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## Official Guide Explanation:Problem Solving #149

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: 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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