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GMAT Sample Questions ›› Data Sufficiency

# Quantitative Section : Data Sufficiency

1. Identify whether the following equation is true or false.
(2)* (2)y = (2)x+y

1. x is a whole number
2. y is a whole number

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 whole numbers; therefore 2x and 2y will also belong to the set of whole numbers.

From data (A), we get x is a whole number. Suppose x = 4, then after substituting this value in the given equation, we get 24 * 2y = 24 + y

Hence only data (A) is not sufficient to answer the question.

Now, from data (B), we get y is whole number. Suppose y = 2, then after substituting this value in the given equation, we get 24 * 22 = 24 + 2 = 26 = 64

Hence only data (A) is also not sufficient to answer the question.

Hence option e is the correct answer.

2. Find out whether the value of ‘m’ for the equation m5 – 48 = (-16) is divisible by 2 or not?

1. ‘m’ is a positive integer
2. ‘m’ is an even number

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), m is a positive integer. Using only this data we can find out the value of ‘m’ as follows:

m5 – 48 = (-16) → m5 = (-16) + 48 → m5 = 32 → m= 321/5 → m = 2. Therefore, ‘m’ is divisible by 2.

Hence, we can find whether the value of ‘m’ is divisible by 2 or not using only the data (A).

Similarly, it is possible to find out the correct answer by using only the data in (B) i.e. ‘m’ is an even number.

Hence, the correct answer is option d

3. Find out the value of ‘x’?

1. 6x – 4y = 4
2. y = 5

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 get, 6x – 4y = 4 → 6x = 4 + 4y → x = (4 + 4y) / 6

Hence, we are not able to find the value of ‘x’ with the help only the data in (A).

Now, according to the data in (B), y = 5.

After substituting the value of y in the equation given in data (A), we get,

6x – 4(5) = 4 → 6x = 4 + 20 → 6x = 24 → x = 24/6 → x = 4.

Therefore, we are able to find the value of ‘x’ using both the data (A) as well as (B), but not using any of the statements alone.

Hence, the correct answer is option c.

4. Find out whether the number ‘x’ is completely divisible by 8 or not?

1. x is an odd number and belongs to the set of integers
2. x = 4567

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), x is an odd number and belongs to the set of integers. Using this data it is not possible to find out the answer for the question.

Hence, data (A) alone is not sufficient to find the answer to the question.

Now, according to the data in (B), x = 4567

The divisibility rule for the integer 8 states that, a number is completely divisible by 8 if the last three digits are zero or the number formed by the last three digits is divisible by 8 completely.

According to this rule, the last three numbers are not equal to 0. Hence, we will check whether the number formed by the last three digits i.e. ‘567’ is divisible by 8 or not.

The number ‘567’ is not divisible by 8. Hence, it the number ‘4567’ i.e. ‘x’ is not divisible by 8 completely.

Hence, it is proved that, we can answer the question using the data in (B) alone, but not the data in (A).

Hence, the correct answer is option b.

5. Find out the value of the divisor ‘d’, where d is a positive integer.

1. ‘d’ when divided by 7 gives a remainder of 3
2. The quotient is a prime number between 3 and 7

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 rule of divisibility,

Dividend = divisor * quotient + remainder--------(I)

Now, according to the data in (A), 7 is the divisor and 3 is the remainder,

After substituting these values in the equation (I), we get,

Dividend (d) = 7 * quotient + 3

Hence, it is not possible to find the value of the dividend using only the data in (A).

Now, according to the data in (B), quotient is a prime number between 3 and 7.

Hence, we can conclude that the quotient is 5 as it is the only prime number that lies between 3 and 7.

Hence, we can write equation (I) as follows,

Dividend (d) = 7 * 5 + 3 → d = 35 + 3 → d = 38.

Thus we are able to answer the question if we use both the data in (A) and (B) together.

Hence, the correct answer is option c.

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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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