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## Official Guide Explanation:Problem Solving #217

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: 217
Page: 183
Difficulty: 7 (Very Difficult)
Category 1: Arithmetic > Properties of Integers > Primes
Category 2: Arithmetic > Properties of Integers > Factors and Multiples
Category 3: Word Problems > Other >

Explanation: If the product of the point values is 147,000, then some number of 2's, 3's, 5's, and 7's multiply to 147,000. Since we're interested in the number of red beads (the 7 - pointers), we only care how many 7's go into the factorization of 147,000. To make things simpler, divide out 1,000--7 doesn't divide into 1,000, so we can forget about that. Then, all we need to do is figure out how many 7's are in the factorization of 147. 147 = 3(49) = 3(7)(7), so the number of red beads is 2, choice (D).

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