Cl Pre Mock 3

PRE MOCK CAT - 3

Test Booklet Serial Number: 7 7 0 3 5 7

INSTRUCTIONS Before the Test: 1. 2.

3. 4. 5. 6.

DO NOT OPEN THIS BOOKLET UNTIL THE SIGNAL TO START IS GIVEN. Keep only the Admit Card, pencil, eraser and sharpener with you. DO NOT KEEP with you books, rulers, slide rules, drawing instruments, calculators (including watch calculators), pagers, cellular phones, stop watches or any other device or loose paper. These should be left at a place as indicated by the invigilator. Use only an HB pencil to fill in the Answer Sheet. Enter in your Answer Sheet: (a) in Box 10 the Test Form Number, which appears at the bottom of this page, (b) in Box 11 the Test Booklet Serial number, which appears at the top of this page. Ensure that your personal data have been entered correctly on Side 1 of the Answer Sheet. Check whether you have entered your 7-digit Enrollment ID in Box 2 of the Answer sheet correctly.

At the Start of the Test: 1. As soon as the signal to start is given, open the Booklet. 2. This Test booklet contains 20 pages, including the blank ones. Immediately after opening the Test Booklet, verify that all the pages are printed properly and are in order. Also that the Test form Number indicated on the cover page and at the bottom of the inner pages is the same. If there is a problem with your Test Booklet, immediately inform the invigilator/supervisor. You will be provided with a replacement. How to answer: 1. This test has three sections which examine various abilities. These 3 sections have 75 questions in all with each section having 25 questions. You will be given two and half hours to complete the test. In distributing the time over the three sections, please bear in mind that you need to demonstrate your competence in all three sections. 2. Directions for answering the questions are given before some of the questions wherever necessary. Read these directions carefully and answer the questions by darkening the appropriate circles on the Answer Sheet. There is only one correct answer to each question. 3. All questions carry 4 marks each. Each wrong answer will attract a penalty of 1 mark. 4. Do your rough work only on the Test Booklet and NOT on the Answer Sheet. 5. Follow the instructions of the invigilator. Candidates found violating the instructions will be disqualified. After the Test: 1. At the end of the test, remain seated. The invigilator will collect the Answer Sheet from your seat. Do not leave the hall until the invigilator announces. “You may leave now.” The invigilator will make the announcement only after collecting the Answer Sheets from all the candidates in the room. 2. You may retain this Test Booklet with you. Candidates giving assistance or seeking/receiving help from any source in answering questions or copying in any manner in the test will have their Answer Sheets cancelled.

MCT-0003/08

Test Form Number:

333

SECTION – I Number of questions = 25 DIRECTIONS for Questions 1 to 5: Answer the questions on the basis of the information given below. The following table provides information about the Population Density of 25 states in United States. These 25 states are ranked as per their population density with the state having greater population density being given a numerically lesser rank. Area of all the 25 states (in square kilometer) is always an integer. Population density of any state is the number of people living in the state per square kilometer of the area.

Rank 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

1.

State New Jersey Rhode Island Massachusetts Connecticut Maryland New York Delaware Florida Ohio Pennsylvania Illinois California Hawaii Virginia Michigan Indiana North Carolina Georgia Tennessee New Hampshire South Carolina Louisiana Kentucky Wisconsin Washington

Population Density 438.00 387.35 312.68 271.40 209.23 195.18 154.87 114.43 107.05 105.80 86.27 83.85 72.83 69.03 67.55 65.46 63.80 54.59 53.29 53.20 51.45 39.61 39.28 38.13 34.20

Find the minimum possible aggregate population of Rhode Island, New York, Pennsylvania, New Hampshire and Louisiana. (1) 21,522 (2) 23,442 (3) 22,262 (4) 21,682 (5) 20,426

PRE MOCK CAT - 3

1

2.

If the mentioned states are re-ranked as per their area with the state having larger area being given a numerically lesser rank, then which state among Michigan, North Carolina, Washington, Massachusetts and Connecticut would have the numerically least rank? [Assume, these five mentioned states have minimum possible area.] (1) Connecticut (2) Massachusetts (3) Michigan (4) North Carolina (5) Washington

3.

How many of the mentioned 25 states definitely have an area not less than 100 square kilometers? (1) 12 (2) 11 (3) 10 (4) 9 (5) 8

4.

If the area of New York is 150 square kilometers and the average number of people in a family in New York is 3, then find the total number of families in New York. (1) 9759 (2) 9653 (3) 9741 (4) 9661 (5) 9619

5.

If both Kentucky and Washington have minimum possible area and the area of both the states are interchanged, with population of both the states remaining unchanged, then find the percentage increase in the Population Density of Kentucky. (1) 100% (2) 200% (3) 300% (4) 600% (5) 400%

50

14000 12000 10000 8000 6000 4000 2000 0

40 30 20 10

DA as % of basic

Basic

DIRECTIONS for Questions 6 to 9: Answer the questions on the basis of the information given below. In an organisation, the salary component of four empolyees viz. Swapi, Yeshu, Manik and Vinita are shown below. The salary consists of four parts — Basic and DA being two of them.

0 Swapi

Yeshu Basic

Manik

Vinita

DA as % of Basic

In addition to Basic and DA, they also get HRA (House Rent Allowance) and Bonus, which are the other two parts. HRA depends upon empolyee’s city of residence. Bonus depends upon the percentage of sales targets achieved by the employee. The following tables provide information about the percentage sales targets achieved and the class of the city in which they reside. Each empolyee resides in a city of a different class and earns a different amount in bonus.

2

Sales target achieved

Bonus (Rs.)

Class of City

HRA(Rs.)

100% 90% 80% 70%

10000 8000 6000 5000

Metro A B C

7000 5000 4000 2000

PRE MOCK CAT - 3

Swapi lives in Delhi. He has achieved the lowest percentage sales target. Yeshu lives in Pune and Manik lives in Raipur. Vinita lives in Bokaro. She has achieved a lower percentage sales target than that achieved by Yeshu. She gets Rs. 8000 in Bonus. Delhi is a Metro class city. Pune is a B class city. Bokaro is a C class city. Tota tax on the salary is calculated as per the formula given below: Total tax = 30% of Basic + 20% of HRA + 10% of Bonus DA is exempted from tax. 6.

7.

8.

9.

What is the salary of Vinita? (1) Rs. 25000 (2) Rs. 20000

(3) Rs. 32000

What is the total tax on the salary of Swapi? (1) Rs. 5100 (2) Rs. 5400 (3) Rs. 4000

(4) Rs. 26000

(5) Rs. 21400

(4) Rs. 4800

(5) Rs. 4900

The total tax on Yeshu’s salary is what percent of his salary ? (1) 20% (2) 18% (3) 15% (4) 22%

(5) 25%

The DA component of Manik’s salary is what percent of the HRA component of his salary ? (1) 60% (2) 50% (3) 55% (4) 48% (5) 75%

DIRECTIONS for Questions 10 to 14: Answer the questions on the basis of the information given below. Five friends Chris, Matthew, Shane, Graham and Greame bought 10 cookies and distributed among themselves such that each of them received a distinct integral number of cookies. Each of them likes a different biscuit from amongst Hide n seek, Bon-Bon, Maska Chaska, Krackjack and Good day (not necessarily in that order) and likes to watch a different TV shows from amongst Sportscenter, Raw, Wrestlemania, Smackdown and Hitz (not necessarily in that order). Sportscenter and Hitz are sports shows and rest are wrestling shows. No two persons like same type of biscuit or same TV show. Following information is also given: 1. 2. 3. 4. 5. 6. 7. 8. 10.

11.

12.

13.

Shane who didn’t receive any cookies does not like any wrestling show. Chris likes Maska Chaska and received more cookies than Matthew. Difference in the number of cookies with Shane and with Chris is equal to the difference in the number of cookies with Matthew and with Graham. Greame didn’t receive the maximum number of cookies. Matthew and Shane like TV shows starting with the same alphabet. Person who received the maximum number of cookies likes Krackjack and a wrestling show. Persons whose names start with the same alphabet, like the same type of TV shows. Greame didn’t like Bon-Bon and Shane didn’t like Hide n seek. Who likes Krackjack? (1) Graham (2) Matthew

(3) Shane

(4) Greame

(5) Cannot be determined

Which biscuit does Greame like? (1) Good Day (2) Hide n Seek

(3) Bon-Bon

(4) Krackjack

(5) Cannot be determined

If Shane likes Good Day, then which biscuit does Matthew like? (1) Good Day (2) Hide n Seek (3) Bon-Bon (4) Krackjack

(5) Cannot be determined

Which TV show is liked by Chris? (1) Wrestlemania (2) Raw

(5) Cannot be determined

PRE MOCK CAT - 3

(3) Smackdown

(4) Hitz

3

14.

Which of the following pairs of TV show and biscuit was definetely not liked by the same person? (1) Hitz – Maska Chaska (2) Smackdown – Good Day (3) Raw – Bon-Bon (4) Smackdown – Bon-Bon (5) None of these

DIRECTIONS for Questions 15 to 19: Answer the questions on the basis of the information given below. The average annual salary figures of five leading B-schools have been shown below.

