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## Official Guide Explanation:Data Sufficiency #136

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.

Question: 136
Page: 285
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Descriptive Statistics > Average

Explanation: If the average of 6 numbers is 75, that means that the six numbers sum to 6(75) = 450. Statement (1) is sufficient: if none of the numbers are less than 75, none of the numbers can be greater than 75, either. If any of the numbers were greater than 75, there would need to be a number less than 75 to "balance out" the average. Since there aren't any, all the numbers must be 75.

Statement (2) is the same thing, in reverse: if none of the numbers is greater than 75, none can be less than 75, either, so all six numbers must be 75. Both statements are sufficient, so choice (D) is correct.

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