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GMAT Sample Questions ›› Data Sufficiency

Quantitative Section : Data Sufficiency

Directions for answering the Data sufficiency type of GMAT questions:

Each of the data sufficiency problems consists of a question followed by two statements, namely (A) and (B). Here, you must decide whether the given data to solve the question is sufficient or not.

The correct answer to each question will be one of the following:

1. if statement (A) alone is sufficient to answer the question but statement (B) alone is not sufficient
2. if statement (B) alone is sufficient to answer the question but statement (A) alone is not sufficient
3. if the two statements (A) and (B) taken together, are sufficient to answer the question, but neither statement alone is sufficient
4. if each statement alone is sufficient to answer the question
5. if the two statements taken together are still not sufficient to answer the question

1. Identify whether the result of the following equation is an integer or not; if both x and y are integers?

(x2) - (y2)
(A) x = y
(B) y = 2

1. if statement (A) alone is sufficient to answer the question but statement (B) alone is not sufficient
2. if statement (B) alone is sufficient to answer the question but statement (A) alone is not sufficient
3. if the two statements (A) and (B) taken together, are sufficient to answer the question, but neither statement alone is sufficient
4. if each statement alone is sufficient to answer the question
5. if the two statements taken together are still not sufficient to answer the question

Explanation:
It is given that both x and y are integers; therefore x2 and y2 will also be integers.
From data (A), we get x = y. After substituting this value in the given equation, we get y2 - y2 = 0 which is an integer.
Hence only data (A) is sufficient to answer the question.
Hence option a is the correct answer.

2. Find out whether the following equation is true or false?

(a)3  - (b)3 = 0
(A) a = 6
(B) b = -6

1. if statement (A) alone is sufficient to answer the question but statement (B) alone is not sufficient
2. if statement (B) alone is sufficient to answer the question but statement (A) alone is not sufficient
3. if the two statements (A) and (B) taken together, are sufficient to answer the question, but neither statement alone is sufficient
4. if each statement alone is sufficient to answer the question
5. if the two statements taken together are still not sufficient to answer the question

Explanation:
According to data in (A), the value of a is 6. Using only this data we cannot find out whether the given equation is true or false.
Similarly, it is not possible to find out the answer by using only the data in (B) i.e. b = -6.
But, if we use both the data (A) and (B) and substitute the values of a and b in the given equation, we get (a)3  - (b)3 = 0 as, (6)3 - (-6)3 = (216) - (-216) = 216 + 216 = 432.
Hence, the given equation is false.
Hence, the correct answer is option c

3. If a = b2 - 9, then find out whether ‘a’ is divisible by 9?

(A)   b = 3
(B)   a - 27 is divisible by 9

1. if statement (A) alone is sufficient to answer the question but statement (B) alone is not sufficient
2. if statement (B) alone is sufficient to answer the question but statement (A) alone is not sufficient
3. if the two statements (A) and (B) taken together, are sufficient to answer the question, but neither statement alone is sufficient
4. if each statement alone is sufficient to answer the question
5. if the two statements taken together are still not sufficient to answer the question

Explanation:
By using the data in (A), we can write the given equation a = b2 - 9 as, a = (3)2 - 9
i.e. a = 9 - 9 i.e. a = 0; and 0 is not divisible by 9.
As we are able to answer the question with the help of only data (A), therefore, the correct answer is option a

4. If x2 + y2 + 2xy = 16; is ‘x’ divisible by 10?

(A) x2 + y2 = 8
(B) y = 2

1. if statement (A) alone is sufficient to answer the question but statement (B) alone is not sufficient
2. if statement (B) alone is sufficient to answer the question but statement (A) alone is not sufficient
3. if the two statements (A) and (B) taken together, are sufficient to answer the question, but neither statement alone is sufficient
4. if each statement alone is sufficient to answer the question
5. if the two statements taken together are still not sufficient to answer the question

Explanation:

According to the data in (A), x2 + y2 = 8. When we substitute this value in the equation given in question, we get, 8 + 2xy = 16 ↔ 2xy = 16 - 8 ↔ 2xy = 8.

Hence, we cannot solve the equation completely to find whether ‘x’ is divisible by 10 or no.

Now, if use the data in (B), then we can write the given equation as,

x2 + (2)2 + 2(x)(2) = 16 ↔ x2 + 4 + 4x = 16 ↔ x2 + 4x = 12 ↔ x2 + 4x - 16 = 0.

Hence, it is proved that, it is not possible to find the value of ‘x’ by using either only (A) or only (B).

But, by using both the data, we get

8 + 2(x) (2) = 16 ↔ 8 + 4x = 16 ↔ 4x = 8 ↔ x = 2.

Thus, the correct answer is option c.

5. Find out the value of ‘m’?

(A)‘m’ is a single digit, non-negative whole number?
(B)‘m’ is an even number and the sum of its factors is less than the even number by 2.

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:
If we use only the data (A), we will not be able to find the exact value of ‘m’; since there may be more than one even numbers whose sum of the factors may be less than the number by 2.
But, if use the data provided in both (A) and (B), we can surely find out the exact value of ‘m’ as follows:
The single digit even numbers that are less than 10 include the numbers 2, 4, 6 and 8.
Now, the factors of 2 are 1 and 2 and its addition is 3; which is not less than 2 by the even number 2.
The factors of 4 are 1, 2 and their addition is 3; which is not less than 2 by the even number 4.
The factors of 6 are 1, 2 and 3 and their addition is 6; which is less than 2 by the even number 6.
The factors of 8 are 1, 2 and 4 and their addition is 7; which is not less than 2 by the even number 8.
Hence, the correct answer is option c.

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