Average Annual Salary (Rs. in lakh) 5

Narsee Monjee K.J. Somaiya

4

IMI

5

IMT

6

FMS

7 0

Average Annual Salary =

1

2

3

4

5

6

7

8

Total salary offered in the B − School Number of students in the B − School

The percentage of students getting PPOs (Pre-Placement Offers) and their average annual salary (in lakhs) is shown below.

Average Annual Salary

% of students

0 FMS

4

5

10

IMT

IMI

15

20

25

K.J. Somaiya

30 Narsee Monjee

PRE MOCK CAT - 3

The number of students, companies visiting the campus and total offers made (including PPO’s) have been shown below for the mentioned five leading B-schools.

250

140 200

120 100

150

80 100

60 40

50

Number of offers

Number of companies and students

160

20 0

0 FMS

IMT

IMI

K.J. Somaiya

Narsee Monjee

B-school Number of Companies

Number of students

Number of offers

15.

The ratio of number of students to the number of companies visiting the campus is lowest for (1) IMT (2) FMS (3) Narsee Monjee (4) Both (1) and (2) (5) Both (2) and (3)

16.

Which B-school has the highest total number of offers per student? (1) IMT (2) Narsee Monjee (4) FMS (5) K.J. Somaiya

(3) IMI

17.

The ratio of the number of offers to the number of companies visiting the campus is highest for (1) IMT (2) K.J. Somaiya (3) IMI (4) FMS (5) Narsee Monjee

18.

At FMS, what is the average salary of students, who did not get PPO? (1) Rs. 7 lakh (2) Rs. 4.5 lakh (4) Rs. 6 lakh (5) Rs. 6.5 lakh

(3) Rs. 8 lakh

Which college had the best placements? (1) FMS (2) IMT (4) Narsee Monjee (5) Cannot be determined

(3) IMI

19.

PRE MOCK CAT - 3

5

DIRECTIONS for Questions 20 and 21: Each question is followed by two statements, A and B. Answer each question using the following instructions: Mark (1) if the question can be answered by using the statement A alone but not by using the statement B alone. Mark (2) if the question can be answered by using the statement B alone but not by using the statement A alone. Mark (3) if the question can be answered by using either of the statements alone. Mark (4) if the question can be answered by using both the statements together but not by either of the statements alone. Mark (5) if the question cannot be answered on the basis of the two statements. 20.

In a year ‘X’, which month(s) will have its first day falling on a Sunday? A: First May is a Sunday in the year (X – 1). B: First December is a Sunday in the year (X + 3).

21.

Is x > y? A: (x – y) × (x – y) > 0. 1 1 B: (x + y) ×  +  = 4 . x y

DIRECTIONS for Questions 22 to 25: Answer the questions on the basis of the information given below. Production department of a multinational company houses seven typists where all of them are working on a project. The given diagrams describe their performance over the four days of the project, one for each day. In each diagram, the four squares reflect the percentage of total number of lines typed in that day by the top four typists of the day whereas the middle circle denotes the number of lines typed by the remaining typists in that day. No two typists type the same number of lines on a given day. A typist may not type even a single line on a given day. The management also computed two parameters for each typist viz. Performance Variance (PV) and Sigma. PV of a typist is the positive difference between the sum of the maximum and minimum possible number of lines typed across 4 days and the sum of the number of lines typed on the remaining two days. The Sigma of a typist is the average of the two middle quantities, if the number of lines typed by him across 4 days are arranged in a non-decreasing order. D ay 2 D ay 1

G au rav

24

23

S a n ja y

K an d a rp

76

S a lim

14

20

A m m ar

K ap il

16

S a n ja y

D ip ak

6

16

22

36

105 G au rav

26

D ip ak

D ay 4 18

17

S alim

70

D ay 3

K ap il

20

18

S a n ja y

45 14

S a lim

A m m ar

18

14

K an d a rp

PRE MOCK CAT - 3

22.

Given that the Sigma for all typists is an integer, for how many of mentioned typists it is not possible to calculate the exact value of Sigma? (1) 2 (2) 3 (3) 4 (4) 5 (5) 6

23.

For whom of Sanajay, Salim and Ammar, the value of PV can come out to be 0? (1) Salim (2) Sanjay (3) Ammar (4) Both (1) and (2) (5) (1), (2) and (3)

24.

How many typists have definitely typed more number of lines than Kapil over the entire project? (1) 1 (2) 2 (3) 3 (4) 4 (5) 5

25.

For which typist, the difference between the minimum and the maximum possible Sigma is the least? (1) Sanjay (2) Salim (3) Gaurav (4) Kandarp (5) Ammar

PRE MOCK CAT - 3

7

SECTION – II Number of questions = 25 DIRECTIONS for Questions 26 to 29: The passage given below is followed by a set of questions. Choose the best answer to each question.

Passage Last week, at a cocktail party on British diplomatic premises somewhere in North America, a question reared itself in my head—oh, for the thousandth time since I began to be aware of it. After all these years of stoical endurance, I can see no reason not to go public in search of an answer: Why are the Brits—no, not you Philip, Daisy, Marcus and Matthew, dear friends all, and generous spirits—such appalling, skinflint hosts? In the hour we spent at this massed British party, I saw just one plate of hors d’ouevres—spring rolls—float by in the distance. Was the food a mirage, wondered my wife, her beguiling thought quickly dispelled by a horde of guests, their hands grabbing at the precious parcels of dough and (one can only presume) bean sprout. No apparitions they, but modern Tuaregs in suits, eking by on the meager rations at this cocktail “Sahara Anglais” friends. I think one answer to why the British are such poor hosts might be found in wartime austerity and the post-war rationing that forced Britons of every class to think that skimpery was smart. I put this relatively obvious point to a friend in London, who responded by saying that, while the general premise was sound, “one can’t help thinking that the post-war frugality tapped into existing norms. I don’t remember anyone handing round the crisps in Jane Austen’s drawing rooms.” Besides, anyone who went to the communist-era Eastern Bloc—Poland, say, or the Ukraine—was always struck by how ordinary folk would save for days to host a guest royally. Those heaps of gherkin, sausage, tomato, bread and cheese, not to mention the vodka on the table, were the result of a sacrificial accumulation calculated to please a visitor. These were—and still are—people determined to be hospitable, come what may. The Brits, by contrast, often appear determined to be anything but, and would regard the aforementioned Poles and Ukrainians as irresponsible. Philosophically there is no shame among Britons in failing to be entirely hospitable. In an attractive little book called The Duchess Who Wouldn’t Sit Down: An Informal History of Hospitality, Jesse Browner discusses the paradox of hospitality—that “we are incomplete alone and compromised in company.” Yet more than any other species, the Briton actually feels complete alone. In fact, so entrenched is his sense of private space—one’s home as one’s castle and all that—that mere admittance through the front door is seen as privilege enough. A friend recalls for me a time when he was invited to a Scottish castle. Upon arrival by overnight express from London, “said castle-residing hosts greeted us to announce that the whole group would go straight from the train to Fort William supermarket to jointly buy supplies for the weekend, including teabags.” There is the fact, of course, that a good time among the British is associated more with drink than food. A peripatetic friend, with experience of years in England, put it to me like this: “The food at their parties is treated as an annoying but necessary incidental. Compare the Indian or Iranian lady who knows that she is going to be judged by the presentation, quantity and quality of her food. When have you ever seen the first guests at an English party take a photo of the laden table?”

8

PRE MOCK CAT - 3

At bottom, there is deep ambivalence about generosity in the English psyche. It is both admired and feared. Falstaff is a lovable, generous rogue; but he comes to a sticky end. Henry V has to grow up and cut back on the canapés. Scrooge repents and becomes generous. But the proto-Scrooge, distrusting hospitality and generosity, was the typical Victorian businessman against whom Dickens was campaigning. Brits have a horror of ostentation (and a frequent inability to distinguish it from generosity). This may have been ground into them by their “public” school system and its hatred of show-offs and swots. In America, the rich and successful are admired, not envied. In Britain, even talking about how much money you have is reckoned very bad form. Self-depreciation is considered a virtue—and so is frugality, its first cousin. The British are a funny, screwed-up people, terrified of making an exhibition of themselves, and generosity is an exhibition of sorts. To be sure, a few unstinting Cavaliers struggle for supremacy in Britain. But the Roundheads usually—no, always—win. 26.

It can be inferred that the author quotes his wife because (1) he wanted to show the lack of etiquette during Brit parties (2) he wants to prove that his opinion is based on experience (3) he was appalled at the cheap choice of food at a cocktail party (4) he was taken aback at how soon the food arrived (5) he was not surprised at the behaviour of the guests

27.

The author cites the example of the behaviour of the citizens of the countries of the Eastern Bloc in order to (1) show how people around the world differ in their culture and in the way they treat guests (2) showcase varying interpretations of hospitality (3) point out how adverse times seem to have not had the same behavioural impact on all people (4) display how strangers are more welcome in a new country than citizens (5) show how some people are more hospitable than others.

28.

