# GMAT Question of the Week: Data Sufficiency and Averages – The Explanation

- Feb 13, 07:00 AM Comments [0]

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

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

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

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 $\frac{\left&space;(&space;3m+3n&space;\right&space;)}{2}&space;=&space;90$

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

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

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

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

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).

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