Data Sufficiency

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

Statement 1

Take the first 5 numbers 1,2,3,4,5 sum=15 divisible by 3
Take first 7 consecutive numbers 1,2...7 sum= 28 not divisible by 3

Hence statement 1 is not sufficient

Lets continue finding the summatios

Sum of first 9 numbers = 45 -- divisible by 3

We are seeing a pattern here

when n= 5 (n-1)/2 = 2

1+2 = 3 is divisible by 3..

When n= 9 also statement B is satisfied

Hence Statement B alone is sufficient

1)just pluggin values and you will see that it is INSUFFICIENT
ex:1,2,3- avg not divisible by 3
1,2,3,4,5- avg divisible by 3

2) the numbers are in a sequence with common difference 1
sum=n/2(2a+(n-1))
=n(a+(n-1)/2)
given that a+(n-1)/2 is divisible by 3. so sum is divisible by 3

bro, It has asked for n > 1 in the question

indir0ver wrote:bro, It has asked for n > 1 in the question

Every example shown has an n value greater than 1. Remember, n is the number of terms in the set.