Data 20 Sufficiency 1
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The MBA Center Data Sufficiency
Ready… Part One
Ready… Hi, my name is Jeff. I’ll be your instructor for today’s lesson, Data Sufficiency. The speed of this lesson is up to you. Click on the yellow action buttons at the bottom of each screen to move forward or backward Beginning of section
The buttons on the far right and far left take you to the next or to the previous section. Previous screen
Click on the forward (Next Screen) button to begin the lesson. Next screen Next section
Uh oh! Hey you! What happened? I hope you were just playing.
Beginning of section
Previous screen
Click on the Previous Screen button and try again.
Next screen Next section
Aim… Part Two
Not Only Math, but also Logic Like Problem Solving, Data Sufficiency questions test basic math skills - arithmetic, algebra, geometry and word problems. The strategies discussed in the Problem Solving lesson are applicable here in Data Sufficiency questions as well. But your approach will be quite different.
Data Sufficiency tests not only math, but also logic skills. To crack them, you’ll need the following: 1. The ability to distinguish between relevant and irrelevant data. 2. The ability to determine whether you have enough information to answer a question. In this section, you’ll be provided with strategies that will give you the necessary logic skills to solve Data Sufficiency questions.
A Data Sufficiency question is made up of three parts: 1.
The question will either ask for the value of a variable or for an answer to a yes-or-no question. We’ll discuss these two types of DS questions in a moment.
2.
Each DS problem contains two statements. These represent pieces of information which can be added in order to answer the question. One or both of the statements may or may not be sufficient to answer the question. That’s what you’ll be asked to determine!
3.
Answer choices are the same for all Data Sufficiency questions. As you practice, you’ll become familiar with the standard set of choices, and you’ll soon have them memorized without even trying. But do make sure you truly have the answer choices memorized! You’ll waste a great deal of time reading through the same set of answer choices for every Data Sufficiency question.
Answer choices are the same for every Data Sufficiency question. Know them now and you won’t need to refer to them during the test.
(A)
Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. (B) Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. (C) NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. (D) EACH statement BY ITSELF is sufficient. (E) Statement (1) and statement (2) COMBINED are not sufficient.
Do memorize the answer choices in their proper order. It would be a shame if you studied hard, mastered the DS question types and bombed them anyway, just because you clicked on the wrong oval each time.
Can you answer this question?
What is x + 5 ?
No way! To do so, you need to know the value of x. What if I gave you this piece of information?
x2 = 1
That’s no good. (1)2 = 1, but (– 1)2 = 1 too! Try solving the equation with only this piece of information…
x2 + 5x – 6 = 0
Remember the quadratic equations we looked at in the Problem Solving lesson? If neither the first nor the second piece of information enables you to answer the question, combine the two and see what you can do. Let’s look at this again as a Data Sufficiency question...
Click on the oval that corresponds with the correct answer choice.
What is x + 5 ? (1) x2 = 1 (2) x2 + 5x – 6 = 0 (A) Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. (B) Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. (C) NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. (D) EACH statement BY ITSELF is sufficient. (E) Statement (1) and statement (2) COMBINED are not sufficient.
Hey, way to go! That’s right, the answer is (C). Try another one...
What is x + 5 ? (1) x2 = 1 (2) x2 – 2x + 1 = 0 (A) Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. (B) Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. (C) NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. (D) EACH statement BY ITSELF is sufficient. (E) Statement (1) and statement (2) COMBINED are not sufficient.
Click on the oval that corresponds with the correct answer choice.
Sorry, the correct answer is (C). Click on the explanation icon to see how the previous question is done. Then try another one...
What is x + 5 ? (1) x2 = 1 (2) x2 – 2x + 1 = 0 (A) Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. (B) Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. (C) NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. (D) EACH statement BY ITSELF is sufficient. (E) Statement (1) and statement (2) COMBINED are not sufficient. Click on the oval that corresponds with the correct answer choice.
Good job! Try one more...
What is 3x4 + 5 ? (1) x2 = 1 (2) x2 + 5x – 6 = 0 (A) Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. (B) Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. (C) NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. (D) EACH statement BY ITSELF is sufficient. (E) Statement (1) and statement (2) COMBINED are not sufficient. Click on the oval that corresponds with the correct answer choice.
