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## Official Guide Explanation:Problem Solving #78

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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: 78
Page: 71
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Properties of Integers > Primes

Explanation: To find the "prime sum" of any number, we'll need to find the prime factorization of the number. Fortunately, once we find a choice with a prime sum greater than 35, we can stop. Try each one:

(A)    440 = 2(2)(2)(5)(11) --- 2 + 2 + 2 + 5 + 11 = 22

(B)    512 = 2(2)(2)(2)(2)(2)(2)(2)(2) = 29 --- 9(2) = 18

(C)    620 = 2(2)(5)(31) --- 2 + 2 + 5 + 31 = 40

Here we can stop; choice (C) is correct. In case you started at the bottom, here are the rest:

(D)    700 = 2(2)(5)(5)(7) --- 2 + 2 + 5 + 5 + 7 = 21

(E)    750 = 2(3)(5)(5)(5) --- 2 + 3 + 5 + 5 + 5 = 20

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