What is 10 - 8 + 6 - 4 + ... - (-20) ? : GMAT Problem Solving (PS)
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# What is 10 - 8 + 6 - 4 + ... - (-20) ?

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What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

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01 Apr 2012, 21:21
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What is 10 - 8 + 6 - 4 + ... - (-20) ?

A. 8
B. 10
C. 12
D. 14
E. 16
[Reveal] Spoiler: OA
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Re: Brute Force or Some Pattern [#permalink]

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01 Apr 2012, 22:12
Expert's post
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GMATPASSION wrote:
What is $$10 - 8 + 6 - 4 + ... - (-20)$$ ?

8
10
12
14
16

I solved this by brute force? Any other way.

Pair them up.

10 - 8 = 2
6 - 4 = 2
2 - 0 = 2
.
.
-18 - (-20) = 2

There are a total of 16 terms (2*5 to 2*-10 gives you 5-(-10)+1 = 16 terms) so you will get 8 pairs. Hence the sum will be 2*8 = 16
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews VP Status: Top MBA Admissions Consultant Joined: 24 Jul 2011 Posts: 1122 GMAT 1: 780 Q51 V48 GRE 1: 1540 Q800 V740 Followers: 120 Kudos [?]: 526 [1] , given: 19 Re: Brute Force or Some Pattern [#permalink] ### Show Tags 01 Apr 2012, 22:18 1 This post received KUDOS Note that 10-8 =2 and 6-4 =2. The next two terms, i.e. 2 and 0 also yield 2. Therefore the series is simply the sum of 2 over many terms. How many such terms are there? The first negative term is 8 and the last is -20, with a common difference of -4. Alternatively, we could calculate the number of terms by taking the first term as 10, the common difference as -4, and the last term as -18. -20 = 8 + (n-1) (-4) => n = 8 Therefore the answer is simply 2*8 = 16 , or option (E). _________________ GyanOne | Top MBA Rankings and MBA Admissions Blog Top MBA Admissions Consulting | Top MiM Admissions Consulting Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7076 Location: Pune, India Followers: 2088 Kudos [?]: 13299 [0], given: 222 Re: Brute Force or Some Pattern [#permalink] ### Show Tags 01 Apr 2012, 22:20 Expert's post 2 This post was BOOKMARKED GMATPASSION wrote: What is $$10 - 8 + 6 - 4 + ... - (-20)$$ ? 8 10 12 14 16 I solved this by brute force? Any other way. Or consider them as sum of 2 arithmetic progressions (though it would be much better if you see the pairing pattern) I) 10 + 6 + 2 + (-2) ....+(-18) AP with first term = 10 and common diff = -4 Sum = (8/2)(2*10 + 7*(-4)) = -32 II) -8 -4 - 0 - (-4) +..- (-20) AP with first term = -8 and common diff = 4 Sum = (8/2)(2*(-8) + 7*(4)) = 48 Sum of the series = -32 + 48 = 16 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Brute Force or Some Pattern [#permalink]

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01 Apr 2012, 22:34
Yep - I was gonna post the same reply below. there are 2 APs here, you can just sum them
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

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09 Jun 2012, 11:27

please list the whole series and how a common difference of -4 is obtained .

Sorry my limited wisdom is unable to grasp the process

as far as I can see the terms are decreasing by 2 with alternating + and - sign

so the series should continue as 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

some one please explain how common difference is - 4

please include the complete series so that we can see how this works
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

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09 Jun 2012, 11:56
3
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Expert's post
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stne wrote:

please list the whole series and how a common difference of -4 is obtained .