It can be inferred that the phrase “Sahara Anglais” is used to highlight (1) the theme of the cocktail party (2) the location where the cocktail party was hosted (3) the amusing nature of the situation (4) the name of the hosts (5) the desert-like lack of food

29.

How does the author credit public schools in creating skinflint Brits? (1) They ingrain condescension towards showing off (2) They are so expensive that parents have to be frugal in order to afford a good education for their children (3) They create children who are told to be economical in order to make the best of their fortunes (4) Both (1) and (2) (5) Both (2) and (3)

PRE MOCK CAT - 3

9

DIRECTIONS for Questions 30 to 34: There is one blank in each of the following sentences. From the words given, choose the one that fills the blank most appropriately. 30.

___ is the branch in philosopy that studies the origin of knowledge. (1) Axiology (2) Cosmology (3) Ontology (4) Epistemology (5) Metaphysics

31.

___ is a collection of selected passages or excerpts from one or more authors. (1) Eulogy (2) Anthology (3) Edition (4) Panegyric (5) Analects

32.

Non-poetic compositions are said to be written in ___. (1) verse (2) prose (3) script (4) meter

(5) cadence

33.

___ learners learn best in hands-on learning settings in which they can physically manipulate something to learn. (1) Parse (2) Tactile (3) Feeble (4) Quick (5) Active

34.

Adhering strictly to scholarly methods is termed _____. (1) pedantic (2) laconic (3) bucolic (4) philosophy

(5) semantics

DIRECTIONS for Questions 35 to 37: The sentences given in each question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph. 35.

A. It tells the story of the campaign to repeal the estate tax (what we would call inheritance tax) in the United States, which culminated in the inclusion of the measure in George Bush’s massive taxcutting legislation of 2001. B. Politics of another country’s tax system is unlikely to be of much interest to anyone with any sort of normal life. C. Listening to the ins and outs of other people’s fiscal battles can be like listening to other people’s dreams: interminable and almost completely unreal. D. Death by a Thousand Cuts is something different. (1) BADC

36.

(3) CBAD

(4) CABD

(5) BACD

A. Lottery officials suspected a scam until they traced the sequence to a fortune printed with the digits “22-28-32-33-39-40” and Donald Lau’s prediction: “All the preparation you’ve done will finally be paying off.” B. As a vice-president at Wonton Food, Inc., in Long Island City, Donald Lau manages the company’s accounts payable and receivable, negotiates with insurers, and, somewhat incidentally, composes the fortunes that go inside the fortune cookies, of which Wonton is the world’s largest manufacturer. C. Each day, Wonton’s factory churns out four million Golden Bowl-brand cookies, which are sold to several hundred vendors, who, in turn, sell them to most of the forty thousand Chinese restaurants across the country. D. Wonton’s primacy in the industry and, for that matter, in the gambler’s imagination is such that when, in March, five of six lucky numbers printed on a fortune happened to coincide with the winning picks for the Power ball lottery, a hundred and ten people, instead of the usual handful, came forward to claim prizes of around a hundred thousand dollars. (1) CBAD

10

(2) BCDA

(2) CBDA

(3) ADCB

(4) DCAB

(5) DBAC

PRE MOCK CAT - 3

37.

A. The service of the Church accordingly, and the translation of the Bible which was read in churches, were both in that corrupted Latin which was the common language of the country. B. When Christianity was first established by law, a corrupt form of Latin had become the common language of all the western parts of Europe. C. Two different languages were thus established in Europe: a language of the priests and a language of the people. D. However, although Latin was no longer understood anywhere by the great body of the people, Church services still continued to be performed in that language. (1) BACD

(2) BADC

(3) ABCD

(4) ABDC

(5) BCDA

DIRECTIONS for Questions 38 and 39: In each question, the word at the top of the table is used in five different ways, numbered 1 to 5. Choose the option in which the usage of the word is INCORRECT or INAPPROPRIATE. 38.

39.

ENSHRINED

1.

The right to vote is enshrined in our constitution.

2.

The priests enshrined the holy pendant inside the sacred vault.

3.

The diamond was enshrined in the bank vault.

4.

Respect for elders is enshrined in our religious books since time immemorial.

5.

'Service to all' is deeply enshrined in the policy of the mission.

FURTHER

1. Further to the letter sent by you, we would like to meet you on Wednesday morning. 2.

Rishi was alarmed when he realized he had climbed further up the mountain than anyone else.

3. I plan to study abroad in order to further my future. 4.

The family was grief stricken when they realized that the disease had progressed further than what was diagnosed.

5. Understanding the implications of this argument requires further investigation.

PRE MOCK CAT - 3

11

DIRECTIONS for Questions 40 and 41: Each of the following questions has a paragraph from which the last sentence has been deleted. From the given options, choose the one that completes the paragraph in the most appropriate way. 40.

Teaching creationism in American public schools has been outlawed since 1987 when the Supreme Court ruled that the inclusion of religious material in science classes was unconstitutional. In recent years, however, opponents of the theory of evolution - first developed by Charles Darwin, have regrouped, challenging science education with the doctrine of “intelligent design”, which has been carefully stripped of all references to God and religion. Unlike traditional creationism, which claims that God created the earth in six days, proponents of intelligent design say the workings of this planet are too complex to be ascribed to evolution. There must have been a designer working to a plan - that is, a creator. _____________________ (1) However, these kinds of teachings are unacceptable to the American public. (2) However, there are many schools that are in favour of teaching traditional creationism to the students. (3) However, such beliefs are not substantial enough to convince the American courts to allow teaching the subject in its schools. (4) However, the American government believes that the students must have the knowledge of traditional creationism, as well as, intelligent design. (5) However, some believe that parents should decide what subjects should be taught to their children.

41.

Linguistics is the scientific study of language. It endeavours to answer the question—what is language and how it is represented in the mind? Linguists focus on describing and explaining language and are not concerned with the prescriptive rules of the language (i.e. do not split infinitives). Linguists are not required to know many languages and linguists are not interpreters. The underlying goal of the linguist is to try to discover the universals concerning language. That is, what are the common elements of all languages. _____________________ (1) The linguist then tries to place these elements in a theoretical framework that will describe all languages and also predict what specific rules can occur in a language. (2) The linguist then tries to place these elements in a theoretical framework that will describe all languages and also predict what specific rules cannot occur in a language. (3) The linguist then tries to place these elements in a theoretical framework. (4) The linguist then tries to place these elements in a theoretical framework that will describe particular languages and track changes from time to time. (5) Knowing the common elements in these languages makes interpreting a particular language relatively easy.

DIRECTIONS for Questions 42 to 50: The two passages given below are followed by a set of questions. Choose the best answer to each question.

Passage - I Eight-million Iraqi voters have finished risking their lives to endorse freedom and defy fascism. Three things happen in rapid succession. The right cheers. The left demurs. I walk away from a long-term intimate relationship. I’m separating not from a person but a cause: the political philosophy that for more than three decades has shaped my character and consciousness, my sense of self and community, even my sense of cosmos. I choose this day for my departure because I can no longer abide the simpering voices of self-styled progressives — people who once championed solidarity with oppressed populations everywhere — reciting all the ways Iraq’s democratic experiment might yet implode.

12

PRE MOCK CAT - 3

My estrangement hasn’t happened overnight. Out of the corner of my eye I watched what was coming for more than three decades, yet refused to truly see. Now it’s all too obvious. Leading voices in America’s “peace” movement are actually cheering against self-determination for a long-suffering Third World country because they hate George W. Bush more than they love freedom. Like many others who came of age politically in the 1960s, I became adept at not taking the measure of the left’s mounting incoherence. To face it directly posed the danger that I would have to describe it accurately, first to myself and then to others. That could only give aid and comfort to Jerry Falwell, Pat Robertson, Rush Limbaugh, Ann Coulter and all the other Usual Suspects the left so regularly employs to keep from seeing its own reflection in the mirror. Now, I find myself in a swirling metamorphosis. Think Kafka, without the bug. Think Kuhnian paradigm shift, without the buzz. Every anomaly that didn’t fit my perceptual set is suddenly back, all the more glaring for so long ignored. The insistent inner voice I learned to suppress now has my rapt attention. “Something strange — something approaching pathological — something entirely of its own making — has the left in its grip,” the voice whispers. “How did this happen?” The Iraqi election is my tipping point. The time has come to walk in a different direction — just as I did many years before. I grew up in a northwest Ohio town where conservative was a polite term for reactionary. When Martin Luther King Jr. spoke of Mississippi “sweltering in the heat of oppression,” he could have been describing my community, where blacks knew to keep their heads down, and animosity toward Catholics and Jews was unapologetic. Liberal and conservative, like left and right, wouldn’t be part of my lexicon for a while, but when King proclaimed, “I have a dream,” I instinctively cast my lot with those I later found out were liberals (then synonymous with “the left” and “progressive thought”). The people on the other side were dedicated to preserving my hometown’s backward-looking status quo. This was all that my 10-year-old psyche needed to know. The knowledge carried me for a long time. Mythologies are helpful that way. 42.

The ‘long term intimate relationship’ mentioned by the author in the first paragraph means (1) separation from politics (2) breaking away from his left beliefs (3) political philosophy (4) the long-held belief in democracy (5) separating from his progressive counterparts

43.

