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## Official Guide Explanation:Problem Solving #31

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: 31
Page: 65
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Evens and Odds

Explanation: Knowing that both x and y are not both odd isn't much: they could both be even, or one could be even and one odd. We'll have to go through each choice to find the answer:

(A): if both numbers are even, xy is even. If one is even and one odd, xy is also even. Thus, (A) is the correct answer.

(B): if both are even, x + y is even. If one is even and one odd, x + y is odd.

(C): if both are even, x - y is even. If one is even and one odd, x - y is odd.

(D): if both are even, x + y - 1 is odd. If one is even and one odd, x + y - 1 is even.

(E): No matter what x + y is, 2(x + y) is even. Thus, 2(x + y) - 1 is odd.

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