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Quantitative Section : Data Sufficiency

  1. Find the value of the variable ‘b’; if a*b = 15 and both the variables belong to the set of integers.

    1. a is less than b
    2. a is an odd number

    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

    Correct answer: e

    Explanation:

    First we will find the number of ways through which we get the product of two integers as 15.

    1 * 15 = 15 -1 * -15 = 15 3 * 5 = 15 -3 * -5 = 15

    There are in all 4 ways that give the product 15. But, not all of them satisfy the given conditions to find the correct value of ‘b’.

    Now, according to (A), a is less than b. There are two numbers 1 and 3 that satisfy this condition. Hence, it is not possible to find the exact value of ‘b’ using only (A).

    Now, according to (B), a is an odd number. From the above results, 1, -1, 3, -3, 5, -5, 15, -15 are all odd numbers. Hence, it is not possible to find the exact value of ‘b’ using only (B).

    Now, using both the given conditions, we can find the value of ‘b’ as, 1 and 3. Still we are unable to find the exact value of ‘b’.

    Therefore, we need more information to find the correct value of ‘b’.

    Hence, the correct answer is option e.

  2. Find out whether ‘m’ is an integer or not?

    1. m2  is an integer
    2. 2m is an integer

    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

    Correct answer: c

    Explanation:

    According to (A), m2 is an integer.

    Suppose, m2 = 3, then m is not an integer.

    But, if m2 = 16, then m = 4 is definitely an integer.

    Thus, using only the data (A), we cannot find the correct answer for the given question.

    Now, according to data (B), 2m is an integer.

    Say, 2m = 1, then m is not an integer.

    But, if 2m = 4, then, m = 2 i.e. m is an integer.

    Thus, using only the data (B), we cannot find the correct answer for the given question.

    But, if we use both the data (A) and (B) together, only then, we can say that the given question is true or false.

    Hence, the correct answer is option c.

  3. State whether x = 5 is true or false.

    1. (x – 5) (y – 4) = 0
    2. y – 4 = 1

    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

    Correct answer: e

    Explanation:

    As per the data (A), we can say that, (x-5) = 0 or (y-4) = 0 i.e. x = 5 or y = 4.

    But, we cannot tell whether x = 5 is always true. Hence (A) alone is not sufficient.

    As per the data (B), y – 4 = 1 i.e. y = 1 + 4 → y = 5. There is no information regarding the value of ‘x’ in the given data (B).

    Now, using both (A) and (B), still we cannot say anything about the value of x.

    Hence, the correct answer is option e.

  4. Find out whether a4 is greater than a2?

    1. a is non-negative
    2. a is not greater than 1

    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

    Correct answer: e

    Explanation:

    As per the data given in (A), a is a non-negative number i.e. a > 0.

    Suppose, a = 2, then, a2 = 4 and a4 = 16. Hence, a4 > a2

    Now, as per the data given in (B), a is less than 1.

    Suppose, a = -0.9, then, a2 = 0.81 and a4 = 0.6561. Hence, a4 < a2 for all the values of a less than 1

    The results obtained from both the given data (A) and (B) are not sufficient to find out whether a4 is greater than a2.

    Hence, the correct answer is option e.

  5. Find out whether m is completely divisible by n or not.

    1. m is a positive integer and is divisible of 3
    2. n is a positive integer and is a multiple of 4

    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

    Correct answer: e

    Explanation:

    According to the data (A), m > 0 and m is divisible by 3. There is no data about the value of n.

    Suppose, m = 3 and n = 4, then m is not completely divisible by n.

    But, if m = 12 and n = 4, then m is completely divisible by n.

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

    Now, according to the data (B), n > 0 and n is a multiple of 4. There is no data about the value of m.

    Suppose, n = 4 and m = 3, then m is not completely divisible by n.

    But, if n = 8 and m = 24, then m is completely divisible by n.

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

    Now, using both the data (A) and (B),

    Suppose, m = 9 and n = 8, then m is not completely divisible by n.

    But, if m = 12 and n =12, then m is completely divisible by n.

    Thus, using both (A) and (B) also, we cannot find the correct 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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