## Overview

While problem solving questions may be familiar to you, data sufficiency questions are—within the standardized test world—unique to the GMAT. You’ll be given a question followed by two statements that provide information that might be useful in answering the question. The true task is not necessarily to answer the actual question (though that may happen in the process), but to determine what information you’ll need in order to answer it in the first place. You may need one of the statements, maybe the other, maybe both together, maybe either would work individually, or maybe neither helps at all!

Data sufficiency questions are designed to measure the test-taker’s ability to:

• Analyze a quantitative problem
• Recognize which information is relevant
• Determine at what point there is sufficient information to solve a problem

This section requires knowledge of the following:

• Arithmetic
• Elementary algebra
• Basic concepts of geometry

Click through our practice questions to test your data sufficiency problem-solving skills. Each question is followed by the answer and a detailed explanation of how to solve the problem.

## Question 1

If a is an integer, is b an integer?

1. The average (arithmetic mean) of a and b is not an integer.
2. The average (arithmetic mean) of 3a, 2b, and a + 12, is 2b.

We need to determine whether or not b is an integer.

Statement 1 tells us that the average of a and b is not an integer. Recall that the average of a group is equal to the sum of the group’s terms divided by the number of terms. Thus, the average of a and b is $data sufficiency problem$. The average will not be an integer whenever a + b is not an even number.

If a = 1 and b = 2, the average of the two numbers is $dat sufficiency$, which is not an integer. If a = 1 and b = 1.5, the average of a and b is , which is also not an integer. Since we can pick both integer and non-integer values for b that satisfy Statement 1, Statement 1 alone is insufficient to answer the question. The answer must be either B, C, or E.

Statement 2 tells us that the average of 3a, 2b, and a + 12 is 2b. Using the average formula, we can write this statement as the equation $data sufficiency equation$. If we combine the a terms in the numerator of the fraction on the left side, we get $data sufficiency equation$. Multiplying both sides of the equation by 3 gives us: 4a + 2b + 12 = 6b. Subtracting 2b from both sides, we get: 4a + 12 = 4b. Finally, dividing both sides of the equation by 4, we get a + 3 = b. Since a is an integer, a + 3 must also be an integer; therefore, b is an integer. Statement 2 alone is sufficient to answer the question.

The correct answer choice is B.

## Question 2

Is the positive integer k a multiple of 54?

1. k is a multiple of 6.
2. k is a multiple of 9.

We must determine whether or not k is a multiple of 54.

Statement 1 tells us that k is a multiple of 6. Let’s look at a few multiples of 6 to see if any/all of them are multiples of 54. 6 and 12 are multiples of 6, but neither is a multiple of 54. On the other hand, 54 is a multiple of both 6 and 54. Since there are multiples of 6 that both are and are not multiples of 54, Statement 1 alone is insufficient to answer the question. The answer must be B, C, or E.

Statement 1 tells us that k is a multiple of 9. We can use the same logic we applied above: 9 and 18 are both multiples of 9, but neither is a multiple of 54. However, 54 is a multiple of both 9 and 54. Therefore, we can also conclude that Statement 2 alone is insufficient to answer the question. The answer must be C or E.

Taken together, Statements 1 and 2 tell us that k is a multiple of both 6 and 9. We cannot simply multiply together 6 × 9 = 54 and conclude that k is a multiple of 54. For example, k could be 18 or 36, since 18 and 36 are multiples of both 6 and 9. (The reason for this is that the Least Common Multiple of 6 and 9 is 18, not 54).

Since we can still find values ofk that both are and are not multiples of 54, Statements 1 and 2 together do not provide us with enough information to answer the question. The correct answer choice is E.

## Question 3

Is n negative?

1. (1 – n2) < 0
2. n2 – n – 2 < 0