It can be inferred that the author feels that the ‘self styled progressives’ have (1) been selfish and shallow in opposing Iraq’s democratization (2) been wrong about furiously opposing George Bush (3) opposed Iraq’s democratization because they like George Bush (4) shortchanged their ideals for money (5) rebelled against Iraq’s democratization because they do not want a puppet government.

44.

Which of these best describes the author’s tone in the passage? (1) Critical (2) Argumentative (3) Pessimistic (4) Truculent (5) Introspective

PRE MOCK CAT - 3

13

45.

It can be inferred that the mythologies the author is talking about mean (1) the stories of black superiority (2) Martin Luther King’s lecture (3) generalised idea about political positions (4) white supremacists (5) the stories of black minority

Passage - II In a few days, the United Kingdom hosts the heads of the world’s wealthiest eight nations in Gleneagles, Scotland for a summit that has tackling poverty, especially in Africa, at the top of its agenda. In September, G8 leaders join others in New York for a United Nations General Assembly Summit on the Millennium Development Goals, which include a commitment to halve the proportion of the world’s population living in poverty by 2015. In December, the top most decision-making council of the World Trade Organisation will meet in Hong Kong to discuss a “development agenda” for world trade. As Asian governments, development agencies, and citizen sector organisations grapple with the realities of poverty at the heart of tsunami relief and recovery, in Africa disease, starvation, and a lack of clean water have ensured that life expectancy in some countries has shrunk to a level last seen in AD 500. Just five years after the promise was made to halve poverty by 2015, the world is running 135 years behind schedule. The year 2005 has seen the launch of a campaign aiming to consign poverty to the past. Building on the strengths of civil society movements, it aims to make the most of the political opportunities for change this year. Unlike Live Aid or tsunami relief, this is not a campaign to raise funds for food crops. The ‘Make Poverty History’ campaign is about mobilising people to create the political will to drive lasting policy change. It is engaging a new generation in holding their governments accountable for their actions on the world stage. Comprising more than 450 development agencies, campaigns, faith groups, trade unions, and other organisations, ‘Make Poverty History’ is the largest campaign coalition ever assembled in the U.K. Taking a white band as their symbol of commitment, the campaigners have sent tens of thousands of emails to Prime Minister Tony Blair and Chancellor of the Exchequer Gordon Brown. In the run-up to Gleneagles, at least 200,000, dressed in white, will have converged on Edinburgh for a show of solidarity with the victims of poverty. They will be joined by two million people campaigning locally across the U.K. The campaign has brought in an impressive range of public figures and celebrities, among them actors Brad Pitt, Hugh Grant, and Colin Firth, screenwriter Richard Curtis, models Kate Moss and Claudia Schiffer, and musicians Bono, Lemar, Cold Play, Kylie Minogue, and Paul McCartney. Bob Geldof’s Live 8 concerts, being staged in five continents, are a huge global boost to the campaign. In the U.K., a movement of this kind is particularly significant. The country holds the presidency not only of the G-8 group, but from July also of the European Union. Moreover, both Mr. Blair and Mr. Brown have an expressed interest in global poverty, and in particular, African development. The British Prime Minister chaired a 17-member international “Commission for Africa,” which came out with a visionary set of recommendations in March 2005. Over the past eight years, Mr. Brown has been working to persuade the world’s wealthiest nations to write off £140 billion debt owed by the African continent. Unveiling his “modern Marshall Plan,” he called for global action to “reverse the fortunes” of Africa and change the lives of millions in the developing world. There are those who fear that the “positive outcomes” contained in a communiqué will amount to nothing more than hot air. Corruption, political weaknesses, rampant HIV infection, and civil war present major challenges. However, humankind has never been richer, or better armed with the medical knowledge, technological prowess, and intellectual firepower needed to beat poverty. While finding ways to get badly

14

PRE MOCK CAT - 3

governed countries to raise their game is hard and hugely controversial for outsiders to do, this should not be a barrier to action on the critical issues. The ‘Make Poverty History’ campaign addresses three key policy areas — more and better aid for the world’s poorest countries; debt cancellation; and trade justice. Back in 1970 donor countries promised to give 0.7 per cent of their national income in aid to the developing world. While personal incomes in rich countries have increased by 200 per cent since 1960, wealthy nations spend collectively half the amount on aid they did in the early 1960s as a proportion of national income. Of the 22 major bilateral donors, only five have met the 0.7 per cent target. Significantly, not one of them is a G8 member. The ‘Make Poverty History’ movement is campaigning not just for more aid but also for better aid. International aid tends to be volatile. More than a quarter of it arrives more than six months late. About 70 per cent is committed for three years or less — to guarantee primary education for a whole generation, a commitment of six years is necessary. Even in circumstances where aid has been shown to work, sudden policy changes in donor countries tend to undermine worthy efforts. Furthermore, there are many examples of aid with strings attached. These ensure that most of the benefits go to firms in the donor country in the form of goods and services; or that the assistance is tied to specific policies that have a counter-productive effect because they are not a part of national government or civil society consultation. The Brown-Blair response to this situation has given campaigners cause for some hope. The Africa Commission called for international aid to be increased by $25 billion by 2010, and then by a further $25 billion by 2015. Mr. Brown’s International Finance Facility (IFF) is a means through which this aid can be doubled. This scheme will let donors increase their total aid by borrowing against future aid budgets, and allow it to be spent in a more predictable way. Part of the argument is that if the right investment in heath and education is made now, the developed world will not need to spend so much in poverty alleviation in the future. The hope is that G-8 leaders will make some significant announcements on aid. Nearly 90 per cent of the debt of 52 of the poorest and most indebted countries has yet to be cancelled. In the post-colonial era, many countries were lent money that was squandered on arms used for the benefit of a tiny minority in power. As interest rates have risen, many countries still owe more than the original loan after years of repayment. This prevents critical investment in health and education infrastructure. For example, Malawi spends more on servicing its debt than on health although nearly one in five Malawians is HIV positive. 46.

The author means by the comment “Just five years after the promise was made to halve poverty by 2015, the world is running 135 years behind schedule”, that (1) The present level of poverty remains at the same level as 135 years ago (2) The present level of poverty is lower than what it was 135 years ago (3) The current level of poverty is at the same level as it was in 1970 (4) Poverty levels are gradually getting worse instead of getting better (5) It has become difficult to estimate the present poverty levels.

47.

Which one of these have not been mentioned as a reason making UK’s involvement in the ‘Make poverty history’ campaign important? (1) Tony Blair and Gordon Brown have expressed interest in the subject (2) Gordon Brown has been lobbying for debt sign-offs to loans given to Africa (3) Tony Blair chairs the “Commission for Asia” (4) UK is the president of the G-8 (5) The U.K. holds the presidency of the European Union.

PRE MOCK CAT - 3

15

48.

Which one of these correctly states the author’s position with reference to the “positive outcomes” of the campaigns mentioned? (1) They will not work since there are other pressing problems such as corruption, HIV infection etc. (2) They will fail because the countries’ they are trying to change are international outcasts (3) They cannot overhaul governmental policies of states but can selectively work on important issues (4) They can put political pressure and wield it to implement the changes (5) None of the above.

49.

What is the author trying to say by phrasing “Make Poverty History’s” agenda as being “better aid not more aid”? (1) Too much aid has been seen to have a detrimental effect on the recipient countries (2) The eventual impact of the aid on the recipient country is what has to be focused at (3) Involving donors who are more committed to the cause will eradicate history (4) More aid has led to corruption in recipient countries. (5) Countries cannot manage the flow of aid if the quantum is high.

50.

What is the essential rationale behind the issue of debt cancellation? (1) Countries’ past rulers made erroneous use of the money and this has deleterious effects in the present (2) Countries’ which provided this aid now want it back since their economy is not in a healthy state (3) The interest rates on the debts are so high that countries’ have to borrow more (4) The international organizations do not want to be involved with the situation since the chief donors also provide them with financial help (5) The countries which have provided aid do not want to reduce the interest rates.

16

PRE MOCK CAT - 3

SECTION – III Number of questions = 25 51.

Find the number of positive integral solutions of the equation (xy)z = 64. (1) 14 (2) 15 (3) 16 (4) 17 (5) 18

52.

5 concentric squares each having different area are drawn on a sheet of paper. If the area of the circle inscribed in the smallest square is 77 square units and the distance between the corresponding vertices of consecutive squares is 1.5 units, then find the difference between the areas of the largest and the

22   smallest square in square units.  Take π =  7   (1) 240 (2) 264 (3) 224 53.

(5) 256

The list price of an article was increased by 10%. It was then decreased by 10%. If the final price became Rs. 20, then find the initial list price (in Rs.) (1)

54.

(4) 216

10 × 100 2 100 2 – 20 2

(2)

20 2 × 10 2 100 2 – 10 2

(3)

20 × 100 2 100 2 – 10 2

(4)

10 × 20 2 100 2 – 20 2

 100 2 − 10 2   (5) 20 ×   100 2   

A class of 24 boys was divided into two sub-sections containing 12 boys each. What is the probability that the two shortest boys of the class are in different sub-sections, if all boys have different heights? (1)

7 24

(2)

6 23

(3)

12 23

(4)

14 23

(5) None of these

55.

