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## Official Guide Explanation:Data Sufficiency #24

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: 24
Page: 274
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Properties of Integers > Evens and Odds

Explanation: Simplify each statement to isolate n.

Statement (1) is sufficient:

n2-1 = odd

n2 = odd + 1

n2 = even

Since n is an integer and n2 is even, n must be even as well.

Statement (2) is also sufficient:

3n + 4 = even

3n = even - 4

3n = even

If the product of two integers is even, at least one of the integers must be even. Since 3 is not even, n must be. Choice (D) is correct.

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