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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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).
_________________

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.

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
_________________

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

Show Tags

01 Nov 2014, 13:36

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

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

Show Tags

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

gmatclubot

Re: What is 10 - 8 + 6 - 4 + ... - (-20) ?
[#permalink]
20 May 2016, 22:38

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...