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

- Nov 9, 09:00 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. Here’s a breakdown:

The average formula is Average = Sum of the terms / Number of terms.

The average of m and n is (m + n) / 2  . The question stem says “Is  (m + n) / 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 (3m + 3n) / 2 = 90.

Pull the 3 out of the numerator to get 3(m + n) / 2 = 90,

Multiply both sides by 2 to get 3(m + n) = 180,

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

So, the average of m and n is  =  = 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).