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# If the sum of n consecutive integers is 0, which of the

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Intern
Joined: 08 Jan 2007
Posts: 42
Followers: 1

Kudos [?]: 1 [0], given: 0

If the sum of n consecutive integers is 0, which of the [#permalink]  16 Jan 2007, 09:43
If the sum of n consecutive integers 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 n integers is 0.

A) I only
B) II only
C) III only
D) I and III
E) II and III
Intern
Joined: 15 Jan 2007
Posts: 38
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Kudos [?]: 1 [0], given: 0

E.
if sum is 0, average 0.
and if you take sample set, -1 0 1 .. n will always be odd.
Intern
Joined: 08 Jan 2007
Posts: 42
Followers: 1

Kudos [?]: 1 [0], given: 0

with even/odd, I thought 0 was even? how is it always odd?
SVP
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 98 [0], given: 0

Agree... it is (E).

cucrose, svas was actually giving an example

This is all sarting cases of such a consecutive numbers' list:
o n=1 , List = {0}
o n=3 , List = {-1, 0, 1}
o n=5 , List = {-2, -1, 0, 1, 2}

We have to preserve the symetry : each number found in one side of 0 has its opposite number present in the other side of 0.

So:
> n is always odd (min value : n=1)
> average = sum(terms) / n = 0/n = 0

Last edited by Fig on 16 Jan 2007, 11:25, edited 1 time in total.
Intern
Joined: 08 Jan 2007
Posts: 42
Followers: 1

Kudos [?]: 1 [0], given: 0

Fig, you concluded by saying:
> n is always even (min value : n=1), do u mean odd? shouldnt min value: n=-1?
SVP
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 98 [0], given: 0

cucrose wrote:
Fig, you concluded by saying:
> n is always even (min value : n=1), do u mean odd? shouldnt min value: n=-1?

Sorry.... it was of course odd .... Edited, thanks
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