Two wheels of diameters 7 cm and 14 cm start rolling simultaneously towards each other from two points which are 1990.5 cm apart. Both wheels make the same number of revolutions per second. If both the wheels meet (touch externally) after 10 seconds, then what is the speed of the smaller wheel? (1) 132 cm / sec (2) 66 cm / sec (3) 44 cm / sec (4) 22 cm / sec (5) 67 cm / sec

56.

‘S’ denotes the sum to infinity and ‘Sn’ denotes the sum to ‘n’ terms of the series 1 +

5 If S − Sn < , then the least value of ‘n’ is 2 (1) 2 (2) 3 (3) 4 57.

(4) 5

4 16 + + …. 5 25

(5) 6

Three positive real numbers ‘x’, ‘y’ and ‘z’ exist such that they are in an arithmetic progression and the product of x, y and z is 25. If the common difference of the arithmetic progression is 2 5, then find the value of (x + y + z). (1) 10 + 2 5

(2) 15

PRE MOCK CAT - 3

(3) 8 + 4 5

(4) 20

(5) 10

17

58.

Mr. X bought 10 identical chocolates. He ate 2 chocolates and sold the remaining 8 chocolates for Rs.60 making a net profit of 32%. Find the profit percent had he eaten 6 chocolates and sold the remaining 4 chocolates for Rs.48. (1) 4.8% (2) 5.6% (3) 6.4% (4) 7.2% (5) 6.8%

59.

From a point P, the tangents PQ and PT are drawn to a circle with centre O and radius 2 units. From the centre O, OA and OB are drawn parallel to PQ and PT respectively. The length of the chord TQ is 2 units. Find the measure of the ∠AOB.

A

B

O Q

T

P (1) 30° 60.

(2) 90°

(3) 60°

(4) 120°

(5) 45°

Let a, b, c and d be four distinct positive integers such that a2 + b2 = c2 + d2 = x and a2 – c2 = mn, where ‘m’, ‘n’ are prime numbers greater than 2. What is the value of ‘x’? (1)

m 2 + n2 4

(2)

m 2 + n2 2

(4)

1 (1 + m 2 ) (1 + n 2 ) 2

(5)

3 2 m + n2 4

(

(3)

1 (1 + m 2 ) (1 + n 2 ) 4

)

DIRECTIONS for Questions 61 and 62: Answer the questions on the basis of the information given below. In an exam there are 30 questions. If a person solves a question correctly, he is awarded 5 marks and if he solves it incorrectly 2 marks are deducted from his score. There are no marks awarded or deducted for not attempting any question. 61.

Arjun got 60% of the maximum possible marks he can get in the exam. Let ‘a’ denote the number of questions attempted correctly and ‘b’ denote the number of questions attempted wrongly. The total number of possible pairs (a, b) can be at most (1) 2 (2) 4 (3) 6 (4) 7 (5) 8

62.

How many natural numbers less than 150 can never be the total number of marks got by any student writing this test? (1) 0 (2) 6 (3) 10 (4) 11 (5) 12

63.

Given that f(0) = 0, f(1) = 1 and f(2) = 1. If f(n) = f(n+1) – f(n–1), then find the value of

(1)

18

13 5

(2)

9 2

(3)

16 5

(4)

16 7

(5)

f(8) − f(7) + f(5) . f(7) − f(6) − f(4)

13 2

PRE MOCK CAT - 3

64.

Anup purchased a few chocolates for his three grandsons such that the number of chocolates got by each grandson is atleast 2 and is not a prime number. Which of the following cannot be the number of chocolates purchased by Anup. (All the three grandsons got a distinct number of chocolates by Anup.) (1) 21 (2) 23 (3) 16 (4) 18 (5) None of these

65.

There is a two-digit number, which is equal to the sum of the squares of its digits. What is the sum of the digits of that number? (1) 7 (2) 5 (3) 6 (4) 8 (5) Such a number is not possible

66.

There is a trapezium ABCD such that the sides AB and CD are parallel to each other. The diagonals AC and BD intersect at O. The area of the triangle COD is 10 square cm and the area of the triangle AOB is 40 square cm. Find the area of the trapezium.

D

C O B

A (1) 90 square cm (4) 45 square cm

(2) 100 square cm (5) 120 square cm

(3) 250 square cm

67.

What is the product of all factors of the number N = 64 x 102 which are divisible by 5? (2) 2210 × 3140 × 5105 (3) 2140 × 3210 × 5102 (1) 2210 × 3102 × 5140 140 102 210 102 210 140 (4) 2 × 3 × 5 (5) 2 × 3 × 5

68.

Nitin has exactly 50 mangoes and lots of empty boxes with him. He puts ‘x’ mangoes in the first box, (x + 1) mangoes in the 2nd box, (x + 2) mangoes in the 3rd box and so on till he has put (x + k) mangoes in the (k + 1)th box till there are no more mangoes to be put in a box. In how many ways he can put the mangoes in the boxes? (‘x’ and ‘k’ are positive integers) (1) 2 (2) 3 (3) 4 (4) 5 (5) 6

69.

In the figure given below O, Q, P and R are respective centres of circles of different radii. It is further given that the length of the line segements OP, PQ, OR, PR are 98, 157, 92 and 170 units respectively. Find the radii of the circles with centres O, Q, P and R respectively.

Q P O R

(1) 190, 92, 43, 66 (4) 180, 75, 82, 88

PRE MOCK CAT - 3

(2) 180, 75, 64, 88 (5) 180, 75, 80, 88

(3) 190, 92, 64, 66

19

70.

Out of 4 different roses and 9 different sunflowers, a bouquet of flowers is to be prepared. Find the number of ways of preparing a bouquet consisting of eight flowers containing at least one rose. (1) 1384 (4) 1360

(2) 12C7 (5) 1278

(3) 1244

71.

The content development team was working at a uniform rate to develop 2500 questions in ten weeks. But after working for six weeks, the content team was informed by the management that the remaining questions had to be developed in one week. By what percentage does the team need to increase its rate of development of questions so that it can complete developing the remaining questions in one week? (1) 100% (2) 250% (3) 300% (4) 400% (5) 500%

72.

If a + b = 9, where ‘a’ and ‘b’ are positive integers, then which of the following cannot be the unit’s digit of a 243 + b243 − (ab)243 ? (1) 1 (4) 3

73.

(3) 7

If the equation x3 + ax2 + bx = c does not have all real roots, then which of the following is the sufficient condition to make it true? (1) (4)

74.

(2) 9 (5) Both (3) and (4)

a2 < 4b a2 > 4b

(2) a2 < 2b (5) a = 3c

(3) a2 > 2b

Two sprinters are running in clockwise direction on a circular track ‘x’ km long (x > 1). Their second meeting takes place at a point C which is 200 m from their starting point in the anticlockwise direction on the circular track. If both of them started at the same time, then the location of their first meeting point is: I. 100 m from the starting point in the anticlockwise direction. II. 100 m, in the anticlockwise direction, from the point diametrically opposite to the starting point. III. 200 m from the starting point in the anticlockwise direction. (1) Definitely I (4) Either I or II

(2) Definitely II (5) Either II or III

(3) Definitely III

75.

Find the smallest natural number which when divided by 7, 8 and 9 leaves the remainder 2, 4 and 6 respectively. (1) 492 (2) 436 (3) 212 (4) 380 (5) None of these

20

PRE MOCK CAT - 3

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PRE MOCK CAT – 3

Answers and Explanations

1

3

2

2

3

3

4

1

5

5

6

1

7

5

8

2

9

4

10

1

11

5

12

3

13

4

14

3

15

4

16

1

17

3

18

4

19

5

20

5

21

2

22

5

23

5

24

2

25

1

26

2

27

3

28

5

29

1

30

4

31

5

32

2

33

2

34

1

35

2

36

2

37

2

38

3

39

3

40

3

41

3

42

2

43

1

44

5

45

3

46

1

47

3

48

3

49

2

50

1

51

3

52

1

53

3

54

3

55

2

56

3

57

2

58

2

59

4

60

3

61

1

62

5

63

5

64

3

65

5

66

1

67

2

68

1

69

4

70

5

71

3

72

3

73

2

74

4

75

1

MY PERFORMANCE Total Time Taken Total Correct Incorrect Net Questions (Min) Attempts Attempts Attempts Score Logical Reasoning based Section I Data Interpretation Language Comprehension Section II and English Usage Quantitative Ability TOTAL

Section III

25 25 25 75

150

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MCT-0003/08 PRE MOCK CAT - 3

1

Washington → population density = 34.20 So for integral number of people at least 5 km2 area should be there.

For questions 1 to 4: The number of people cannot be in decimals, so they should be in integers only. Now consider the two digits after the decimal point in every figure of population density column.

Massachusetts → population density = 312.68 So for integral number of people at least 25 km2 area should be there.

Out of the given states for all those states which have an odd number (except multiple of 5) after the decimal, the population density must be multiplied by 100 to get minimum possible number of people living in that state. e.g. Maryland.

