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## Official Guide Explanation:Data Sufficiency #118

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: 118
Page: 161
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Descriptive Statistics > Average
Category 2: Algebra > Equations >

Explanation: Statement (1) is sufficient. To determine that, set up an equation:

((x + y + (y - 2))/3) = x

x + y + y - 2 = 3x

2y - 2 = 2x

y - 1 = x

y = x + 1

If x is an integer, then x + 1 is also an integer, so y is an integer. Statement (2) is insufficient. If x is 10, the the average of x and y is not an integer if y is 11 (in which case y is an integer), and it is also not an integer if y is 10.5 (in which case y is not an integer). Choice (A) is correct.

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