (scholarships, grants, subsidies, etc.), their personal funds saved or borrowed for the purpose, or from their families. As a graduate student, you are considered independent: only your financial status and resources are relevant, not those of your family. Further, financial aid for graduate students in the form of grants or scholarships is very rare in the U.S. Which means that most candidates take on sizeable debts in their pursuit of an MBA, mainly in the form of loans, and count on high future earnings to pay them off. It’s a vicious cycle, but other choices are few. If your loans are arranged by your target school’s financial aid office, then they are very likely need-based – by far the most common type of loan – though a very small percentage are unsubsidized, or non-need-based which carry higher interest rates in any case. The financial aid office of your intended school is the best resource for specific and current information on what money is available, to whom, and how.

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BANK LOANS Are you getting the idea that there’s no free money? If there is, there sure isn’t enough of it. Which might explain why over 55 percent of all MBA candidates finance their degree with bank loans. Many banks have loan programs already set up for MBA students – you didn’t think you were the first to need money for an MBA, did you? Ask your bank if they have something like an MBA Loan or a Business Access Loan, or ask what they can do specifically for MBA students. If you have a good relationship with a bank now, your path to funds is going to be that much smoother. If you don’t, and you do think you’ll have to borrow, make sure your credit history is accurate and up to date. Banks are willing to loan money to MBA candidates who demonstrate a responsible past and a high probablity for success in the future, they naturally want those with the highest likelihood of paying off their loans. The future Wall Streeters, the potential lions of the Bourse, the tigers of the Nikkei...

FINANCING

FROM BUSINESS

Some of the best-known companies like Microsoft, Intel, Rolls-Royce, and Dow Chemical have programs for financing an employee’s MBA. They know the benefits of lifelong learning, they know the advantages to employing MBA graduates, and they consider financing an MBA for a qualified individual a wise and profitable investment. Tuition reimbursement programs are what they’re generally called, and unless you already know the policy of your company, a little checking (call the Human Resources office) can go a long way. Some companies pay 100 percent of the costs of the MBA program, some pay for a lower percentage, expecting you to cover the difference. These companies, rich as they are, don’t cut you a check for $50,000 and send you on your way. They want a little something from you in return: it’s usually an understanding that after your MBA you’ll continue to work for them for at least another two or three years. You may have been, or would like to be, hired by a company that allows you to go off for an MBA with the stipulation that you begin work for them immediately upon its completion. Either way, about 10 percent of all MBA candidates go to school (most often in part-time programs) on the tuition reimbursement plan sponsored by their company.

PERSONAL FINANCING Financing an MBA through personal ways and means is sharply on the increase: about 35 percent of all MBA students today finance the degree themselves compared to about 20 percent only fifteen years ago. Maybe more students are gifted stock-pickers, who knows, but in most cases the money comes from three to five years of savings while in a profession. Contributions from family are also part of this personal financing package, and in some lucky cases, family contributions are the entire package. Schools figure that in these cases it's a combination of savings, family contributions, and in more and more cases, spousal support. If you can manage to pay for your own degree, great – no bank or government loans to worry about. If you can’t manage on your own resources, it is time to get creative and investigate the possibilites mentioned above. Or ask your parents if they have any wealthy brothers or sisters that you’ve never met – it’s a long shot, but you never know.

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TOTAL PREPKIT FOR THE GMAT® Copyright 2001-2007 by MBA Center Publications MBA Prep ltd. 40 Woodford Avenue Gants Hill, Ilford Sussex IG2 6XQ United Kingdom Printed in France – March 2007 C L’Imprimerie 7, rue de Liège 95190 Goussainville France N° d’impression : NA-986/2007 Dépôt légal à parution Written by: Dr. Hubert Silly Desktop Publisher: Ilya Krupin e-Learning: Alex Nagorov Albert Panyukov

ISBN: 978-2-916729-02-2

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© The MBA Center