Connecticut → population density = 271.40 So for integral number of people at least 5 km2 area should be there.

For all those states which have an even number (except multiple of 10 and multiple of 4) after the decimal, the population density must be multiplied by 50, if the even number after the decimal is a multiple of 4 the population density must be multipled by 25 to get minimum possible number of people living in that state. e.g. New York.

So out of the given states in terms of area Massachusetts will definitely have a numberically higher rank than the other states. 3. 3

All those states which have an odd number (except multiple of 5) after the decimal will have an area of at least 100 km2 Among the given states 10 states will definitely have area of 100 km2, i.e. Maryland, Delaware, Florida, Illinois, Hawaii, Virginia, Georgia, Tennessee, Louisiana and Wisconsin.

4. 1

Total population of New York = 195.18 × 150 = 29277

If the even number after the decimals is a multiple of 4 as well as 10, the population density must be multipled by 5, to get minimum possible number of people living in the state. For all those states which have odd multiples of 5 after the decimal, the population density must be multiplied by 20 to get minimum possible number of people living in that state. e.g. Rhode Island.

Total number of families in New York = For all those states which have multiples of 20 after the decimal, the population density must be multiplied by 5 to get the minimum possible number of people living in that state. e.g. Pennsylvania. 1. 3

5. 5

Rhode Island → population density = 387.35 For integral number of people in Rhode Island it must have atleast an area of 20 km2. In this case population of Rhode Island will be 387.35 × 20 = 7747

Pennsylvania → population density = 105.80 For integral number of people in Pennsylvania must have atleast an area of 5 km2. In this case population of Pennsylvania will be 105.80 × 5 = 529 New Hampshire → population density = 53.20 For integral number of people New Hampshire must have atleast an area of 5 km2. In this case population of New Hampshire will be 53.20 × 5 = 266 Louisiana → population density = 39.61 For integral number of people Louisiana must have atleast an area of 100 km2. In this case population of Louisiana will be 39.61 × 100 = 3961 Minimum possible aggregate of these four states population = 7747 + 9759 + 529 + 266 + 3961 = 22262 2. 2

State that will be definitely ranked higher in terms of area will be the one whose minimum possible area is more than the minimum possible area of other states. Michigan → population density = 67.55 So for integral number of people at least 20 km2 area should be there. North Carolina → population density = 63.80 So for integral number of people at least 5 km2 area should be there.

2

3

= 9759

Minimum possible area of Kentucky = 25 km2 Minimum possible area of Washington = 5 km2 Now areas of both Kentucky and Wisconsin are interchanged So new area of Kentucky = 5 km2 Population of Kentucky = 39.28 × 25 New Population density of Kentucky =

New York → population density = 195.18 For integral number of people in New York must have at least an area of 50 km2. In this case population of New York will be 195.18 × 50 = 9759

29277

39.28×25 5

= 39.28 × 5 Population density of Kentucky changes by

=

39.28 × 5 – 39.28 × 100 = 400% 39.28

For questions 6 to 9:

Basic

DA

Bonus HRA

Total

Tax

Swapi

10000 4000

Yeshu

12000 4200 10000 4000 30200 5400

5000 7000 26000 4900

Manik

8000 2400

6000 5000 21400 4000

Vinita

12000 3000

8000 2000 25000 4800

All answers are evident from the table above. 6. 1

7. 5

8. 2

9. 4

For questions 10 to 14: From statement 1 Shane received 0 cookies. From statement 3, [Shane and Chris], and [Matthew and Graham] can have [(0,1)(2,3)] or [(0,2)(1,3)] or [(0,3)(1,4)] cookies respectively. Using statements 2 and 4 we can conclude that only possible case is [(0,3)(1,4)]. So Greame must have got 2 cookies. Using statement 1 and statement 7 we can say that Graham and Greame like wrestling shows, as Shane likes a sports show and there are only two sports shows. From statement 5, Matthew likes Smackdown and Shane likes Sports Center. So Chris likes Hitz. From statement 6 Graham likes Krackjack. From statement 8 Greame likes Hide n Seek or Good Day. Shane likes Good Day or Bon-Bon. Matthew likes Hide n Seek or Bon-Bon or Good Day.

PRE MOCK CAT - 3

21. 2

TV show

Type of Biscuit

Shane

No. of cookies 0

Sports Center

Matthew

1

Smackdown

Greame

2

Raw/Wrestlemania

Chris

3

Hitz

Good Day/Bon-Bon Hide n Seek/BonBon/Good Day Hide n Seek/Good Day Maska Chaska

Graham

4

Wrestlemania/Raw

Krackjack

Name

Statement (A) : (x – y)2 > 0. It cannot be inferred that (x – y) > 0. It can even be (y – x) > 0 So, statement (A) itself is not sufficient. Statement (B) : (x + y) (x + y) = 4xy (x + y)2 – 4xy = 0⇒x – y)2 = 0⇒x = y. So, x >/  y. So, statement (B) in itself is sufficient. Hence, option (2) is the correct choice.

For questions 22 to 25: From the given information, we can calculate the aggregate number of lines typed by the typists in a day. Day 1 (Nu m b er of lines 400)

10. 1

Graham likes Krackjack.

11. 5

Greame likes either Hide n Seek or Good Day. Hence cannot be determined. G au ra v

12. 3

If Shane likes Good Day then Greame likes Hide n Seek and then Matthew likes Bon-Bon.

13. 4

Chris likes Hitz.

14. 3

Raw – Bon Bon cannot be a matching pair, which is liked by the same person.

96

92

S a njay

76

S a lim

56

80

A m m ar

For questions 15 to 19: The following table can be drawn.

Number Number Of f ers Of f ers of of per per students of f ers company student

B-school

Number of companies

FMS

60

100

125

2.08

IMT

90

150

225

2.5

1.5

IMI

50

120

150

3

1.25

K.J.Somaiya

70

150

150

2.14

1

Narsee Monjee

80

150

200

2.5

1.33

Day 2 (Nu m b er of lines 350)

1.25 K a nd arp

The ratio of number of students to the number of companies visiting the campus is lowest for both FMS and IMT, i.e. 1.67.

16. 1

IMT has the highest number of offers per student.

17. 3

IMI has the highest ratio.

18. 4

Total salary of the students of FMS = 100 × 7 = Rs. 700 lakh PPO salary = 25% of 100 × 10 = Rs. 250 lakh Average annual salary of students not getting the PPO’s

56

20. 5

Though FMS had the best average salary, what constitutes best placements has not been defined. So, option (5) is the correct choice, i.e. cannot be determined.

S a lim

91

D ip a k

Day 3 (N u m b er o f lines 300)

K a pil

54

51

700 − 250 450 = = = Rs. 6 lakh 100 − 25 75 Hence option (4) is the correct choice. 19. 5

70

70

K a pil

15. 4

63

S a njay

1 05

G au ra v

48

42

S a lim

No information is provided about the year ‘X’, if it is a leap year or not. Hence option (5) is the correct choice.

PRE MOCK CAT - 3

3

22. 5

For only Sanjay, the minimum possible sigma and the maximum possible sigma lie within an integer. Hence, for remaining six typists, exact sigma cannot be calculated.

23. 5

For Sanjay, Salim and Ammar, the value of PV can be zero as per the following conditions.

Day 4 Num ( ber of lines 450)

99

16 2

S an jay

45

81

A m m ar

63

Day 1 (Total Day 2 (Total Day 3 (Total Day 4 (Total = 400) = 350) = 300) = 450)

Gaurav

92

Salim

56

Sanjay

96

Ammar

80

48 70

Dipak

91

162

Kandarp

63

63

Gaurav Salim Sanjay

Minimum possible sigma 0 + 48 = 24 2 56 + 42 =49 2

96 + 54

= 75

2 Ammar

=52

2 Kapil

41/24

=25.5

63 + 24 91 + 24 2

4

Maximum possible sigma 55 + 48 =51.5 2

56 + 44

=50

2 96 + 55

= 75.5

80 + 55

96

51

54

99

0

Ammar

80

26

25

81

0

The author starts off the passage by talking about the Brits being skinflint hosts. The second paragraph talks about a cocktail party he attended with his wife and using the word ‘mirage’ – an illusion, means that she has had the same experience as the author and shares in his opinion. He is trying to substantiate his opinion and using an experience where his wife comments on something makes it look realistic. This makes option (2) correct.

27. 3

The author makes this point in the fourth paragraph. He has introduced his reasoning in the third paragraph regarding the explanation for the skinflint nature of the Brits being the wartime austerity, which became an ingrained habit. This is refuted if one looks at some countries where the same wartime situations prevailed with no impact on the hospitality of the people. This makes option (3) correct.

28. 5

The author uses this phrase in the second paragraph which uses the name of a famous desert to indicate his main point – the skinflintness of the Brits so that their cocktail parties seem like being in a desert. This makes option (5) correct.

29. 1

The author mentions in the last paragraph one of the aspects of the Brit nature to look down upon ostentation, which might serve to explain the skinflint nature. The public schools are guilty in that they teach students not to show off. This makes option (1) correct.