Sorry, the correct answer is (B). Click on the explanation icon to see how the previous question’s done. Then try one more... What is 3x4 + 5 ? (1) x2 = 1 (2) x2 + 5x – 6 = 0 (A) Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. (B) Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. (C) NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. (D) EACH statement BY ITSELF is sufficient. (E) Statement (1) and statement (2) COMBINED are not sufficient. Click on the oval that corresponds with the correct answer choice.
The correct answer to the last question is (A). Click on the Explanation icon to see why. The preceding quadratic equations were all examples of value questions. Value questions ask for one, and only one, single value for x.
Ask yourself this: “Can the first statement find one (and just one) value which can be placed in the original question?” If the answer is no, then it’s not sufficient. If yes, then it is. Then move on to statement number two. Ask yourself the same question for the second statement. If necessary combine both statements and ask the question one more time.
This is a value question. A statement is not sufficient if it contains more than one value for the variable x. Look at each statement separately… Statement 1
Statement 2
x2 = 1 What is x + 5?
x2 + 5x - 6 = 0
x could be 1 x could also be –1
(1)2 = 1 (–1)2 = 1
two values, not sufficient
Factor the equation: (x – 3)(x – 2) = 0 x could be 3 or x could be 2
x–3=0 x–2=0
two values, not sufficient Statements 1 and 2 There is no one common variable that links the two equations. x = 1 or x = – 1 or x = 2 or x = 3 The statements combined are not sufficient.
This is a value question. A statement is not sufficient if it contains more than one value for the variable x. Look at each statement separately… Statement 1 What is x + 5?
x2 = 1 x could be 1 x could also be -1
Statement 2 x2 - 2x + 1 = 0
(1)2 = 1 (-1)2 = 1
two values, not sufficient
Factor the equation: (x - 1) (x - 1) = 0 x could be 1 or x could be 1
x-1 =0 x-1 =0
one value, sufficient
The answer is (B). Statement (2) BY ITSELF is sufficient to solve the problem.
This is a value question. A statement is not sufficient if it contains more than one value for the variable x. Look at each statement separately… Statement 1
Statement 2
x2 = 1 What is 3x4 + 5 ?
x2 + 5x - 6 = 0
x could be 1 x could also be -1
(1)2 = 1 (-1)2 = 1
two values… but remember our original equation: What is 3x4 + 5 ? Know the rules of parity.
Factor the equation: (x - 3) (x - 2) = 0 x could be 3 or x could be 2
x-3 =0 x-2 =0
two values, not sufficient
If (-1)2 = 1 then (-1)4 = 1 also. Statement (1) is sufficient! The answer is (A). Statement (1) alone is sufficient to solve the problem.
Now take a lookWhat at thisisone… 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 is unmowed. (A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the Click on the ovalquestion. that corresponds with the correct answer choice.
The correct answer is (C). Click on the Explanation icon to see how it’s done. And what’s the total area of the lawn? If you don’t know, don’t worry. You don’t need to know. In fact, If you can tell me the lawn’s area, then you’ve gone too far. Never solve a Data Sufficiency problem! At no time will you ever be asked to actually solve a DS problem. You’re only asked to determine which statements are sufficient to answer it. The best timesaving device you have when tackling Data Sufficiency questions will be your ability to determine if there is or is not enough information to answer a question without actually answering the question. Use the Data Sufficiency flowchart to eliminate wrong answer choices.
Understand that this is a value question, so you’ll need to know the area of the entire lawn to answer it. area mowed = x% of total area Now, examine each statement separately, eliminating answer choices as you go. ☞ Statement 1: not suff. Eliminate (A) and (D). ☞ Statement 2: not suff. Eliminate (B).
We still haven’t eliminated four answer choices, so combine Statements 1 and 2. ☞ Combined: Sufficient! Eliminate (E).
Statement 1: mowed = 75% of total Statement 2: 120 = x % of total Statements 1 and 2: 120 = 75% of total
Process of Error Identification The flowchart helps you to use the Process of Error Identification as you work your way through Data Sufficiency questions. Determining if a statement is, or is not, sufficient will automatically rule out a number of answer choices.
Because answer choices for all DS questions are always the same, the chart will apply for all DS questions in the GMAT! As with all question types in the GMAT, eliminating some wrong answer choices is always better than eliminating none. It also improves your chances of guessing the correct answer.
Begin with statement (1) Insufficient Use this flow chart to eliminate wrong answer choices when you examine the statements.
