If n is a positive integer, then n(n+1)(n+2) is (A) even only when n is even (B) even only when n is odd (C) odd

BTGmoderatorDC wrote: ↑

Tue Feb 04, 2020 7:29 pm

If n is a positive integer, then n(n+1)(n+2) is

(A) even only when n is even
(B) even only when n is odd
(C) odd whenever n is odd
(D) divisible by 3 only when n is odd
(E) divisible by 4 whenever n is even



OA E

Source: Official Guide

The problem is easiest to solve by substituting numbers for n. We'll try an odd number first and then an even number.

For an odd number, let’s let n = 1:

1(1+1)(1+2) = 1(2)(3) = 6

We see that choices A and C can’t be the correct choices. Choice A is false because, while the product is even, n is not even. Choice C is false because, while n is odd, the product is even.

For an even number, let’s let n = 2:

2(2+1)(2+2) = 2(3)(4) = 24

We see that choices B and D can’t be the correct choices. Choice B is false because, while the product is even, n is not odd. Choice D is false because, while the product is divisible by 3, n is even.

Therefore, the only correct answer is choice E. When n is even, the product is indeed divisible by 4.

Answer: E