Translate the question.sukhman 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.
Does n have among its prime factors at least one 2 and one 3?
Statement 1:
If k is odd, then k + 7 is even. So if k + 7 is a factor of n, then n is even, meaning that n has 2 among its prime factors.
However k could be 3 or another positive integer.
If k = 3, then n has 3 among its prime factors.
If, for instance, k = 19, then k(k + 7) = 19(26) and n does not have 3 among its prime factors.
So there is not enough information for determining whether n has 3 among its prime factors.
Insufficient.
Statement 2:
This means that k = 3x + 2. So k + 7 = 3x + 9. So 3 is a factor of k + 7 and of n.
If k is even, then n has 2 among its prime factors. If k is odd, then k + 7 is even and n has 2 among its prime factors.
So Statement 2 makes clear that n has 2 and 3 among its prime factors and is divisible by 6.
Sufficient.
The correct answer is B.
