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m22 #21

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Director
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Joined: 23 Apr 2010
Posts: 593
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Kudos [?]: 14 [0], given: 7

m22 #21 [#permalink] New post 04 Dec 2011, 06:45
00:00

Question Stats:

75% (02:43) correct 25% (03:38) wrong based on 4 sessions
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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Joined: 09 Sep 2011
Posts: 122
Location: India
Concentration: General Management, Entrepreneurship
Schools: Kellogg '15 (D), CBS '15 (D), Ross '15 (D), Anderson '15 (D), Johnson '15 (WL), McDonough '15 (M), ISB '14 (D), Olin '15 (A)
GMAT 1: 710 Q49 V38
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Kudos [?]: 68 [1] , given: 15

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Re: m22 #21 [#permalink] New post 04 Dec 2011, 11:39
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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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Director
Director
Joined: 23 Apr 2010
Posts: 593
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Kudos [?]: 14 [0], given: 7

Re: m22 #21 [#permalink] New post 05 Dec 2011, 06:19
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, 06:19
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