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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

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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

by BTGmoderatorDC » 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
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Re: 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

by swerve » Thu Feb 06, 2020 10:26 am
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
If \(n\) is even \(\Longrightarrow\) even \(\cdot\) odd \(\cdot\) even (Prod of two even numbers always divisible by 2\(\cdot\)2)
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Re: 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

by Scott@TargetTestPrep » Sat Feb 08, 2020 7:21 pm
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

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