30. 4

epistemology is correct.

31. 5

analects is correct.

32. 2

prose is correct.

33. 2

tactile is correct.

34. 1

pedantic is correct.

35. 2

The best option for the first sentence is sentence B. It introduces the topic by talking about the disinterest regarding the politics of taxation of another country. Sentence C takes that further by elaborating upon why it is a cause of such disinterest and Sentence D introduces a book that is “different”. Sentence A is next with information about what lies inside the book. DA is a mandatory pair in this case. This makes option (2) correct.

=67.5

51 + 55

=53

2 =43.5

2 Dipak

0

Sanjay

26. 2

44/0

2

2 Kandarp

PV

2

80 + 24 51 + 0

28

The difference between the maximum and the minimum possible Sigma is least i.e. 0 for Sanjay.

51

6able shows the minimum and maximum possible sigma’s. Name

Day 4

42

25. 1

99

56

55/0

Day 3

70

Maximum lines that Kapil can type is 55 + 56 + 51 + 44 = 206. Now Sanjay and Dipak have already crossed that mark. Hence, both of them have definitely typed more number of lines than Kapil.

81

55/0

Day 2

56

24. 2

42 54

Kapil

Maximum / Minimum number of lines typed by those who are not in the top four

Day 1

Salim

K an darp

Table shows the number of lines typed by a typist.

Name

Name

63 + 55

=59

2 =57.5

91 + 55 2

=73

PRE MOCK CAT - 3

36. 2

The author introduces the Wonton factory in sentence C and sentence B mentions its Vice President and his role. Sentence D talks about an interesting incident related to the company and sentence A provides the rationale behind it. DA is a mandatory pair and this makes option (2) correct.

48. 3

The author mentions this in the fifth paragraph “While finding ways to get badly governed countries to raise their game is hard and hugely controversial for outsiders to do, this should not be a barrier to action on the critical issues.” This makes option (3) correct.

37. 2

BA is a mandatory pair. The link word is ‘corrupted latin’. Conclusion C arises from D. Hence DC is also a mandatory pair. Hence best choice is option (2).

49. 2

The author makes this comment in the seventh paragraph while talking about the problems that plague aid coming into country. The issue is not so much the amount as much as the use it is put to. This makes option (2) correct.

38. 3

‘enshrined’ means to cherish as sacred & has the association of respect, ruling out option (3).

50. 1

The author looks at this issue in the ninth paragraph and the basic logic for the demand is that the money was wasted by earlier governments and now countries’ need to pay more interest than the principal amount. This has to be channeled from important causes and has a deleterious effect on the present state. This makes option (1) correct.

51. 3

(xy)z = 26 = 43 = 82 = 641 When z = 1, xy = 64. The total number of factors of 64 is 7. z = 2, xy = 8. The total number of factors of 8 is 4. z = 3, xy = 4. The total number of factors of 4 is 3. z = 6, xy = 2. the total number of factors of 2 is 2 Hence, total number of positive integral solutions is 16.

52. 1

Diameter of the circle is equal to the side of the smallest

39. 3

The correct sentence should be ‘further my education/ career’, ‘… future’ is incorrect.

40. 3

The passage refers to the subject of creationism, teaching evolution and the stance taken by the American courts. The beginning of the passage provides the hint. (1) is vague. (2) restricts the idea to the point of view of the schools. (4) mentions the opinion of the American government whereas the passage refers to the opinion of the American court. (5) refers to another idea and does not provide an appropriate ending.

41. 3

In the para it is stated that one of the linguists’ goals is to discover the universals concerning language. (1) and (2) talk about specific rules which is negated by the paragraph. (4) is incorrect because it talks about particular languages. (5) is incorrect because it talks of interpretation. (3) is best in line with the universal theme of the paragraph.

42. 2

The author mentions in the passage a set of political happenings and then clarifies after he mentions the ‘long term intimate relationship’ – “I’m separating not from a person but a cause…”. This makes option (2) correct.

43. 1

The author mentions in the second and third paragraph the incident of the ‘self styled progressives’ opposing Iraq’s democratization. What he finds objectionable about this is the fact that they have for long supported democratization of oppressed people, but in case of Iraq have changed their stance because they dislike George Bush. This makes option (1) correct.

44. 5

45. 3

46. 1

47. 3

2 square is πr = 77

⇒ r = 3.5 2 ⇒ 2r = 7 2 , side of the smallest square. Diagonal of the innermost square = 14 units. Diagonal of the largest square will be 14+ [(1.5) × 2] × 4 = 14 + 12 = 26 units ⇒ Area of the largest square =

(

square = 7 2

The author makes this point in the second paragraph and it means that the time at which the comment is made, the level of poverty is the same as it was 135 years ago with no reference to the year 2015. This makes option (1) correct.

)

2

= 98 sq. units.

Required difference = 338 – 98 = 240 square units. 53. 3

The author starts off the passage by talking about a decision he has taken regarding his political affiliations. He then proceeds to provide reasons for it and traces various points across his life relevant to this event. He is critical of the left, but the tone is about his decision and the rationale behind it. This makes option (5) correct. The author mentions his beginnings into the political landscape from his childhood. He mentions that he was 10 years old and did not know much about politics, all he knew was that – “The people on the other side were dedicated to preserving my hometown’s backward-looking status quo”. This was the mythology that simplified the decision for him. This makes option (3) correct.

1 × (diagonal)2 = 338 sq units and area of the smallest 2

List price first increases by 10% and then decreases by 10%.

 100 + 10   100 – 10  ⇒ ×  × initial list price = final list price  100   100  ⇒ Initial list price = 54. 3

20 × 1002 1002 – 102

Total number of ways of dividing 24 boys in two distinct

24! 12!12! There can be two ways in which two shortest boys lie in different sub-section and correspondingly the remaining 22 boys can be divided into two distinct sub-sections in 22 C 11 ways.

sub-sections is

∴ Probability =

24

C12 =

2× 24

22

C11

C12

=

12 23

The author lists the reasons in the fourth paragraph and option (3) is incorrect as the Commission chaired was for Africa, not Asia.

PRE MOCK CAT - 3

5

57. 2

55. 2

Let, the values of ‘x’ and ‘z’ be denoted by (y − 2 5) and

(y + 2 5) In th e be ginn in g

25 = (y – 2 5 ) (y) (y + 2 5 ) ⇒ y3 = 25 + 20y ⇒ y=5 Therefore, x + y + z = 3y = 15

1 99 0.5 cm

58. 2 1 0 .5

7

3.5

Selling price of 8 chocolates = Rs. 60. Since Mr. X made a profit of 32%, the cost price of 10

6000   500  chocolates = Rs.   = Rs.    132   11 

W h en in con ta ct

Selling price of 4 chocolates = 48.

9.89

500    48 − 11    × 100 = 5.6% Profit percent = 500 11

Let the number of revolutions per sec = x. Then, the speed of the smaller wheel 7  =  2 π  × ( x ) = 7πx cm / sec 2 

Speed of the larger wheel = 14 π x cm / sec In 10 sec, together they travel a distance

1

59. 4

A

B

= (1990.5 − 9.89) cm = 1980.61 cm ∴

2

O T

1980.61 = 10 14 π x + 7π x

1

M

Q

Or, 21 π x = 198 Or, x =

198 × 7 =3 21 × 22

P

22 ×3 7 = 66 cm/sec

∴ Speed of smaller wheel = 7 ×

Since, OQ = TQ = 2 units, therefore ∆OTQ is an equilateral. ∴ ∠TOQ = 60°

Since, PQ is a tangent to the circle, therefore ∠OQP = 90°. 56. 3

S=

1 4 1− 5

Since, PQ is a parallel to OA therefore ∠AOQ = 90°.

=5

For the same reason ∠BOT = 90°.

  4 n  1×  1 −    n  5    = 5 1 −  4   Also, Sn =   4 5 1−     5 n

4 ⇒ S − Sn = 5 ×   5 3 S − Sn <

5 2

∴ ∠AOB = 360° – (∠TOQ + ∠AOQ + ∠BOT ) = 120°. 60. 3

a2 – c2 = d2 – b2 = mn. Assuming m > n; we can say a + c = m, a – c = n ...(i) OR a – c = 1, a + c = mn ...(ii) Similarly; d – b = 1 and d + b = mn ...(iii) OR d – b = n and d + b = m ...(iv) If (i) & (iv) OR (ii) & (iii) are the cases; we get a = d & c = b; but a, b, c & d are distinct. Hence, only (ii) & (iv) OR (i) & (iii) are correct. cases (i) & (iii) give a =

n

5 4 ⇒ 5×  < 2 5 n

1 4 ⇒   < 2 5 n

5 ⇒   >2 4

⇒ x = a2 + b2 =

m+n mn − 1 &b= 2 2

)(

(

1 1 + m2 1 + n2 4

Cases (ii) & (iv) give a =

(

mn + 1 m−n and b = 2 2

)(

1 1 + m2 1 + n2 4 Hence, (3) is the correct choice. ⇒ x = a2 + b2 =

) )

∴ Minimum possible value of ‘n’ is 4.

