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## Official Guide Explanation:Problem Solving #D15

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: D15
Page: 22
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Powers and Roots of Numbers > Powers

Explanation: First, list all the prime numbers less than 20:

2, 3, 5, 7, 11, 13, 17, 19

Next, look for ways to approximate their products in ways that are related to powers of 10:

2(5) = 10

3(7) = 2(10) (plus a little bit)

11(19) = 2(102) (it's about the same as 10 times 20, which is 200)

13(17) = 2(102) (like the above, it's about the same as 10 times 20)

This leaves us with:

10(2)(10)(2)(102)(2)(102)

More directly: 23106

23 is 8, which we can round up to 10, especially since three of our four approximations were slightly rounded down. Finally, then, our answer is 107, choice (C).

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