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# Magoosh Brain Twister: Series Fun – Explanation

## Question

Here’s the question from Monday:

The sum of m consecutive integers is 8. If the sum of n consecutive integers is m, what is the value of n?
(A) 15
(B) 16
(C) 31
(D) 32
(E) Cannot be determined by the information provided.

## Answer and Explanation

The trick here is taking into account negative numbers. Anytime you sum negative integers and end with a positive integer that is equal to the absolute value of the lowest number, you get zero. For instance, if I add -2 + -1 + 0 + 1 + 2, I get zero. Using this logic, I can figure out that a bunch of consecutive numbers that sum to 8 must start at -7, since all the numbers up to, and including, 7 will cancel out to zero, leaving 8 (meaning the series sums to 8).

Counting all the integers from -7 to 8, inclusive, can be a little bit tricky, because we will have to include zero. Doing so, gives us 16, the value of m. So now, which consecutive integers sum to 16? Using the same logic, we can see that the series would have to start at -15 so that all the digits are canceled out, leaving us with 16. That gives us a total of 32 digits (donโt forget the zero!). Answer: (D)

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### 6 Responses to Magoosh Brain Twister: Series Fun – Explanation

1. hossein October 7, 2014 at 1:23 am #

thanks for the try-error solution.
but it should a formulated solution available too.

2. RISHABH September 30, 2014 at 7:37 pm #

Hi Chris,
I am a student from India and in my final year of engineering. I decided to continue my studies by going for MS about two months ago. There were a lot many sites, materials and guides that i found online. But nothing compared to MAGOOSH. If it wasn’t for your 90-day study plan, the vocab rich wednesdays and this amazing blog I don’t think i would have secured anything north of 320. I gave my gre yesterday and got 327 (V:157 Q:170).
A great part of this success lies with all the work the MAGOOSH team has done. God knows how weak i was particularly in vocab. But the apps you guys have provided us with are just another boon for people like me. I would also like to congratulate the whole MAGOOSH team for the new app you guys have come up with. It really looks and feels great… and being a MAGOOSH app the content is obviously awesome.

I would like to sincerely thank you for all your fantastic efforts and amazing support. If it wasn’t for you guys, I would still be panicking about things..

Wish you even greater highs and achievements… Keep up the good work..

Thank you thank you thank you !!!!

• Chris Lele October 2, 2014 at 2:47 pm #

Wow, thanks! That really made my day :). I’ll pass on your words to the rest of the team.

Congrats on your great accomplishment and I’m happy that we are able to play a role in your success!

Good luck ๐

3. payal September 25, 2014 at 9:47 am #

I have a doubt.
For eg if a question like m consecutive integers has m=1 as one of its solution so does it translates to 1 consecutive integer meaning a single integer or is it invalid.

• Chris Lele September 25, 2014 at 10:01 am #

Hi Payal,

Interpreting the phrase “consecutive integers” as one integer is not valid. One integer is neither consecutive (which implies more than one), nor “integers” (it is an integer).

Hope that helps ๐

• payal September 25, 2014 at 11:14 am #

Thanks.
When you put it that way it makes sense.

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