Sufficient
Eliminat e A, D
Eliminat e B, C, E
Then try statement (2)
Then try statement (2)
Insufficient
Sufficient
Insufficient
Sufficient
Eliminat eB Consider both statements together Insufficient Answer E
Sufficient Answer C
Answer B
Answer D
Answer A
Begin with statement (2) Insufficient
The flow changes if you begin with the second statement.
Sufficient
Eliminat e B, D
Eliminat e A, C, E
Then try statement (1)
Then try statement (1)
Insufficient
Sufficient
Insufficient
Sufficient
Eliminat eA Consider both statements together Insufficient Answer E
Sufficient Answer C
Answer A
Answer B
Answer D
The MBA Center Approach Part Three
MBA Center Approach Follow the MBA Center approach to Data Sufficiency questions every time to assure you won’t be tripped up by ETS traps. Work systematically through each problem. Read and understand the question first. Then start with one statement and move to the next, eliminating wrong answer choices as you go. Finally, look at both statements combined, if necessary, to determine the correct answer choice. Following the MBA Center approach is a proven method which helps you: ⇒ save time, ⇒ avoid common ETS traps, and ⇒ improve your chances of guessing (if necessary) the right answer.
MBA Center Approach Step 1: Read and understand the question before you move on to the statements Ask yourself, “What information do I need in order to answer the question?” Step 2: Examine the statements separately, eliminating wrong answer choices Step 3: If necessary, consider the statements together
Use the MBA Center approach on the following Data Sufficiency questions…
If x and y are positive integers, what is the value of x + y? (1) (2)
x2 = y x > 16
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Good job. Now try this one…
If x and y are positive integers, is x + y less than 20 ? (1) (2)
x2 = y x > 16
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Click on the oval that corresponds with the correct answer choice.
Sorry, the correct answer is (E). Click on the explanation icon to see how it’s done. Then try this one… If x and y are positive integers, is x + y less than 20 ? (1) (2)
x2 = y x > 16
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Click on the oval that corresponds with the correct answer choice.
To answer the question, you would need to be able to determine the values of two variables: x and y .
If x and y are positive integers, what is the value of x + y ?
Statement 1
Statement 2
x2 = y
x > 16
x could be any number, as could y. not sufficient
x could be any number greater than 16 not sufficient
Statements 1 and 2 Together, we still don’t know much. We can’t determine the value of x and, therefore, we don’t know y either. Not sufficient.
The correct answer to the last question is (A). Did you see the difference between those last two questions?
Understand the meaning of “ sufficient”
The first, a value question, should be familiar to you by now. The second question asked only for a yes-or-no answer and is, therefore, a yes-or-no question. Take a look at them again...
If x and y are positive integers, what is the value of x + y? If x and y are positive integers, is x + y less than 20 ? It’s not necessary to find one value for the variable in a yes-or-no question. Only determine whether the answer to the question is definitely “yes” or definitely “no.” Take a look at the following yes-or-no questions…
Definition of “Sufficiency” For value questions: A statement is sufficient if, and only if, it gives you enough information to narrow down the answer to exactly one numerical value.
For yes-or-no questions: A statement is sufficient if, regardless of the values, you can answer the question with either a “yes” or a “no.”
A statement in a yes-or-no question is sufficient if it can be answered with a “yes” or a “no.”
Is the odd integer x a prime number? (1) (2)
x + 2 is a prime number. x – 3 is a prime number.
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Click on the oval that corresponds with the correct answer choice.
Good job! Try another one…
Is the integer m odd ? (1) (2)
m is a multiple of both 3 and 7. m - 7 is an odd integer.
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Click on the oval that corresponds with the correct answer choice.
Sorry, the correct answer is (B). This one’s a bit easier.
Does a = 1 ? (1) (2)
b = 2a b=2
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Click on the oval that corresponds with the correct answer choice.
The correct answer is (B). Statement (1) says that m is a multiple of both 3 and 7. 3 * 7 = 21 (odd number) Double that and you’ve got 42, an even number. Statement (1) is not sufficient!
Only an odd integer can satisfy the statement. Statement (2) alone is sufficient to answer the question. So is m odd? It’s not important, but, no, m is an even number. Click on the forward Next Screen button to try some Data Sufficiency questions on your own.
The correct answer is (C). Statement (1) simply has too many variables. Statement (2) gives us the value of b . This doesn’t help at all! Combine the two and we’re getting somewhere. Statements (1) and (2) combined are sufficient to answer the question.
