Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
Go ahead and build set P by listing the desired multiples of 4.
12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52.
There are 11 numbers in this list. Set Q consists of 9 different integers drawn from set P. You are asked for the average (arithmetic mean) of set Q, so you need to know which integers are included. That’s the same as knowing which integers have been left out. So you can rephrase the question to ask which integers in set P are NOT in set Q.
Statement 1: INSUFFICIENT. Set Q may contain at most 4 consecutive multiples of 4, but there are many ways to construct such a set. For instance, leave out 24 and 40, or leave out 28 and 40. These two versions will produce sets with different arithmetic means.
Statement 2: INSUFFICIENT. Set Q may contain exactly 1 perfect square, but again, there are many ways to construct such a set. You have to include either 16 or 36 (not both), but the other integer that you leave out is up to you.
Statements 1 and 2 TOGETHER: INSUFFICIENT. It turns out that you have to include 16 in set Q, because if you leave 16 out, you must include 36, and then no matter which other integer you leave out, you will have a string of 5 or more consecutive multiples of 4. However, once you have omitted 36, you have a few choices for the other integer to omit (20, 24, or 28). These different choices will produce sets with different averages.
The correct answer is E.