I tried finding this question before in this thread, no avail. Sorry if its duplicate post.

Given a series of n consecutive positive integers, where n>1, is the average value of this eries an integer divisble by 3?

1) n is odd

2) The sum of the first number of the series and (n-1)/2 is an integer divisible by 3

A) Statement 1 alone is suff, but stat. 2 alone is not suff
B) Stat 2 alone is suff but stat 1 alone is not suff
C) Both stats together are suff, but neither statement alone is suff
D) Each stat alone is suff
E) Stats 1 and 2 together are not suff

OA is B