So Does a = 1 ? It’s not important, but, yes, a = 1 Go through the lesson again if you’re having trouble. Or, if you’re ready, click on the forward Next Screen button to try some Data Sufficiency questions on your own.
Fire! Part Four
Fire! Now it’s time for some tough ones! Remember, because Data Sufficiency questions rely on logic as well as math, a systematic approach is critical. If Lydia is exactly 1.5 times as old as Francis, how old is Francis? (1) old as (2) exactly 25
Seven years ago Lydia was exactly twice as Francis. Fourteen years from now Lydia will be percent older than Francis.
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Good job. Now try this one…
I
II
III
What is the total area of the rectangle above ? (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 . (A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Sorry, the correct is a(D). Try this Theanswer value of certain carone… depreciates by 10 percent each year. What was the original price of the car? (1) ago, and
The car was purchased 2 years
its present value is $ 10,000. (2) Two years after the car was purchased, its depreciated value was 81% of its original price. (A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the with question. Click on the oval that corresponds the correct answer choice.
Way to go! Try one more…
✪ x 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) (2)
✪=8 ▲=3
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is sufficient. (B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient (C) Statement (1) and (2) COMBINED are sufficient to answer the question, but neither alone is sufficient. (D) Each of statements (1) and (2), alone or combined, are not sufficient to answer the question. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Sorry, the correct answer is (E). This one’s a bit easier…
If n is an integer, is 3n less than 100 ? (1) (2)
3n + 1 > 100 3n - 1 = 3n - 162
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is sufficient. (B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient (C) Statement (1) and (2) COMBINED are sufficient to answer the question, but neither alone is sufficient. (D) Each of statements (1) and (2), alone or combined, are not sufficient to answer the question. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Click on the oval that corresponds with the correct answer choice.
That’s right! You’re one for one. Try one more...
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 dollars on credit card X . If Mr. Pavlov got a travel voucher equal in value to 380 dollars, what was the value of Mrs. Pavlov’s travel voucher? (1)
The vouchers were equal in value to 0.05 dollars for each dollar charged to credit
card X (2)
in 1995. d = 7,600
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is sufficient. (B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient (C) Statement (1) and (2) COMBINED are sufficient to answer the question, but neither alone is sufficient. (D) Each of statements (1) and (2), alone or combined, are not sufficient to answer the question.
Sorry, the correct answer is (A). This one’s easier…
If a and b are positive integers, what percent of a is b ? (1) (2)
3a = 5b a + b = 80
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is sufficient. (B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient (C) Statement (1) and (2) COMBINED are sufficient to answer the question, but neither alone is sufficient. (D) Each of statements (1) and (2), alone or combined, are not sufficient to answer the question. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Click on the oval that corresponds with the correct answer choice.
Fire! Remarkable, three out of three! Look’s like you’re getting the hang of it, but don’t stop practicing.
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Fire! Ahh! I got you that time. The correct answer is (D).
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Fire! You got two out of three correct. That’s not bad.
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Fire! Sorry, the correct answer is (B). You got the first question correct, but you missed the next two.
Download more Data Sufficiency questions from our web site, and order our textbook for comprehensive coverage of all question types within the GMAT
Fire! Good job. You got the first one wrong, but you pulled it up with the next two. Remember: in the actual exam, it is the early questions that hold the greatest point value. Read about the Computer-adaptive test (CAT) in the Introduction lesson.
Download more Data Sufficiency questions from our web site, and order our textbook for comprehensive coverage of all question types within the GMAT
Fire! Sorry, the correct answer is (D). You got the second question right, but you missed the other two.
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Fire! Good job. You missed the first two questions, but you got the last one right.
Download more Data Sufficiency questions from our web site, and order our textbook for comprehensive coverage of all question types within the GMAT
Fire! Oops, the correct answer is (A). Take some time to review your math skills and try this lesson again.
Then download more Data Sufficiency questions from our web site. Our textbook offers comprehensive coverage of Data Sufficiency and all question types within the GMAT.
Summary Part Five
Summary Data Sufficiency answer choices are always the same. Memorize them! Don’t waste time reading them during the actual test. DS questions are especially tricky and it’s important that you closely follow the MBA Center 3-step approach to each question.
Step 1: Step 2:
Step 3:
Read and understand the question before you move to the statements. Examine each statement separately, using the Process of Error Identification to eliminate wrong answer choices. Second, if necessary, consider the two statements together.
Click on the MBA Center logo to end this lesson and return to the MBA Center home page.
