Official Guide Explanation:
Problem Solving #D18

Background

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Solution and Metadata

Question: D18
Page: 22
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: n is equal to (1)(2)(3)(4)(5)(6)(7)(8). Don't multiply all those numbers! The largest possible prime factor of the product must be no larger than 8. There's no way for, say, 11 to be a prime factor unless 11 (or a multiple of 11) is one of the numbers multiplied to get the product.

Thus, the only possible prime factors are 2, 3, 5, and 7, the primes less than 8. Since all four of those numbers are present in the list of numbers to be multiplied, all are factors of the product. Thus, there are 4 different prime factors of n, choice (A).

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