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GMAT Sample Questions ›› Data Sufficiency

# Quantitative Section : Data Sufficiency

1. Find the value of the variable 'x'; if 24 = 4x.

1. x belongs to the set of integers
2. x is an even 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

Explanation:

According to the data in statement A, 'x' belongs to the set of integers. Means that 'x' can attain either positive or negative values.

Now, using this data, let us try to solve the question.

It is given that 24 = 4x

We have to find the value of 'x' which is an integer.

Now, 2 * 2 * 2 * 2 = 16

And 4 * 4 = 16

Hence, the value of 'x' = 2

Thus, with the help of this data alone we can find the exact answer to the question.

Now, according to the data in statement B, 'x' is an even number.

With the help of this data also we can find out the answer to the question by starting with the smallest even number and substituting it in place of 'x' as follows.

The smallest even number = 2.

Now, substituting x = 2 in 4x we get the answer as 16.

Also, 24 = 16, hence, the value of x is 2.

Since, we are able to answer the question using each of the data alone hence the correct answer is option d.

2. Find out whether 'a' is a positive or a negative integer?

1. a + b = 10
2. a  - b = 5

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:

From the data in statement A, a + b = 10.

Using this data alone, it is not possible to say whether the value of 'a' is positive or negative.

Hence, option 'a' and option 'd' cannot be the right answer.

Now, from the data in statement B, a – b = 5.

Using this data alone also it is not possible to say whether the value of 'a' is positive or negative.

Hence, option 'b' and option 'd' cannot be the right answer.

Now, using both the data together as follows,

a + b = 10 …………i

a – b = 5 …………..ii

Adding equations I and ii, we get,

2a = 15

∴ a = 7.5

This, proves that using both the data A and B together, we can say that the value of 'a' is a positive integer.

Hence, the correct answer is option c.

3. Find out whether y = 7 is true or false?

1.  (x – 6) (y – 7) = 0
2. y – 7 = 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

Explanation:

As per the data in statement (A), we can say that, (x - 6) = 0 or (y - 7) = 0 i.e. either x = 6 or y = 7.

But, there is no proof that y = 7 is always true. Hence data (A) alone is not sufficient to answer the question.

Hence, option 'a' cannot be the answer.

Now, as per the data in statement (B), y – 7 = 1 i.e. y = 1 + 7 → y = 8.

Thus, we are able to answer the question with the help of only the data in (B).

Hence, the correct answer is option b.

4. What is the value of q for the following?

1. Sin q = 1
2. Cos q is positive

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:

As per the data given in (A), the value of sin q = 1.

∴ q = sin-1 (1)

∴ q = 90 degree

Thus, we are able to find out the answer of the question, using only the data in statement (A).

Now, let us see if we can find out the answer using the data in statement (B).

As per the data in (B), Cos Θ is positive.

But, the value of Cos Θ is positive for more than one values of Θ

Hence, we cannot determine the answer to the question using only the data in (B).

Hence, the correct answer is option a.

5. Calculate the time required to cover a distance of 10 km.

1. Speed is positive
2. Speed = 5 km / hr

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 in (A), speed is a positive factor. But, there is no data about the exact value of speed.

Thus, it is not possible to calculate the time factor using only the data in (A).

Now, as per the data in statement (B), speed = 5 km / hr

According to the standard mathematical formula for calculating distance, time and speed,

Time = distance / speed

After substituting the values of distance and speed in this formula, we can calculate the time factor as,

Time = 10 km / 5 km per hour

∴ Time = 2 hours.

Thus, we are able to answer the question using the data in (B) alone.

Hence, the correct answer is option b.

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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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