Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 17 Jul 2019, 02:10

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

If the sum of the first n positive integers is S, what is the sum of

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 04 Feb 2011
Posts: 48
Location: US
If the sum of the first n positive integers is S, what is the sum of  [#permalink]

Show Tags

New post 08 Mar 2011, 06:07
8
35
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (01:28) correct 36% (01:41) wrong based on 1019 sessions

HideShow timer Statistics


If the sum of the first n positive integers is S, what is the sum of the first n positive even integers, in terms of S ?

(A) S/2
(B) S
(C) 2S
(D) 2S + 2
(E) 4S
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56267
Re: If the sum of the first n positive integers is S, what is the sum of  [#permalink]

Show Tags

New post 08 Mar 2011, 06:32
7
15
Lolaergasheva wrote:
If the sum of the first n positive integers is S, what is the sum of the first n positive even integers, in terms of S ?
(A) S/2
(B) S
(C) 2S
(D) 2S + 2
(E) 4S


1+2+3+...+n=S
2+4+6+...+2n=2(1+2+3+...+n)=2S.

Or you can simply take n=2 --> 1+2=3=S --> 2+4=6=2S.

Answer: C.

Generally:
Sum of n first integers: \(1+2+...+n=\frac{1+n}{2}*n\)

Sum of n first odd numbers: \(a_1+a_2+...+a_n=1+3+...+a_n=n^2\), where \(a_n\) is the last, \(n_{th}\) term and given by: \(a_n=2n-1\). Given \(n=5\) first odd integers, then their sum equals to \(1+3+5+7+9=5^2=25\).

Sum of n first positive even numbers: \(a_1+a_2+...+a_n=2+4+...+a_n\)\(=n(n+1)\), where \(a_n\) is the last, \(n_{th}\) term and given by: \(a_n=2n\). Given \(n=4\) first positive even integers, then their sum equals to \(2+4+6+8=4(4+1)=20\).

For more check Number Theory chapter of Math Book: math-number-theory-88376.html
_________________
General Discussion
Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 704
Reviews Badge
Re: If the sum of the first n positive integers is S, what is the sum of  [#permalink]

Show Tags

New post 08 Mar 2011, 06:24
1
2
Let n = 6.
S = n(n+1)/2 = 3 * 7 = 21
Sum of first 6 even = 2 + 4 + 6 + 8 + 10 + 12 = 42 = 2S

Hence C.

Lolaergasheva wrote:
If the sum of the first n positive integers is S, what is the sum of the first n positive even integers, in terms of S ?
(A) S/2
(B) S
(C) 2S
(D) 2S + 2
(E) 4S
Director
Director
avatar
Joined: 01 Feb 2011
Posts: 629
Re: If the sum of the first n positive integers is S, what is the sum of  [#permalink]

Show Tags

New post 09 Mar 2011, 17:22
Answer is C

Given sum of 1 2 3.....n = S

sum of 2 , 4 , 6 ....2n = 2[sum(1 2 3....n) ] = 2S
Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 313
WE 1: Business Development
GMAT ToolKit User
Re: If the sum of the first n positive integers is S, what is the sum of  [#permalink]

Show Tags

New post 12 Mar 2011, 14:18
hmm... lets say the series is

{1,2,3,4,5} then S = 15
the sum of the even numbers - 6.

what am i missing?
_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56267
Re: If the sum of the first n positive integers is S, what is the sum of  [#permalink]

Show Tags

New post 12 Mar 2011, 14:30
1
Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 313
WE 1: Business Development
GMAT ToolKit User
Re: If the sum of the first n positive integers is S, what is the sum of  [#permalink]

Show Tags

New post 12 Mar 2011, 14:53
damn... got confused bc of the S.

thanks!
_________________
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9437
Location: Pune, India
Re: If the sum of the first n positive integers is S, what is the sum of  [#permalink]

Show Tags

New post 12 Mar 2011, 20:43
4
1
Lolaergasheva wrote:
If the sum of the first n positive integers is S, what is the sum of the first n positive even integers, in terms of S ?
(A) S/2
(B) S
(C) 2S
(D) 2S + 2
(E) 4S


I see that most people would solve it by taking some value of n... that's great... One suggestion - don't shy away from taking the lowest and simplest value.
I read 'sum of the first n positive integers', I say 'n = 1'... First 1 positive integer is 1 so S = 1. First 1 positive even integer will be 2 which is equal to twice of S. Only one options works out here so you are done. (In some cases, more than one option could work out e.g. if \(2S^2\) were another option. In that case you might want to check for n = 2 as well)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Re: If the sum of the first n positive integers is S, what is the sum of  [#permalink]

Show Tags

New post 09 Jan 2017, 20:02
Intern
Intern
avatar
S
Joined: 14 Oct 2016
Posts: 35
Location: India
WE: Sales (Energy and Utilities)
CAT Tests
Re: If the sum of the first n positive integers is S, what is the sum of  [#permalink]

Show Tags

New post 08 Sep 2017, 20:52
Well, this one can be solved in less than 10 secs if we know some formulas

Sum of firs n natural numbers = n(n+1)/2

Sum of first n even natural numbers = n(n+1)

Sum of first n off natural numbers is n^2

ok
we are given that n(n+1)/2=S
that means n(n+1)=2S and we know that n(n+1) is sum of first n even natural numbers . And that's the answer.
2S
_________________
Abhimanyu
Senior Manager
Senior Manager
User avatar
S
Joined: 12 Sep 2017
Posts: 295
Re: If the sum of the first n positive integers is S, what is the sum of  [#permalink]

Show Tags

New post 31 Dec 2018, 20:02
AbhimanyuDhar wrote:
Well, this one can be solved in less than 10 secs if we know some formulas

Sum of firs n natural numbers = n(n+1)/2

Sum of first n even natural numbers = n(n+1)

Sum of first n off natural numbers is n^2

ok
we are given that n(n+1)/2=S
that means n(n+1)=2S and we know that n(n+1) is sum of first n even natural numbers . And that's the answer.
2S


Hello!

Could someone mind to explain to me where do we infer that n(n+1) must be divided by 2?

I am really confused about that.

Thank you so much!
GMAT Club Bot
Re: If the sum of the first n positive integers is S, what is the sum of   [#permalink] 31 Dec 2018, 20:02
Display posts from previous: Sort by

If the sum of the first n positive integers is S, what is the sum of

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne