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## Official Guide Explanation:

Data Sufficiency #133

**Background**

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

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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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