Ready… Part One
Ready… Hi, my name is Jeff. I’ll be your instructor for today’s lesson, Data Sufficiency. The speed of this lesson is up to you. Click on the yellow action buttons at the bottom of each screen to move forward or backward Beginning of section
The buttons on the far right and far left take you to the next or to the previous section. Previous screen
Click on the forward (Next Screen) button to begin the lesson. Next screen Next section
Uh oh! Hey you! What happened? I hope you were just playing.
Beginning of section
Previous screen
Click on the Previous Screen button and try again.
Next screen Next section
Aim… Part Two
Not Only Math, but also Logic Like Problem Solving, Data Sufficiency questions test basic math skills - arithmetic, algebra, geometry and word problems. The strategies discussed in the Problem Solving lesson are applicable here in Data Sufficiency questions as well. But your approach will be quite different.
Data Sufficiency tests not only math, but also logic skills. To crack them, you’ll need the following: 1. The ability to distinguish between relevant and irrelevant data. 2. The ability to determine whether you have enough information to answer a question. In this section, you’ll be provided with strategies that will give you the necessary logic skills to solve Data Sufficiency questions.
A Data Sufficiency question is made up of three parts: 1.
The question will either ask for the value of a variable or for an answer to a yes-or-no question. We’ll discuss these two types of DS questions in a moment.
2.
Each DS problem contains two statements. These represent pieces of information which can be added in order to answer the question. One or both of the statements may or may not be sufficient to answer the question. That’s what you’ll be asked to determine!
3.
Answer choices are the same for all Data Sufficiency questions. As you practice, you’ll become familiar with the standard set of choices, and you’ll soon have them memorized without even trying. But do make sure you truly have the answer choices memorized! You’ll waste a great deal of time reading through the same set of answer choices for every Data Sufficiency question.
Answer choices are the same for every Data Sufficiency question. Know them now and you won’t need to refer to them during the test.
(A)
Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. (B) Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. (C) NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. (D) EACH statement BY ITSELF is sufficient. (E) Statement (1) and statement (2) COMBINED are not sufficient.
Do memorize the answer choices in their proper order. It would be a shame if you studied hard, mastered the DS question types and bombed them anyway, just because you clicked on the wrong oval each time.
Can you answer this question?
What is x + 5 ?
No way! To do so, you need to know the value of x. What if I gave you this piece of information?
x2 = 1
That’s no good. (1)2 = 1, but (– 1)2 = 1 too! Try solving the equation with only this piece of information…
x2 + 5x – 6 = 0
Remember the quadratic equations we looked at in the Problem Solving lesson? If neither the first nor the second piece of information enables you to answer the question, combine the two and see what you can do. Let’s look at this again as a Data Sufficiency question...
Click on the oval that corresponds with the correct answer choice.
What is x + 5 ? (1) x2 = 1 (2) x2 + 5x – 6 = 0 (A) Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. (B) Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. (C) NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. (D) EACH statement BY ITSELF is sufficient. (E) Statement (1) and statement (2) COMBINED are not sufficient.
Hey, way to go! That’s right, the answer is (C). Try another one...
What is x + 5 ? (1) x2 = 1 (2) x2 – 2x + 1 = 0 (A) Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. (B) Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. (C) NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. (D) EACH statement BY ITSELF is sufficient. (E) Statement (1) and statement (2) COMBINED are not sufficient.
Click on the oval that corresponds with the correct answer choice.
Sorry, the correct answer is (C). Click on the explanation icon to see how the previous question is done. Then try another one...
What is x + 5 ? (1) x2 = 1 (2) x2 – 2x + 1 = 0 (A) Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. (B) Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. (C) NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. (D) EACH statement BY ITSELF is sufficient. (E) Statement (1) and statement (2) COMBINED are not sufficient. Click on the oval that corresponds with the correct answer choice.
Good job! Try one more...
What is 3x4 + 5 ? (1) x2 = 1 (2) x2 + 5x – 6 = 0 (A) Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. (B) Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. (C) NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. (D) EACH statement BY ITSELF is sufficient. (E) Statement (1) and statement (2) COMBINED are not sufficient. Click on the oval that corresponds with the correct answer choice.
