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## Official Guide Explanation:Problem Solving #224

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: 224
Page: 184
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples
Category 2: Arithmetic > Properties of Integers > Evens and Odds
Category 3: Arithmetic > Properties of Integers > Other

Explanation: n(n + 1)(n + 2) is just a fancy way of saying, "the product of three consecutive integers." Since all of the answer choices hinge on n being odd or even, it's worth taking a moment to work out a few possibilities, one each for when n is odd and when n is even:

If n = 2, n(n + 1)(n + 2) = 2(3)(4) = 24

If n = 3, n(n + 1)(n + 2) = 3(4)(5) = 60

Now we have some information to help us go through each answer choice:

(A) false, because the result is even in both an even and an odd instance.

(B) false, for the same reason as (A).

(C) false: the result is even when n is odd.

(D) false, because both of our examples are divisible by 3.

(E) looks good, if only because the first four are wrong. Our example returns a multiple of 4; we can see that this will always be the case because, when n is even, the three consecutive integers include two evens. When two evens are multiplied together, the result is always a multiple of 4.

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