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Inequality - Sum of numbers

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Manager
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Inequality - Sum of numbers [#permalink] New post 27 Aug 2010, 22:09
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A
B
C
D
E

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100% (00:00) correct 0% (00:00) wrong based on 1 sessions
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
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Re: Inequality - Sum of numbers [#permalink] New post 28 Aug 2010, 06:11
-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.
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Re: Inequality - Sum of numbers [#permalink] New post 28 Aug 2010, 06:21
Expert's post
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.

Answer: D.

Hope it's clear.
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Re: Inequality - Sum of numbers   [#permalink] 28 Aug 2010, 06:21
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