Official Guide Explanation:
Problem Solving #149

Background

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Solution and Metadata

Question: 149
Page: 81
Difficulty: 7 (Very Difficult)
Category 1: Algebra > Functions > other
Category 2: Arithmetic > Properties of Integers > Factors and Multiples
Category 3: Arithmetic > Properties of Integers > Evens and Odds

Explanation: Given the rule in the question f(24) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24. To find the greatest prime factor, we could find the prime factors of all of the numbers, but that would take a long time. For starters, we can ignore 2, 4, 8, and 16, whose only prime factors are 2.

That leaves us with 6, 10, 12, 14, 18, 20, 22, and 24. 6, 12, 18, and 24 only have 2 and 3 as prime factors, so we can focus elsewhere.

That leaves us with 10, 14, 20, and 22. The largest prime factor of any of those numbers is 11, which is a factor of 22. 10 and 20's biggest prime factor is 5, while 14's biggest prime factor is 7. Choice (E) is correct.

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