(1) n - 3 = 2k implies n = 2k + 3grandh01 wrote:If k and n are integers, is n divisible by 7?
(1) n - 3 = 2k
(2) 2k - 4 is divisible by 7.
If n = 7, k = 2, then n is divisible by 7.
If n = 5, k = 1, then n is not divisible by 7.
No definite answer; NOT sufficient.
(2) 2k - 4 is divisible by 7.
Let 2k - 4 = 7a, where s is an integer.
Then k = (7a + 4)/2 but we do not know the value of a; NOT sufficient.
Combining (1) and (2), k = (7a + 4)/2 and n = 2k + 3
So, n = 2 * {(7a + 4)/2} + 3
n = 7a + 7
n = 7(a + 1), which clearly implies that n is divisible by 7; SUFFICIENT.
The correct answer is C.
