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## Official Guide Explanation:

Problem Solving #185

**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.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.

**Solution and Metadata**

**Question****: 185**

Page: 178

Difficulty: **6** (Moderately Difficult)

Category 1: Arithmetic > Properties of Integers > Factors and Multiples

Category 2: Arithmetic > Properties of Integers > Primes

Category 3: Arithmetic > Properties of Integers > Evens and Odds

**Explanation:** In questions like this one, there's no alternative but to go through the choices until you find a correct one.

(A): knowing nothing except for the even - ness and odd - ness of the variables, ((p)/(q)) could be even, odd, or a non - integer.

(B): pq = even(odd) = even

(C): 2p + q = 2(even) + odd = even + odd = odd. That's it!

(D): 2(p + q) = 2(even + odd) = 2(odd) = even.

(E): this is unclear for the same reason that (A) is.

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