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# consecutive integer

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Intern
Joined: 02 Jan 2009
Posts: 9

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23 Jul 2009, 19:43
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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

Thanks.

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Senior Manager
Joined: 04 Jun 2008
Posts: 285

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23 Jul 2009, 19:51
n is the number OF integers, not one of the several integers, and 0 will be one of them
Intern
Joined: 02 Jan 2009
Posts: 9

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23 Jul 2009, 19:57
rashminet84 wrote:
n is the number OF integers, not one of the several integers

I understand that n is the number of integers.

-10, -6, -2, 2, 6, 10 (n = 6, or EVEN)
-4, -2, 0, 2, 4 (n = 5, or ODD)

rashminet84 wrote:
and 0 will be one of them

please explain why 0 will be one of them ?
Senior Manager
Joined: 04 Jun 2008
Posts: 285

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23 Jul 2009, 20:06
Intern
Joined: 02 Jan 2009
Posts: 9

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23 Jul 2009, 20:21
rashminet84 wrote:

-10 (+4) -6 (+4) -2 (+4) 2 (+4) 6 (+4) 10
it's a consecutive of 4, is it not?
-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, 20:38, edited 1 time in total.
Senior Manager
Joined: 04 Jun 2008
Posts: 285

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23 Jul 2009, 20:26
a consecutive list means - 1,2,3,4,..........

or -3-2-1 0 1 2 3 4.5.........

list of consecutive EVEN integers

-4 -2 0 2 4 6 .......

list of ODD consecutive integers

-5-3-1 1 3 5 7......

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),
Intern
Joined: 02 Jan 2009
Posts: 9

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23 Jul 2009, 20:53
Okay got it. thanks

Btw, this question is from OG11 PS #201

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Re: consecutive integer   [#permalink] 23 Jul 2009, 20:53
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