Official Guide Explanation:
Problem Solving #198




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Solution and Metadata

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.

Click here for the full list of GMAT OG12 explanations.


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