A set of numbers contains 7 integers and has an average

Hi applebear,

Your example has a couple of 'problems' with it:
1) It has 9 terms - and there should only be 7 terms
2) You assume that the LARGEST number shows up repeatedly.

Since the average of the 7 terms is 23, we know that the SUM of those terms is 161. That sum is a big 'limiter' in terms of what is possible. The other limiter is that if the smallest number is X, then the largest number is 4X+15 (meaning that the value of the smallest number limits how big the value of the largest number can get).

In these types of situations, to make one number as big as possible, we must make ALL of the other numbers as small as possible (based on the restrictions described in the prompt). We need those three "23s" to get to the solution because that is the smallest that we can make THOSE three values.

GMAT assassins aren't born, they're made,
Rich