Jem2905 wrote:
If k is a positive integer and n = k(k + 7), is n divisible by 6?
(1) k is odd.
(2) When k is divided by 3, the remainder is 2.
Statement 1:
Case 1: k=1, with the result that n=1(1+7) = 8
In this case, n is not divisible by 6, so the answer to the question stem is NO.
Case 2: k=2, with the result that n = 2(2+7) = 18
In this case, n is divisible by 6, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.
Statement 2:
k = 3x+2, where x is an nonnegative integer, with the result that n = (3x+2)(3x+9) =
(3x+2)(3)(x+3)The resulting expression in blue has a factor of 3 and thus is a MULTIPLE OF 3.
If x is EVEN, then 3x+2 = EVEN.
If x is ODD, then x+3 = EVEN.
Either way, the blue expression is an EVEN MULTIPLE OF 3, with the result that n is divisible by 6.
Thus, the answer to the question stem is YES.
SUFFICIENT.
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