m22 #21 : GMAT Problem Solving (PS)
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# m22 #21

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Director
Joined: 23 Apr 2010
Posts: 584
Followers: 2

Kudos [?]: 77 [0], given: 7

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04 Dec 2011, 05:45
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Difficulty:

(N/A)

Question Stats:

80% (02:54) correct 20% (03:38) wrong based on 5 sessions

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What is 10-8+6-4+...+(-20)?

(A) 8
(B) 10
(C) 12
(D) 14
(E) 16

Please explain how do you figure out how the sum looks like. Because I wrote the sum like this:

10 - 8 + 6 - 4 + 2 - 0 +2 -4 + 6 - 8 + 10 - 12 + 14 - 16 + 18 - 20

And I got something completely different than what's given in the question.

What's the logic behind the sum?

Thanks.
[Reveal] Spoiler: OA
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Status: Enjoying the MBA journey :)
Joined: 09 Sep 2011
Posts: 137
Location: United States (DC)
Concentration: General Management, Entrepreneurship
GMAT 1: 710 Q49 V38
WE: Corporate Finance (Other)
Followers: 19

Kudos [?]: 120 [1] , given: 16

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04 Dec 2011, 10:39
1
KUDOS
Hi

This is a simple addition/subtraction based question where the total number of digits in the expression is less and hence countable manually.
You have made a mistake considering signs on the negative side. That is the reason why your answer was different to those given in the answer options.

The expression considers all even numbers between 10 and -20 with alternate addition and subtraction of the numbers.
The numbers to be used are: 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -12, -14, -16, -18 and -20.

Now, the first term is positive and the next term is subtracted. So, the required expression becomes,

10 - 8 + 6 - 4 + 2 - 0 + (-2) - (-4) + (-6) - (-8) + (-10) - (-12) + (-14) - (-16) + (-18) - (-20)
= 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 + 12 - 14 + 16 - 18 + 20
= 78 - 62
= 16

Hence the correct answer choice is E.
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MBA Candidate 2015 | Georgetown University

Director
Joined: 23 Apr 2010
Posts: 584
Followers: 2

Kudos [?]: 77 [0], given: 7

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05 Dec 2011, 05:19
Quote:
The expression considers all even numbers between 10 and -20 with alternate addition and subtraction of the numbers.

Thanks. Got it. I think it'd be better if a couple of last numbers in the sequence were indicated.
Re: m22 #21   [#permalink] 05 Dec 2011, 05:19
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# m22 #21

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