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## Official Guide Explanation:Data Sufficiency #106

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: 106
Page: 282
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: For the product of two integers to be even, at least one of the integers must be even.

Statement (1) is sufficient. If x is 1 greater than y, one of the numbers is odd and one is even. (We don't know which one, but it doesn't matter.) Since one of the numbers is even, the product is even.

Statement (2) is also sufficient. It's easier to understand this if you multiply both sides by y:

((x)/(y)) = even

x = even(y)

Any integer multiplied by an even is even, so even * y = even, so x is even. Since x is even, we know that the product of the two integers is even. Choice (D) is correct.

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