GMAT Question of the Week: Data Sufficiency and Averages

If you haven't already, visit our GMAT Data Sufficiency and Averages practice problem and give it a try on your own before reading the explanation.

To get this question correct, you must combine your knowledge of fundamental math concepts with use of the Kaplan Method and strategies for approaching Data Sufficiency and Averages. Here’s a breakdown:

The average formula is

$Average = \frac{sum -of- terms}{number- of- terms}$

The average of m and n is $\frac{\left ( m+n \right )}{2}$

The question stem asks “Is $\frac{\left ( m+n \right )}{2} < 50$ ?”

Remember, with a Yes/No Data Sufficiency question, you are looking at the statements and trying to determine whether they provide a consistent YES or NO answer to this question. A consistent answer of yes OR no is sufficient. An inconsistent answer (yes and no) is insufficient.

Statement (1): Sufficient. This statement says that $\frac{\left ( 3m+3n \right )}{2} = 90$

Pull the 3 out of the numerator to get $\frac{\left ( 3(m+n) \right )}{2} = 90$

Multiply both sides by 2 to get $3\left ( m+n \right )=180$

Then divide both sides by 3 to get $m+n = 60$

So, the average of m and n is $\frac{m+n}{2}= \frac{60}{2} = 30$ .

The average of m and n is definitely less than 50, and the answer to the question in the stem is always “yes.” Statement (1) is sufficient, so you can eliminate (B), (C), and (E).

Statement (2): Insufficient. This does not allow us to determine the average of m and n, because it does not give us the values or the right relationship between m and n. Eliminate (D).

Answer choice (A) is correct.

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