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## Official Guide Explanation:Data Sufficiency #17

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: 17
Page: 274
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Properties of Integers > Evens and Odds

Explanation: Simplify each of the statements.

Statement (1) is sufficient. The sum of the three expressions is 3P + 15. Simplify:

3P + 15 = even

3P = even - 15

3P = odd

Since P is an integer, the only way 3P can be odd is if P is odd.

Statement (2) is also sufficient. The sum of these three expressions is 3P + 8. Simplify:

3P + 8 = odd

3P = odd - 8

3P = odd

By the same reasoning as in (1), P must be odd. Choice (D) is correct.

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