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# M22-21

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Math Expert
Joined: 02 Sep 2009
Posts: 58333

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16 Sep 2014, 01:17
00:00

Difficulty:

15% (low)

Question Stats:

78% (01:02) correct 22% (01:16) wrong based on 144 sessions

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What is the value of

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

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

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Math Expert
Joined: 02 Sep 2009
Posts: 58333

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16 Sep 2014, 01:17
Official Solution:

What is the value of

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

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 $$8*2=16$$.

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Joined: 01 Jul 2017
Posts: 6

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03 Aug 2017, 07:44
1
The numbers from 10 to -10 get cancelled out.
So you have to simply add up 12-14+16-18+20
Intern
Joined: 15 Oct 2017
Posts: 28
Schools: Northeastern '20

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07 Mar 2018, 00:33
I don't understand the question ''What is the value of 10 - 8 + 6 - 4 + ... - (-20) ?
'' it can be evrything since .. is unknow?
Math Expert
Joined: 02 Sep 2009
Posts: 58333

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07 Mar 2018, 02:12
thegame12 wrote:
I don't understand the question ''What is the value of 10 - 8 + 6 - 4 + ... - (-20) ?
'' it can be evrything since .. is unknow?

Edited to avoid confusion. Thank you.
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Intern
Joined: 15 Aug 2018
Posts: 3

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10 Oct 2018, 10:58
Cancelling pairs out works the best for me: -2,2; -10;10, -8,8 etc. It leaves you with the last 5 numbers sum of which gives you 16.
Re: M22-21   [#permalink] 10 Oct 2018, 10:58
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# M22-21

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