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.

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:

Re: Brute Force or Some Pattern [#permalink]
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). _________________

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 _________________

Hey everyone, today’s post focuses on the interview process. As I get ready for interviews at Kellogg and Tuck (and TheEngineerMBA ramps up for his HBS... ...

I got invited to interview at Sloan! The date is October 31st. So, with my Kellogg interview scheduled for this Wednesday morning, and my MIT Sloan interview scheduled...

Not all good communicators are leaders, but all leaders are good communicators. Communication is an essential tool that leaders need to use in order to get anything done. Almost...

Despite being a long weekend with Thanksgiving, this week was very tiring for me in various ways. Besides the pressure of learning materials I am not familiar with such...