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# M22-21

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Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129181 [0], given: 12194

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16 Sep 2014, 01:17
Expert's post
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Difficulty:

55% (hard)

Question Stats:

60% (01:16) correct 40% (01:23) wrong based on 19 sessions

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

A. 8
B. 10
C. 12
D. 14
E. 16
[Reveal] Spoiler: OA

_________________

Kudos [?]: 129181 [0], given: 12194

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129181 [0], given: 12194

### Show Tags

16 Sep 2014, 01:17
Official Solution:

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

A. 8
B. 10
C. 12
D. 14
E. 16

We should find the value of the following expression:

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

Notice that we have 8 pairs:

$$10-8=2$$;

$$6-4=2$$;

$$2-0=2$$;

$$(-2)-(-4)=2$$;

$$(-6)-(-8)=2$$;

$$(-10)-(-12)=2$$;

$$(-14)-(-16)=2$$;

$$(-18)-(-20)=2$$;

So, the sum of each pair is 2, which makes the whole sum equal to $$8*2=16$$.

_________________

Kudos [?]: 129181 [0], given: 12194

Intern
Joined: 01 Jul 2017
Posts: 7

Kudos [?]: 0 [0], given: 167

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03 Aug 2017, 07:44
The numbers from 10 to -10 get cancelled out.
So you have to simply add up 12-14+16-18+20

Kudos [?]: 0 [0], given: 167

Re: M22-21   [#permalink] 03 Aug 2017, 07:44
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# M22-21

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