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Official Guide Explanation:Problem Solving #198

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: 198
Page: 180
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Properties of Integers > Primes
Category 2: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: Since the question implies that the answer will be the same no matter which prime number you choose for p. To keep things simple, choose p = 3, so n = 4p = 4(3) = 12. The even divisors of 12 are 2, 4, 6, and 12, for a total of 4, choice (C).

To think about this more generally, recognize that the prime number p will always be odd. If an odd number is multiplied by 4, there will be four even divisors: 2, 4, 2p, and 4p, which correspond to each of the divisors of 12 listed above.

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