Problem Solving

If the sum of n consecutive integer is 0, which of the following must be true?
I. n is an even number
II. n is an odd number
III. The average (arithmetic mean) of the integers is 0

I
II
III
I & II
II & III

OA is E

My answer is C.
Please explain why statement II must be true.
-10, -6, -2, 2, 6, 10 (n = 6 -> EVEN)
-9 -7 -5 -3 -1 1 3 5 7 9 (n = 10 -> EVEN)
-4, -2, 0, 2, 4 (n = 5 -> ODD)

Thanks.

The problem asks for consecutive integers only. It does not ask for consecutive even integers, consecutive odd integers, or even integers spaced apart by 4 with -10 being the least in the range.

Therefore, possible series include:

-1, 0, 1
-2, -1, 0, 1, 2
-3, -2, -1, 0, 1, 2, 3

All of these series have an odd amount of integers b/c there will always be a counterbalancing negative integer for each positive integer to the right of 0.

The answer is E.

Thanks for the explanation. I got it wrong all this time, I thought consecutive integer can be apart by any amount (+1,+2,+3,etc) as long as it's consecutive. Got to look at the exact wording next time.

kudos +1 for you