sherlock wrote:For positive integer k, is the expression (k + 2)(k2 + 4k + 3) divisible by 4?
(1) k is divisible by 8.
(2) (k + 1)/3 is an odd integer.
i chose D but the answer says A .. i think the problem could be solved without the options!! help
MGMAT test question
(k+2)(k² + 4k + 3) = (k+2)(k+1)(k+3) = (k+1)(k+2)(k+3).
Since k is a positive integer, k+1, k+2, and k+3 are 3 consecutive positive integers.
Statement 1: k is divisible by 8.
Thus, k is a multiple of 4.
Since EVERY OTHER even integer is a multiple of 4, k+2 is NOT a multiple of 4.
Thus, (k+1)(k+2)(k+3) = (odd)(even non-multiple of 4)(odd).
Thus, (k+1)(k+2)(k+3) is not a multiple of 4.
SUFFICIENT.
Statement 2: (k + 1)/3 is an odd integer.
It's possible that k=2, since (2 + 1)/3 = 1.
In this case, (k+1)(k+2)(k+3) = 3*4*5, which is a multiple of 4.
It's possible that k=8, since (8 + 1)/3 = 3.
In this case, (k+1)(k+2)(k+3) = 9*10*11, which is a not a multiple of 4.
INSUFFICIENT.
The correct answer is
A.
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