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## Official Guide Explanation:Data Sufficiency #73

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: 73
Page: 279
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Evens and Odds

Explanation: Treat the statements as equations. If ((m)/2) is not an even integer, then:

((m)/2) ≠ 2(\func{integer})    (An even integer is, by definition, twice some other integer.)

m ≠ 4(\func{integer})

In other words, (1) says that m is not a multiple of 4. If m is not a multiple of 4, it could be odd, but it could also be an even number such as 2 or 6, so the statement is insufficient.

Statement (2) can be analyzed the same way:

m - 3 = even

m = even + 3 = even + odd = odd

This statement is sufficient, so the correct choice is (B).

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