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# Inequality - Sum of numbers

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Manager
Joined: 06 Apr 2010
Posts: 143
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Inequality - Sum of numbers [#permalink]

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27 Aug 2010, 23:09
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50% (00:00) correct 50% (00:00) wrong based on 2 sessions

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The sum of all the integers k such that –26 < k < 24 is
A. 0
B. -2
C. -25
D. -49
E. -51

What is the trap here...I am getting answer as -51 where as OA is diff.
[Reveal] Spoiler: OA
Manager
Joined: 09 Jun 2010
Posts: 116
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Kudos [?]: 103 [0], given: 1

Re: Inequality - Sum of numbers [#permalink]

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28 Aug 2010, 07:11
-25------------------0-----------------23

values upto + 23 cancels out & we are left with only -25 & -24 sum of which is - 49. hence option D.

Since this is in equality we dont consider -26 and 24 as values of K. K is greater than -26 & less than +24 therefore range of K is -25 to 23. You might be considering -26 & 24, in that case the range becomes -26 to +24 and the answer will be 51 which is wrong.
Math Expert
Joined: 02 Sep 2009
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Re: Inequality - Sum of numbers [#permalink]

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28 Aug 2010, 07:21
udaymathapati wrote:
The sum of all the integers k such that –26 < k < 24 is
A. 0
B. -2
C. -25
D. -49
E. -51

What is the trap here...I am getting answer as -51 where as OA is diff.

Note that the range is not inclusive: k can not be -26 or 24! That's why you are getting -51.

The sum will be: (-25)+(-24)+(-23)+...+(-1)+0+1+..+23 --> the sum of pairs -23 and 23, -22 and 22 and so on is 0 and we are left only with -25+(-24)=-49.

Or: as we have evenly spaced set: the sum will be average of the first and the last terms multiplied be the # of terms: $$\frac{-25+23}{2}*49=-49$$.

Hope it's clear.
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Re: Inequality - Sum of numbers   [#permalink] 28 Aug 2010, 07:21
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