# Quantitative Section – GMAT Data Sufficiency Problems

## GMAT Data Sufficiency Questions

The GMAT Data Sufficiency questions are interspersed throughout the Quantitative section, and they are likely unfamiliar to most test takers. The questions contain mathematical equations that might involve algebra or geometry, much like the more straightforward Problem Solving questions in the Quantitative section.

What is unique about Data Sufficiency questions is that the test taker does not have to solve the actual equations. Instead, each equation will be followed by two statements containing data pertaining to the equation. The question will then ask, in order to solve the equation, is the first statement alone sufficient? Is the second statement alone sufficient? Are the two statements both required for solving the equation, but neither sufficient on its own? Is either statement sufficient on its own? Is neither sufficient on its own?

In other words, test takers need only discern what information is required to solve the equation. Often, that can be done without actually solving the equation. In fact, if test takers can determine what data is required for solving the equation without actually solving it, valuable time can be saved. Every Data Sufficiency problem follows the same format, with the five multiple choices listed above.

## Sample Data Sufficiency Question

A typical Data Sufficiency question might look like this:

Did David solve more questions than Steve in a 2-hour test?

1. Thrice the number of questions that David solved in the test was greater than 6 less than thrice the number of questions that Steve solved in the test.

2. Twice the number of questions that David solved in the test was greater than 4 less than twice the number of questions that Steve solved in the test.

1. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient to answer the question asked.

2. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient to answer the question asked.

3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Solution Explanation

We have to find out whether David solved more questions than Steve.

Say David solved x number of questions, while Steve solved y number of questions in the 2-hour test.

So, we need to determine whether x>y

Statement 1:

We are given that "Thrice the number of questions that David solved in the test was greater than 6 less than thrice the number of questions that Steve solved in the test."

⇒3x>3y−6

⇒x>y−2

We cannot determine whether x>y, since x is greater than a quantity y, which is reduced by a certain amount, 2.

Let us take an example.

Say y=10, thus x>10−2⇒x>8.

If x=9, then x≯y and the answer is No. However, if x=11, then x>y and the answer is Yes. There is no unique answer, so Statement 1 alone is insufficient.

Statement 2:

We are given that Twice the number of questions that David solved in the test was greater than 4 less than twice the number of questions that Steve solved in the test.

⇒2x>2y−4

⇒x>y−2 ⇒ x

This is the same inequality that we got in Statement 1, making it insufficient.

Statement 1 & 2:

Since each statement renders the same inequality, even combining both the statements cannot help. Finally, even combingin Statement 1 and 2 is insufficient.

Conclusion:

You may have deduced a wrong conclusion with the inequality x>y−2.

We see that x is greater than a number y minus 2; thus, x may or may not be greater than y.

Had the situation been x>y+2, then it's for certain that x>y; since x is greater than a number (y+2), then x must be greater than a relatively smaller number y.