Is k^2 odd?
(1) k - 1 is divisible by 2.
(2) The sum of k consecutive integers is divisible by k.
(1) k - 1 is divisible by 2.
(2) The sum of k consecutive integers is divisible by k.
Statement 1: As (k - 1) is divisible by 2, k must be odd.nidhis.1408 wrote:Is k^2 odd?
(1) k - 1 is divisible by 2.
(2) The sum of k consecutive integers is divisible by k.
Hence, k² is also odd.
Sufficient
Statement 2: Say, k consecutive integers are a, (a + 1), (a + 2), ..., and (a + k - 1)
Hence, the sum of these k consecutive integers, S = ak + k(k - 1)/2 = k[a + (k - 1)/2]
Now, if S is divisible by k, then [a + (k - 1)/2] must be integer.
So, (k - 1)/2 must be integer.
So, (k - 1) must be even.
Hence, k must be odd.
Therefore, k² is also odd.
Sufficient
The correct answer is D.
