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

I decided to let n = 2. I got 24, which is even.

I then let n = 3. This produced 60, which is also even.

The answer is E.

When n is 3, 60 is the answer, which is divisible by 4.

However, when n is 2, the answer is 24, which is also divisible by 4.

Question:

Why is the answer E and not B?