Official Guide Explanation:
Data Sufficiency #103




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Solution and Metadata

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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