It is currently 17 Oct 2017, 00:26

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Status: Retaking next month
Affiliations: None
Joined: 05 Mar 2011
Posts: 212

Kudos [?]: 177 [2], given: 42

Location: India
Concentration: Marketing, Entrepreneurship
GMAT 1: 570 Q42 V27
GPA: 3.01
WE: Sales (Manufacturing)
What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

### Show Tags

01 Apr 2012, 22:21
2
KUDOS
11
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

72% (01:31) correct 28% (01:24) wrong based on 371 sessions

### HideShow timer Statistics

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

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

Kudos [?]: 177 [2], given: 42

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7668

Kudos [?]: 17320 [0], given: 232

Location: Pune, India
Re: Brute Force or Some Pattern [#permalink]

### Show Tags

01 Apr 2012, 23:12
Expert's post
3
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.

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
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17320 [0], given: 232 VP Status: Top MBA Admissions Consultant Joined: 24 Jul 2011 Posts: 1347 Kudos [?]: 641 [1], given: 20 GMAT 1: 780 Q51 V48 GRE 1: 1540 Q800 V740 Re: Brute Force or Some Pattern [#permalink] ### Show Tags 01 Apr 2012, 23:18 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 Kudos [?]: 641 [1], given: 20 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7668 Kudos [?]: 17320 [0], given: 232 Location: Pune, India Re: Brute Force or Some Pattern [#permalink] ### Show Tags 01 Apr 2012, 23:20 Expert's post 4 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

Veritas Prep Reviews

Kudos [?]: 17320 [0], given: 232

Senior Manager
Joined: 02 Feb 2009
Posts: 374

Kudos [?]: 158 [0], given: 27

Concentration: General Management, Strategy
GMAT 1: 690 Q48 V35
GMAT 2: 730 Q49 V42
Re: Brute Force or Some Pattern [#permalink]

### Show Tags

01 Apr 2012, 23:34
Yep - I was gonna post the same reply below. there are 2 APs here, you can just sum them
_________________

Latest Blog Entry:
09-05-13 Its been too long ... Updates & the Tuck Loan

Kudos [?]: 158 [0], given: 27

Senior Manager
Joined: 27 May 2012
Posts: 399

Kudos [?]: 85 [0], given: 478

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

### Show Tags

09 Jun 2012, 12:27

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
_________________

- Stne

Kudos [?]: 85 [0], given: 478

Math Expert
Joined: 02 Sep 2009
Posts: 41872

Kudos [?]: 128492 [4], given: 12179

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

### Show Tags

09 Jun 2012, 12:56
4
KUDOS
Expert's post
2
This post was
BOOKMARKED
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.
_________________

Kudos [?]: 128492 [4], given: 12179

Senior Manager
Joined: 27 May 2012
Posts: 399

Kudos [?]: 85 [0], given: 478

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

### Show Tags

09 Jun 2012, 13:30
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
_________________

- Stne

Kudos [?]: 85 [0], given: 478

Manager
Joined: 12 May 2012
Posts: 80

Kudos [?]: 115 [1], given: 14

Location: India
Concentration: General Management, Operations
GMAT 1: 650 Q51 V25
GMAT 2: 730 Q50 V38
GPA: 4
WE: General Management (Transportation)
Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

### Show Tags

09 Jun 2012, 13:38
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.

Kudos [?]: 115 [1], given: 14

Intern
Joined: 04 Apr 2011
Posts: 10

Kudos [?]: [0], given: 3

Schools: Sloan '16
Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

### Show Tags

17 Jun 2012, 12:52
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

Kudos [?]: [0], given: 3

Senior Manager
Joined: 13 Aug 2012
Posts: 459

Kudos [?]: 539 [0], given: 11

Concentration: Marketing, Finance
GPA: 3.23
Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

### Show Tags

21 Dec 2012, 07:48
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.

_________________

Impossible is nothing to God.

Kudos [?]: 539 [0], given: 11

Intern
Joined: 25 Nov 2014
Posts: 2

Kudos [?]: 2 [1], given: 0

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

### Show Tags

25 Nov 2014, 08:13
1
KUDOS
1
This post was
BOOKMARKED
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

Kudos [?]: 2 [1], given: 0

Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 437

Kudos [?]: 139 [0], given: 169

Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

### Show Tags

12 Jan 2015, 13:06
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.

Kudos [?]: 139 [0], given: 169

Manager
Joined: 11 Apr 2016
Posts: 54

Kudos [?]: 7 [0], given: 15

Location: India
Concentration: Marketing, Technology
Re: What is 10 - 8 + 6 - 4 + ... - (-20) ? [#permalink]

### Show Tags

20 May 2016, 23:38
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

Kudos [?]: 7 [0], given: 15

SVP
Joined: 12 Sep 2015
Posts: 1793

Kudos [?]: 2443 [0], given: 356

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

### Show Tags

18 Apr 2017, 16:28
Expert's post
Top Contributor
1
This post was
BOOKMARKED
GMATPASSION wrote:
What is 10 - 8 + 6 - 4 + ... - (-20) ?

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

Some strategically-places brackets helps here.

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)]
= [2] + [2] + [2] + [2] + [2] + [2] + [2] + [2]
= 16

[Reveal] Spoiler:
E

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Kudos [?]: 2443 [0], given: 356

Re: What is 10 - 8 + 6 - 4 + ... - (-20) ?   [#permalink] 18 Apr 2017, 16:28
Display posts from previous: Sort by