mtripathy wrote:Source:OG 13th Ed.
If n is 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
I found all the answer options can be negated by plugging integers. Is there any trick in the question?
If n is even, then n(n+1)(n+2) = (even)(odd)(even).
Since each of the two even factors must be divisible by 2, the product here must be divisible by 2*2 = 4.
Thus, answer choice
E must be true:
(n)(n+1)(n+2) is divisible by 4 whenever n is even.
The correct answer is
E.
Take-aways:
If n is even, then n and n+2 are CONSECUTIVE EVEN INTEGERS.
The product of any two consecutive even integers will always be a multiple of 4.
If n is a positive integer, then n(n+1)(n+2) is the product of 3 consecutive integers.
Of every 3 consecutive integers, EXACTLY ONE will be a multiple of 3.
Thus, n(n+1)(n+2) will always be a multiple of 3.
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