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GMAT Sample Questions ›› Data Sufficiency

# Quantitative Section : Data Sufficiency

1. Which is the smallest number that is divisible by both 14 as well as 21?

1. The result is a two digit number
2. The sum of the digits is equal to 12

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), the smallest number that is divisible by both 14 as well as 21 is a two digit number.

But, it is not possible to find out the correct answer using only (A), because there are so many two digit numbers.

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

Using only data in (B), we end up with so many numbers whose digits sum up to 12. Hence, it is not possible to find out the correct answer using only (B) as well.

Thus, option (b) also cannot be the right answer.

Now, as per the data in both statement (A) and statement (B), the sum of the digits of the resultant number is equal to 12.

Now, we can find out the numbers whose digits sum upto 12 as follows.

39, 48, 84 and 93

Of all these numbers we can easily find out the number that is divisible by both 14 and 21 as 84.

Hence, we are able to find out the answer using both (A) and (B), therefore the correct answer is option c.

2. Find out the product of 'a' and 'b' i.e. ab.

1. a + b = 3
2. a2 + b2 = 8

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), a + b = 3.

Using this data alone, it is not possible to find out the product of 'a' and 'b'.

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

Now, as per the data in statement (B), a2 + b2 = 8.

Using this data alone also it is not possible to find out the product of 'a' and 'b'.

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

Now, using both the data (A) and (B) together let us try to solve the question as follows

According to the standard mathematical (a + b)2 = a2 + 2ab + b2

Now, substituting the values in this formula we get,

(3)2 = 8 + 2ab → 9 – 8 = 2ab → 1 = 2ab → ab = 1 / 2

Thus, we are able to find the answer using both (A) and (B) together, but neither of them alone.

Hence, the correct answer is option c.

3. Find out the length of the side AB of the following triangle.

1. Triangle ABC is a right angled triangle
2. Length of side AC = 5 cm

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), triangle ABC is a right angled triangle.

From this data we can only say that the side AC is the hypotenuse, but, we cannot find the length of the side AB.

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

Now, as per the data (B), length of side AC i.e. the hypotenuse = 5 cm.

But, from this data also we cannot find the length of side AB as well. Hence, option 'b' also is not the right answer.

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

According to the Pythagoras theorem, AC2 = AB2 + BC2

But, we know the length of only side AC. Thus, we cannot determine the length of side AC.

Hence, option 'c' is not the right answer.

Hence, the correct answer is option e.

4. What is the area of the square?

1. Side of a square = 6 cm
2. Perimeter of a square = 24 cm

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 statement (A), the length of the side of a square = 6 cm.

∴ We can calculate the area of the square as follows,

Area of square = side * side = 6 * 6 = 36 square cm.

Hence, option 'c' and option 'e' cannot be the right answers.

Now, as per the data in statement (B), the perimeter of a square = 24 cm.

Perimeter = sum of all the sides

Since a square has 4 sides, thus perimeter of a square = 4 * side

∴ The length of each side of the square = 24 / 4 = 6 cm.

Hence, we can calculate the area of a square as side * side = 46 * 6 = 36 square cm.

This proves that, we can find the answer using both the data (A) as well as (B) alone.

Hence, the correct answer is option d.

5. Calculate the distance to be covered if

1. Time = 2 hours
2. Speed = 3 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:

As per the data in (A), time = 2 hours.

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

Distance = Speed * Time

As we know only the time factor, it is not possible to calculate the distance using only the data in (A).

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

Now, as per the data in statement (B), speed = 3 km / hr

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

Distance = Time * Speed

As we know only the speed factor, it is not possible to calculate the distance using only the data in (B).

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

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

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

Distance = 2 hours * 3 km / hr

∴ Distance = 6 km.

Thus, we are able to answer the question using data (A) as well as (B), but neither of them alone.

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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