Sorry my limited wisdom is unable to grasp the process

as far as I can see the terms are decreasing by 2 with alternating + and - sign

so the series should continue as 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

some one please explain how common difference is - 4

please include the complete series so that we can see how this works

Here you go:

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

Notice that the odd numbered terms (1st, 3rd, 5th...) form arithmetic progression with common difference of -4 and the even numbered terms (2nd, 4th...) form arithmetic progression with common difference of 4:

The sum of the odd numbered terms is $$10+6+2+(-2)+(-6)+(-10)+(-14)+(-18)=10+6+2-2-6-10-14-18=-32$$;

The sum of the even numbered terms is $$-8-4-0-(-4)-(-8)-(-12)-(-16)-(-20)=-8-4-0+4+8+12+16+20=48$$;

Their sum is $$-32+48=16$$.

Though I wouldn't recommend to solve this question this way. It's better if you 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.

Hope it's clear.
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

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09 Jun 2012, 12:30
Bunuel wrote:
stne wrote:

please list the whole series and how a common difference of -4 is obtained .

Sorry my limited wisdom is unable to grasp the process

as far as I can see the terms are decreasing by 2 with alternating + and - sign

so the series should continue as 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

some one please explain how common difference is - 4

please include the complete series so that we can see how this works

Here you go:

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

Notice that the odd numbered terms (1st, 3rd, 5th...) form arithmetic progression with common difference of -4 and the even numbered terms (2nd, 4th...) form arithmetic progression with common difference of 4:

The sum of the odd numbered terms is $$10+6+2+(-2)+(-6)+(-10)+(-14)+(-18)=10+6+2-2-6-10-14-18=16$$;

The sum of the even numbered terms is $$-8-4-0-(-4)-(-8)-(-12)-(-16)-(-20)=-8-4-0+4+8+12+16+20=48$$;

Their sum is $$-32+48=16$$.

Though I wouldn't recommend to solve this question this way. It's better if you 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.

Hope it's clear.

Thank you , now the previous explanations make sense

Just a small typo in your answer , I think it should be - 32 instead of 16 ( addition of odd terms ) , please do edit , to prevent confusion.

I was not able to see that even and odd terms are making an AP .

as Kudos is a better way of saying thank you , so you have been awarded , will be needing more of your assistance
in the future
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

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09 Jun 2012, 12:38
1
KUDOS
stne wrote:

please list the whole series and how a common difference of -4 is obtained .

Sorry my limited wisdom is unable to grasp the process

as far as I can see the terms are decreasing by 2 with alternating + and - sign

so the series should continue as 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

some one please explain how common difference is - 4

please include the complete series so that we can see how this works

just rearrange the terms you have written with putting all the terms subtracted together and the ones added together.

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

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

Hope that helps.
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

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17 Jun 2012, 11:52
The quickest strategy for me was to pair them up and add the 2s.

10-8=2;
6-4=2;
2-0=2;
(-2)-(-4)=2;
(-6)-(-8)=2;
(-10)-(-12)=2;
(-14)-(-16)=2;
(-18)-(-20)=2;

2+2+2+2+2+2+2+2= 2*8 = 16
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

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21 Dec 2012, 06:48
GMATPASSION wrote:
What is 10 - 8 + 6 - 4 + ... - (-20) ?

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

I wrote them down and started cancelling pairs (+) against (-) then I was left with 16.

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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

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01 Nov 2014, 13:36
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

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25 Nov 2014, 07:13
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GMATPASSION wrote:
What is 10 - 8 + 6 - 4 + ... - (-20) ?

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

last term-first term/(difference) +1
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

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12 Jan 2015, 12:06
I hadn't even realised that this was a series. I thougt this was just an addition, like this:

10 - 8 + 6 - 4 + ... - (-20)
10 - 8 + 6 - 4 + x - (-20)

So, of course, I was waiting to end up with sth like 24+x and to only find one value larger that 24 in the answer options.
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Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

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20 May 2016, 22:38
If you write down all the numbers, the numbers from +10-8+6-4+2-0+(-2)-(-4)+(-6)-(-8)+(-10) is a palindrome and its sum is zero... So just focus on 12-14+16-18+20 = 20-4 = 16
Re: What is 10 - 8 + 6 - 4 + ... - (-20) ?   [#permalink] 20 May 2016, 22:38
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