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GMAT Sample Questions ›› Data Sufficiency

# Quantitative Section : Data Sufficiency

1. Find out whether x is greater than y or not.

1. x + 2y = 20
2. 2x + y = 10

1. (A) ALONE is sufficient to answer the question but (B) alone is not sufficient
2. (B) ALONE is sufficient to answer the question but (A) alone is not sufficient
3. Both (A) and (B) TAKEN TOGETHER, are sufficient to answer the question, but NEITHER (A) nor (B) ALONE is sufficient
4. Both (A) and (B) ALONE are sufficient to answer the question
5. Both (A) and (B) TAKEN TOGETHER are still NOT sufficient to answer the question

Explanation:

According to the data (A), x + 2y = 20 ↔ x = 20 – 2y.

Hence, we cannot the exact answer to the given question using only (A).

Now, according to the data (B), 2x + y = 10 ↔ 2x = 10 – 2y.

Hence, we cannot the exact answer to the given question using only (B).

Now, using both data (A) and (B), we get,

x + 2y = 20 ↔ x = 20 – 2y

2x + y = 10 ↔ 2x = 10 – 2y

Thus, 2(20 – 2y) = 10 – 2y ↔ 40 – 4y = 10 - y ↔ 40 - 10 = 4y – y ↔ 30 = 3y ↔ y = 3.

Substituting y = 3 in either of the equations (A) or (B), we get,

x + 2y = 20 ↔ x + 2(3) = 20 ↔ x + 6 = 20 ↔ x = 14.

Therefore, using both (A) and (B) we can the exact answer to the given question.

Hence, the correct answer is option c.

2. Find out whether x is non negative integer or not.

1. x2 is a positive integer
2. x3 < x2

1. (A) ALONE is sufficient to answer the question but (B) alone is not sufficient
2. (B) ALONE is sufficient to answer the question but (A) alone is not sufficient
3. Both (A) and (B) TAKEN TOGETHER, are sufficient to answer the question, but NEITHER (A) nor (B) ALONE is sufficient
4. Both (A) and (B) ALONE are sufficient to answer the question
5. Both (A) and (B) TAKEN TOGETHER are still NOT sufficient to answer the question

Explanation:

According to data (A), x2 is a positive integer.

Suppose, x = -2, then x2 = 4.

Now if, x = 2, then also x2 = 4. The square of any number, positive or negative will always be positive. Hence, using only (A), we cannot determine the right answer.

According to data (B), x3 < x2

Suppose, x = -2, then, x3 = -8 and x2 = 4 ↔ x3 < x2

But, if x = 2, then, x3 = 8 and x2 = 4 ↔ x3 > x2

Hence, using only (B), we cannot determine the right answer.

Now, using both data (A) and (B), we come to the conclusion that, only for the negative values of x will satisfy both the conditions.

Hence, the correct answer is option c.

3. Find out whether the number ‘p’ is divisible by the number 9 or not.

1. p is a multiple of 3
2. the sum of all the digits in p is divisible by 9

1. (A) ALONE is sufficient to answer the question but (B) alone is not sufficient
2. (B) ALONE is sufficient to answer the question but (A) alone is not sufficient
3. Both (A) and (B) TAKEN TOGETHER, are sufficient to answer the question, but NEITHER (A) nor (B) ALONE is sufficient
4. Both (A) and (B) ALONE are sufficient to answer the question
5. Both (A) and (B) TAKEN TOGETHER are still NOT sufficient to answer the question

Explanation:

According to the data (A), the number p is a multiple of 3.

Suppose, p = 3, then, p is not divisible by 9.

But, if p = 18, then, p is completely divisible by 9.

Hence, using only (A), we cannot determine the right answer.

According to the data (B), the sum of all the digits in p is divisible by 9.

Suppose, p = 27, the, 2 + 7 = 9. Hence p is completely divisible by 9.

Hence, using only (B), we cannot determine the right answer.

Hence, the correct answer is option b.

4. Determine whether the product of the integers a and b is less than 25?

1. The sum of integer a and integer b is less than 25
2. Both the integers a as well as b are even numbers

1. (A) ALONE is sufficient to answer the question but (B) alone is not sufficient
2. (B) ALONE is sufficient to answer the question but (A) alone is not sufficient
3. Both (A) and (B) TAKEN TOGETHER, are sufficient to answer the question, but NEITHER (A) nor (B) ALONE is sufficient
4. Both (A) and (B) ALONE are sufficient to answer the question
5. Both (A) and (B) TAKEN TOGETHER are still NOT sufficient to answer the question

Explanation:

According to the data (A), the sum of the integer a and the integer b is less than 25.

Now, let us find out the pairs of numbers whose sum is less than 25, as follows,

(1, 23), (2, 22), (3, 21), (4, 20), (5, 19), (6, 18), (7, 17), (8, 16), (9, 15), (10, 14), (11, 13), (12, 12)

Hence, using only the data (A), we cannot determine the right answer.

According to the data (B), both the integers a as well as b are even numbers.

From the above pairs, (2, 22), (4, 20), (6, 18), (8, 16), (10, 14), (12, 12) satisfy this condition.

Hence, using only the data (B), we cannot determine the right answer.

But, as per the question, the product of these numbers should be less than 25. This condition is not satisfied by any of these pairs.

Therefore, we cannot determine the correct answer using the two (A) and (B) together as well.

Hence, the correct answer is option e.

5. a, b, c, d are four integers. Find out whether these four integers are consecutive or not.

1. The sum of the squares of these four integers is 30
2. The sum of these four numbers is 10

1. (A) ALONE is sufficient to answer the question but (B) alone is not sufficient
2. (B) ALONE is sufficient to answer the question but (A) alone is not sufficient
3. Both (A) and (B) TAKEN TOGETHER, are sufficient to answer the question, but NEITHER (A) nor (B) ALONE is sufficient
4. Both (A) and (B) ALONE are sufficient to answer the question
5. Both (A) and (B) TAKEN TOGETHER are still NOT sufficient to answer the question

Explanation:

According to the data (A), the sum of the squares of these four integers is 30 i.e. a2 + b2 + c2 + d2 = 30

Hence, using only the data (A), we cannot determine the right answer.

Now, according to data (B), the sum of a, b, c and d is 10 i.e. a + b + c + d = 10.

Hence, using only the data (B), we cannot determine the right answer.

Now, using both (A) and (B), still we are unable to find the right answer to the given question.

Hence, the correct answer is option e.

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GMAT Sample Data Sufficiency Question Number : 1-5 | 6-10 | 11-15 | 16-20 | 21-25 | 26-30
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