6

PRE MOCK CAT - 3

61. 1

5a – 2b = 60% of 150 = 90 or b =

66. 1

5a − 45 2

a

D

Since (a, b) are integers and a + b ≤ 30, the only possible pairs are (18, 0) and (20, 5). 62. 5

h1

A student can leave 0 or 1or 2 or 3 or 4 or 5 or 6 ... or 30 questions unattempted. When a student attempts all the 30 questions and gets 0 or 1 or 2 or 3 or 4 or ... out of them incorrect, then he can have all the scores in the series 150, 143, 136, ... 3. Hence if all the questions are attempted, 22 distinct scores can be achieved. Similarly, we can list all the possible scores when a student leaves 1 or 2 or 3 or 4 or 5 or 6 ... questions, out of the 30. The following table lists the possible scores.

A

Possible Scores (Maximum to Minimum)

0

150, 143, 136, … , 3 7N + 3

1

145, 138, 131, … , 5 7N + 5

21

2

140, 133, 126, … , 0 7N

20

3

135, 128, 121, … , 2 7N + 2

20

4

130, 123, 116, …, 4

7N + 4

19

5

125, 118, 111, … , 6 7N + 6

18

6

120, 113, 106, … , 1 7N + 1

18

Area of the trapezium =

1 (3a) (3h2) 2 = 9 × area of the triangle COD = 90 sq cm.

67. 2

Total product of the factors of N = (26 × 34 × 52)105/2 Total product of the factors of N Which are not multiples of 5 = (26 × 34)35/2= 2105 × 370 So, total product of the factors of N which are multiples of 5.

=

63. 5

1 (a + b) (h1 + h2) 2

=

22

When a student leaves 7 questions, the possible scores will be (115, 108, 101, ... , 3) which are already counted in the case (7N + 3). Similarly, all the possible scores (from 1 to 150) when 8, 9, 10, ... questions are left unattempted are already counted. The total number of possible scores are: 22 + 21 + 20 + 20 + 19 + 18 + 18 = 138. Hence the number of scores which are not possible to achieve are 150 – 138 = 12. Hence (5) is correct.

B

b

Let AB = b; CD = a. Let the perpendiculars from O to AB and CD be h 1 , h 2 respectively. Triangles AOB and COD are similar. Since the ratio of their areas is 1 : 4; the ratio of the proportional sides and the heights h2, h1 must be 1 : 2.

Number General of Possible Form Scores

Number of Questions Unattempted

C

h2 O

= 68. 1

2315 × 3210 × 5105 2105 × 370 × 3140 × 5105

2210

The equation will look like, x + (x + 1).......(x + k) = 50. There are a total of k + 1 terms, average of these k + 1 terms is

(2x + k )

3 f(n) = f(n + 1) − f(n − 1)

. 2 So, (k + 1)(2x + k) = 100 = 22 × 52. Since x, k are positive integers, the only possible values of k + 1 is 4 and 5 for which the value of x is 11 and 8 respectively.

⇒ f(n – 1) = f(n + 1) – f(n)

∴ (x, k) = (11, 3), (8, 4)

∴ f(8) – f(7) = f(6) and f(7) – f(6) = f(5)

⇒ f(n + 1) = f(n) + f(n – 1) ⇒ f(3) = f(2) + f(1) = 1 + 1 = 2

⇒ f(4) = f(3) + f(2) = 2 + 1 = 3

69. 4

When two circles having radii r 1 and r 2 circles touch externally, the distance between their centres = sum of the radii of the two circles = (r1 + r2)

⇒ f(5) = f(4) + f(3) = 3 + 2 = 5 ⇒ f(6) = f(5) + f(4) = 5 + 3 = 8 ∴

f(8) − f(7) + f(5) f(6) + f(5) 8 + 5 13 = = = f(7) − f(6) − f(4) f(5) − f(4) 5 − 3 2

64. 3

Out of the given options only 16 cannot be expressed as a sum of 3 distinct composite numbers. 21 = 4 + 8 + 9, 23 = 6 + 8 + 9 and 18 = 4 + 6 + 8 Hence option (3) is the correct choice.

65. 5

10a + b = a2 + b2 10a – a2 = b2 – b a(10 – a) = b(b – 1) → Now b(b – 1) is always even. ⇒ a(10 – a) can be → 2 × 8 = 16 or 4 × 6 = 24 Neither 16 nor 24 can be the product of two consecutive numbers such as (b – 1) and b.

PRE MOCK CAT - 3

r1

r2

When the circles touch internally, distance between their centres = difference between their radii = (r1 – r2)

r 1– r 2

r 1– r 2

Let the radii of the circles with centers O, Q, P and R be R, r1, r2 and r3 OP = R – r2 = 98 PQ = r1 + r2 = 157 OR = R – r3 = 92 PR = r2 + r3 = 170 ⇒ R = 180, r1 = 75, r2 = 82 and r3 = 88

7

Alternative Method: Can be directly solved by using the options by equating the sum and difference. 70. 5

74. 4 1 00 m

At least one rose means if one rose is there, then 7 sun flowers would be there. Or, if two roses are there, means 6 sun flowers and it goes upto 4 roses & 4 sunflowers. Total number of ways =

4

P

O’

C1 × 9C7 + 4C2 × 9C6 + 4C3 × 9C5 + 4C4 × 9C4

Q O 1 00 m

⇒ 4 × 36 + 6 × 84 + 4 × 126 + 1× 126

⇒ 144 + 504 + 504 + 126 = 1278

C

2 00 m

71. 3

Initial Efficiency per week =

2500

= 250 questions. 10 After six weeks, total developed questions = 250 × 6 = 1500 questions Remaining questions = 2500 – 1500 = 1000 Increase rate = (1000 – 250) ×

100 250

= 300%

72. 3

If a + b = 9, then possible pairs of values of a and b not necessarily in that order is (1,8); (2,7); (3,6) and (4,5) Case 1: (a, b) is (1, 8): a243 + b243 – (ab) 243 = 1 + 2 – 2 = 1. For the below mentioned values of ‘a’ and ‘b’, the value of (ab) 243 is greater than the value of (a243 + b243). Case 2: (a, b) is (2, 7): (ab) 243 – (a243 + b243) = 4 – (8 + 3) = 3. Case 3: (a, b) is (3, 6): (ab) 243 – (a243 + b243) = 2 – (7 + 6) = 9. Case 4: (a, b) is (4, 5): (ab) 243 – (a243 + b243) = 0 – (4 + 5) = 1.

73. 2

Assume α, β and γ be the roots of the equation x3 + ax2 + bx = c Then, α + β + γ = −a, αβ + βγ + γα = b 2 2 2 2 2 So, (α + β + γ ) = α + β + γ + 2(αβ + βγ + γα ) = a ⇒ α2 + β2 + γ2 + 2b = a2

⇒ α 2 + β2 + γ 2 = a2 − 2b

If α, β & γ are all real, then α2 + β2 + γ2 must be positive. But, if α2 + β2 + γ2 is negative, then 2 roots out of (α, β, γ) must be non real numbers (complex numbers). ⇒ If a2 < 2b, then all the roots of the equation are not real.

If their starting point is O, and they are meeting for the second time at C, then Either they are meeting for the first time at Q (I) Or, they are meeting for the first time at P (II) 75. 1

Smallest natural number which when divided by 7 leaves a remainder of 2 is 2. ⇒ The number is of the form 2 + 7K Now when we divide this number by 8, remainder should be 4. (K = 0) ⇒ 2 divided by 8 ⇒ remainder is 2. (K = 1) ⇒ 9 divided by 8 ⇒ remainder is 1. So, with each increment in K, remainder decreases by 1. ⇒ To get remainder as 4 (or 8 – 4 = 4), the decrease must be carried out six times. ⇒K=6 ∴ Smallest natural number which when divided by 7 leaves a remainder of 2 and which when divided by 8 leaves a remainder of 4 is 2 + 7 × 6 = 44. LCM (7, 8) = 56 ⇒ The number is of the form 44 + 56r. Now when we divide this number by 9, the remainder should be 6. (r = 0) ⇒ 44 divided by 9 ⇒ 8 remainder (r = 1) ⇒ 100 divided by 9 ⇒ 1 remainder So, with each increment in r, remainder gets increased by 2. ⇒ To get a remainder of 6, r will be like (r = 1) ⇒ remainder 1 (r = 2) ⇒ remainder 3 (r = 3) ⇒ remainder 5 (r = 4) ⇒ remainder 7 (r = 5) ⇒ remainder 0 (r = 6) ⇒ remainder 2 (r = 7) ⇒ remainder 4 (r = 8) ⇒ remainder 6 So, the smallest such number is 44 + 56 × 8 = 492 Alternative Method: LCM of (7, 8, 9) = 504 When we subtract 3 from the LCM and divide by 7, 8 and 9 respectively, remainders will be 4, 5 and 6. Here, the gap in these remainders is 1. When we subtract 9 from 501, then their remainder gap will be doubled i.e. 2, 4 and 6. So, the required smallest number is 504 – 3 – 9 i.e. 492.

8

PRE MOCK CAT - 3