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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. n can be even -10, -6, -2, 2, 6, 10 n can be odd -4, -2, 0, 2, 4

-10 (+4) -6 (+4) -2 (+4) 2 (+4) 6 (+4) 10 it's a consecutive of 4, is it not? Ok then what about -9, -7, -5, -3, -1, 1, 3, 5, 7, 9 (N = 10, EVEN) is it also not a consecutive integer?

Let me get this straight, so every consecutive integer must include a 0?

Last edited by investasi on 23 Jul 2009, 19:38, edited 1 time in total.

now if the average of consecutive integers is 0, then 0 has to be the central number, because all the positive numbers will get cancelled by all the negatives, so there must be equal number of positives as the negatives on either side of 0, so zero has to be in center (median),