Sorry, the correct answer is (B). Click on the explanation icon to see how the previous question’s done. Then try one more... What is 3x4 + 5 ? (1) x2 = 1 (2) x2 + 5x – 6 = 0 (A) Statement (1) BY ITSELF is sufficient, but statement (2) by itself is not sufficient. (B) Statement (2) BY ITSELF is sufficient, but statement (1) by itself is not sufficient. (C) NEITHER statement BY ITSELF is sufficient, but the two statements COMBINED are sufficient. (D) EACH statement BY ITSELF is sufficient. (E) Statement (1) and statement (2) COMBINED are not sufficient. Click on the oval that corresponds with the correct answer choice.
The correct answer to the last question is (A). Click on the Explanation icon to see why. The preceding quadratic equations were all examples of value questions. Value questions ask for one, and only one, single value for x.
Ask yourself this: “Can the first statement find one (and just one) value which can be placed in the original question?” If the answer is no, then it’s not sufficient. If yes, then it is. Then move on to statement number two. Ask yourself the same question for the second statement. If necessary combine both statements and ask the question one more time.
This is a value question. A statement is not sufficient if it contains more than one value for the variable x. Look at each statement separately… Statement 1
Statement 2
x2 = 1 What is x + 5?
x2 + 5x - 6 = 0
x could be 1 x could also be –1
(1)2 = 1 (–1)2 = 1
two values, not sufficient
Factor the equation: (x – 3)(x – 2) = 0 x could be 3 or x could be 2
x–3=0 x–2=0
two values, not sufficient Statements 1 and 2 There is no one common variable that links the two equations. x = 1 or x = – 1 or x = 2 or x = 3 The statements combined are not sufficient.
This is a value question. A statement is not sufficient if it contains more than one value for the variable x. Look at each statement separately… Statement 1 What is x + 5?
x2 = 1 x could be 1 x could also be -1
Statement 2 x2 - 2x + 1 = 0
(1)2 = 1 (-1)2 = 1
two values, not sufficient
Factor the equation: (x - 1) (x - 1) = 0 x could be 1 or x could be 1
x-1 =0 x-1 =0
one value, sufficient
The answer is (B). Statement (2) BY ITSELF is sufficient to solve the problem.
This is a value question. A statement is not sufficient if it contains more than one value for the variable x. Look at each statement separately… Statement 1
Statement 2
x2 = 1 What is 3x4 + 5 ?
x2 + 5x - 6 = 0
x could be 1 x could also be -1
(1)2 = 1 (-1)2 = 1
two values… but remember our original equation: What is 3x4 + 5 ? Know the rules of parity.
Factor the equation: (x - 3) (x - 2) = 0 x could be 3 or x could be 2
x-3 =0 x-2 =0
two values, not sufficient
If (-1)2 = 1 then (-1)4 = 1 also. Statement (1) is sufficient! The answer is (A). Statement (1) alone is sufficient to solve the problem.
Now take a lookWhat at thisisone… 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 is unmowed. (A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the Click on the ovalquestion. that corresponds with the correct answer choice.
The correct answer is (C). Click on the Explanation icon to see how it’s done. And what’s the total area of the lawn? If you don’t know, don’t worry. You don’t need to know. In fact, If you can tell me the lawn’s area, then you’ve gone too far. Never solve a Data Sufficiency problem! At no time will you ever be asked to actually solve a DS problem. You’re only asked to determine which statements are sufficient to answer it. The best timesaving device you have when tackling Data Sufficiency questions will be your ability to determine if there is or is not enough information to answer a question without actually answering the question. Use the Data Sufficiency flowchart to eliminate wrong answer choices.
Understand that this is a value question, so you’ll need to know the area of the entire lawn to answer it. area mowed = x% of total area Now, examine each statement separately, eliminating answer choices as you go. ☞ Statement 1: not suff. Eliminate (A) and (D). ☞ Statement 2: not suff. Eliminate (B).
We still haven’t eliminated four answer choices, so combine Statements 1 and 2. ☞ Combined: Sufficient! Eliminate (E).
Statement 1: mowed = 75% of total Statement 2: 120 = x % of total Statements 1 and 2: 120 = 75% of total
Process of Error Identification The flowchart helps you to use the Process of Error Identification as you work your way through Data Sufficiency questions. Determining if a statement is, or is not, sufficient will automatically rule out a number of answer choices.
Because answer choices for all DS questions are always the same, the chart will apply for all DS questions in the GMAT! As with all question types in the GMAT, eliminating some wrong answer choices is always better than eliminating none. It also improves your chances of guessing the correct answer.
Begin with statement (1) Insufficient Use this flow chart to eliminate wrong answer choices when you examine the statements.
