sequences and series

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GmatTakerNo.1: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Sat Apr 24, 2010 8:27 am

by GmatTakerNo.1 » Mon May 03, 2010 5:31 am

Hey, can you please show me the way to answer this question with step by step explanations.

In a series of 10 consecutive integers what is the sum of the first 5 integers if the sum of the last 5 is 375?

The answer is 350.

Thank you in advance.

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Source: Beat The GMAT — Problem Solving | Mon May 03, 2010 5:31 am

clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Mon May 03, 2010 5:39 am

GmatTakerNo.1 wrote:Hey, can you please show me the way to answer this question with step by step explanations.

In a series of 10 consecutive integers what is the sum of the first 5 integers if the sum of the last 5 is 375?

The answer is 350.

Thank you in advance.

i think there are many ways to solve this
one way
x, x+1, x+2,.......x+9

mean of last 5 terms=x+7, so sum=5*(x+7)=375, and x=68
mean of first 5 terms=x+2, so sum=5*(68+2)=5*70=350

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Mon May 03, 2010 5:54 am

Let the integers be n, n+1, n+2, n+3............n + 9.
Sum of last five integers is (n+5)+(n+6)+(n+7)+(n+8)+(n+9) which is 5n+35.
Or 5n+35= 375.
Or 5n= 340.
So sum of first five integers is n+(n+1)+(n+2)+(n+3)+(n+4) = 5n+10 = 340+10 = 350

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harshavardhanc: Legendary Member; Posts: 526; Joined: Sat Feb 21, 2009 11:47 pm; Location: India; Thanked: 68 times; GMAT Score:680

by harshavardhanc » Mon May 03, 2010 6:34 am

GmatTakerNo.1 wrote:Hey, can you please show me the way to answer this question with step by step explanations.

In a series of 10 consecutive integers what is the sum of the first 5 integers if the sum of the last 5 is 375?

The answer is 350.

Thank you in advance.

another way to look at it :

->the difference of the 5th and the 6th term will be 1.
->the difference of the 4th and the 7th term will be 3.
->the difference of the 3rd and the 8th term will be 5.
->the difference of the 2nd and the 9th term will be 7.
->the difference of the 1st and the 10th term will be 9.

so the sum of the last 5 terms is greater than the sum of first 5 terms by an amount which is equal to (1+3+5+7+9) OR 25 .

P.S : sum of first n odd integers is n^2

Regards,
Harsha

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susantaiitk: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Sun Aug 10, 2008 5:36 am; Thanked: 1 times

by susantaiitk » Mon May 03, 2010 7:01 am

there is a phase shift of 5 for each number between first 5 and last 5.

take example of 1,2,3,4,5
6,7,8,9,10

hence sum of first 5 = sum of last 5 - 5*5 = 350

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sumanr84: Legendary Member; Posts: 758; Joined: Sat Aug 29, 2009 9:32 pmFollowed by: 2 members; Location: Bangalore,India; Thanked: 67 times

by sumanr84 » Mon May 03, 2010 9:00 am

Although its good to know for knowledge and you may differ in opinion, but Series questions are not asked in GMAT.

Don't put too much of your head into it.

I am on a break !!

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harshavardhanc: Legendary Member; Posts: 526; Joined: Sat Feb 21, 2009 11:47 pm; Location: India; Thanked: 68 times; GMAT Score:680

by harshavardhanc » Mon May 03, 2010 9:09 am

sumanr84 wrote:Although its good to know for knowledge and you may differ in opinion, but Series questions are not asked in GMAT.

Don't put too much of your head into it.

i'm really sorry Suman! follow the link below and see what beautiful question this is :

https://www.beatthegmat.com/post206511.html#206511

it's based on series. Although, you need not know all the concepts of progressions in this one, but still ... it will surely help if you know one or two.

Regards,
Harsha

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