Official Guide Explanation:
Problem Solving #217




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Solution and Metadata

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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