Sufficient
Eliminat e A, D
Eliminat e B, C, E
Then try statement (2)
Then try statement (2)
Insufficient
Sufficient
Insufficient
Sufficient
Eliminat eB Consider both statements together Insufficient Answer E
Sufficient Answer C
Answer B
Answer D
Answer A
Begin with statement (2) Insufficient
The flow changes if you begin with the second statement.
Sufficient
Eliminat e B, D
Eliminat e A, C, E
Then try statement (1)
Then try statement (1)
Insufficient
Sufficient
Insufficient
Sufficient
Eliminat eA Consider both statements together Insufficient Answer E
Sufficient Answer C
Answer A
Answer B
Answer D
The MBA Center Approach Part Three
MBA Center Approach Follow the MBA Center approach to Data Sufficiency questions every time to assure you won’t be tripped up by ETS traps. Work systematically through each problem. Read and understand the question first. Then start with one statement and move to the next, eliminating wrong answer choices as you go. Finally, look at both statements combined, if necessary, to determine the correct answer choice. Following the MBA Center approach is a proven method which helps you: ⇒ save time, ⇒ avoid common ETS traps, and ⇒ improve your chances of guessing (if necessary) the right answer.
MBA Center Approach Step 1: Read and understand the question before you move on to the statements Ask yourself, “What information do I need in order to answer the question?” Step 2: Examine the statements separately, eliminating wrong answer choices Step 3: If necessary, consider the statements together
Use the MBA Center approach on the following Data Sufficiency questions…
If x and y are positive integers, what is the value of x + y? (1) (2)
x2 = y x > 16
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Good job. Now try this one…
If x and y are positive integers, is x + y less than 20 ? (1) (2)
x2 = y x > 16
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Click on the oval that corresponds with the correct answer choice.
Sorry, the correct answer is (E). Click on the explanation icon to see how it’s done. Then try this one… If x and y are positive integers, is x + y less than 20 ? (1) (2)
x2 = y x > 16
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Click on the oval that corresponds with the correct answer choice.
To answer the question, you would need to be able to determine the values of two variables: x and y .
If x and y are positive integers, what is the value of x + y ?
Statement 1
Statement 2
x2 = y
x > 16
x could be any number, as could y. not sufficient
x could be any number greater than 16 not sufficient
Statements 1 and 2 Together, we still don’t know much. We can’t determine the value of x and, therefore, we don’t know y either. Not sufficient.
The correct answer to the last question is (A). Did you see the difference between those last two questions?
Understand the meaning of “ sufficient”
The first, a value question, should be familiar to you by now. The second question asked only for a yes-or-no answer and is, therefore, a yes-or-no question. Take a look at them again...
If x and y are positive integers, what is the value of x + y? If x and y are positive integers, is x + y less than 20 ? It’s not necessary to find one value for the variable in a yes-or-no question. Only determine whether the answer to the question is definitely “yes” or definitely “no.” Take a look at the following yes-or-no questions…
Definition of “Sufficiency” For value questions: A statement is sufficient if, and only if, it gives you enough information to narrow down the answer to exactly one numerical value.
For yes-or-no questions: A statement is sufficient if, regardless of the values, you can answer the question with either a “yes” or a “no.”
A statement in a yes-or-no question is sufficient if it can be answered with a “yes” or a “no.”
Is the odd integer x a prime number? (1) (2)
x + 2 is a prime number. x – 3 is a prime number.
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Click on the oval that corresponds with the correct answer choice.
Good job! Try another one…
Is the integer m odd ? (1) (2)
m is a multiple of both 3 and 7. m - 7 is an odd integer.
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Click on the oval that corresponds with the correct answer choice.
Sorry, the correct answer is (B). This one’s a bit easier.
Does a = 1 ? (1) (2)
b = 2a b=2
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Click on the oval that corresponds with the correct answer choice.
The correct answer is (B). Statement (1) says that m is a multiple of both 3 and 7. 3 * 7 = 21 (odd number) Double that and you’ve got 42, an even number. Statement (1) is not sufficient!
Only an odd integer can satisfy the statement. Statement (2) alone is sufficient to answer the question. So is m odd? It’s not important, but, no, m is an even number. Click on the forward Next Screen button to try some Data Sufficiency questions on your own.
The correct answer is (C). Statement (1) simply has too many variables. Statement (2) gives us the value of b . This doesn’t help at all! Combine the two and we’re getting somewhere. Statements (1) and (2) combined are sufficient to answer the question.
