Official Guide Explanation:
Data Sufficiency #133

Background

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Solution and Metadata

Question: 133
Page: 284
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Descriptive Statistics > Average

Explanation: Statement (1) is insufficient. It's possible that all of the 15 numbers are 4, in which case they are all equal. However, if two of the numbers change from 4 to 3 and 5, the sum is still 60, but the numbers are not equal.

Statement (2) is sufficient. If the sum of any three numbers in the list is always the same, there cannot be any difference between any of the numbers. Take, for instance, the list {3, 4, 4, 5}. It's possible to select three numbers that sum to 12 (3, 4, and 5), but it's also possible to select three numbers that do not (3, 4, 4, or 4, 4, 5). As soon as you introduce one number other than 4 into the list, all of those three - number sums are no longer the same. Choice (B) is correct.

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