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## Official Guide Explanation:Data Sufficiency #103

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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: 103
Page: 160
Difficulty: 5 (Moderate)
Category 1: Algebra > Absolute Value >
Category 2: Arithmetic > Descriptive Statistics > Average

Explanation: Statement (1) is sufficient. On a number line, the average of x and 10 lies precisely at the midpoint between x and 10. Thus, if z is closer to 10 than it is to x, it must be greater than the average. Statement (2) is not sufficient: if x is very small, such as 1, 5x = 5, which is closer to x than it is to 10; the average of x and 10 in this case is ((1 + 10)/2) = 5.5. But if x is larger, such as 5, 5x = 25, which is closer to 10 than it is to 5. Choice (A) is correct.

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