So Does a = 1 ? It’s not important, but, yes, a = 1 Go through the lesson again if you’re having trouble. Or, if you’re ready, click on the forward Next Screen button to try some Data Sufficiency questions on your own.
Fire! Part Four
Fire! Now it’s time for some tough ones! Remember, because Data Sufficiency questions rely on logic as well as math, a systematic approach is critical. If Lydia is exactly 1.5 times as old as Francis, how old is Francis? (1) old as (2) exactly 25
Seven years ago Lydia was exactly twice as Francis. Fourteen years from now Lydia will be percent older than Francis.
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Good job. Now try this one…
I
II
III
What is the total area of the rectangle above ? (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 . (A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Sorry, the correct is a(D). Try this Theanswer value of certain carone… depreciates by 10 percent each year. What was the original price of the car? (1) ago, and
The car was purchased 2 years
its present value is $ 10,000. (2) Two years after the car was purchased, its depreciated value was 81% of its original price. (A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is 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 alone is sufficient. (D) Each statement BY ITSELF is sufficient. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the with question. Click on the oval that corresponds the correct answer choice.
Way to go! Try one more…
✪ x 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) (2)
✪=8 ▲=3
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is sufficient. (B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient (C) Statement (1) and (2) COMBINED are sufficient to answer the question, but neither alone is sufficient. (D) Each of statements (1) and (2), alone or combined, are not sufficient to answer the question. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Sorry, the correct answer is (E). This one’s a bit easier…
If n is an integer, is 3n less than 100 ? (1) (2)
3n + 1 > 100 3n - 1 = 3n - 162
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is sufficient. (B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient (C) Statement (1) and (2) COMBINED are sufficient to answer the question, but neither alone is sufficient. (D) Each of statements (1) and (2), alone or combined, are not sufficient to answer the question. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Click on the oval that corresponds with the correct answer choice.
That’s right! You’re one for one. Try one more...
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 dollars on credit card X . If Mr. Pavlov got a travel voucher equal in value to 380 dollars, what was the value of Mrs. Pavlov’s travel voucher? (1)
The vouchers were equal in value to 0.05 dollars for each dollar charged to credit
card X (2)
in 1995. d = 7,600
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is sufficient. (B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient (C) Statement (1) and (2) COMBINED are sufficient to answer the question, but neither alone is sufficient. (D) Each of statements (1) and (2), alone or combined, are not sufficient to answer the question.
Sorry, the correct answer is (A). This one’s easier…
If a and b are positive integers, what percent of a is b ? (1) (2)
3a = 5b a + b = 80
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is sufficient. (B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not sufficient (C) Statement (1) and (2) COMBINED are sufficient to answer the question, but neither alone is sufficient. (D) Each of statements (1) and (2), alone or combined, are not sufficient to answer the question. (E) Statements (1) and (2), alone or combined, are not sufficient to answer the question.
Click on the oval that corresponds with the correct answer choice.
Fire! Remarkable, three out of three! Look’s like you’re getting the hang of it, but don’t stop practicing.
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Fire! Ahh! I got you that time. The correct answer is (D).
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Fire! You got two out of three correct. That’s not bad.
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Fire! Sorry, the correct answer is (B). You got the first question correct, but you missed the next two.
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Fire! Good job. You got the first one wrong, but you pulled it up with the next two. Remember: in the actual exam, it is the early questions that hold the greatest point value. Read about the Computer-adaptive test (CAT) in the Introduction lesson.
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Fire! Sorry, the correct answer is (D). You got the second question right, but you missed the other two.
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Fire! Good job. You missed the first two questions, but you got the last one right.
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Fire! Oops, the correct answer is (A). Take some time to review your math skills and try this lesson again.
Then download more Data Sufficiency questions from our web site. Our textbook offers comprehensive coverage of Data Sufficiency and all question types within the GMAT.
Summary Part Five
Summary Data Sufficiency answer choices are always the same. Memorize them! Don’t waste time reading them during the actual test. DS questions are especially tricky and it’s important that you closely follow the MBA Center 3-step approach to each question.
Step 1: Step 2:
Step 3:
Read and understand the question before you move to the statements. Examine each statement separately, using the Process of Error Identification to eliminate wrong answer choices. Second, if necessary, consider the two statements together.
Click on the MBA Center logo to end this lesson and return to the MBA Center home page.
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