GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Nov 2018, 10:46

### 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

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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

November 17, 2018

November 17, 2018

07:00 AM PST

09:00 AM PST

Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### GMATbuster's Weekly GMAT Quant Quiz # 9

November 17, 2018

November 17, 2018

09:00 AM PST

11:00 AM PST

Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 04 Feb 2011
Posts: 53
Location: US
If the sum of the first n positive integers is S, what is  [#permalink]

### Show Tags

08 Mar 2011, 05:07
6
23
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:11) correct 36% (01:08) wrong based on 736 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
Math Expert
Joined: 02 Sep 2009
Posts: 50619
Re: p/s sum of integers  [#permalink]

### Show Tags

08 Mar 2011, 05:32
6
13
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.

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
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: 747
Re: p/s sum of integers  [#permalink]

### Show Tags

08 Mar 2011, 05:24
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
Joined: 01 Feb 2011
Posts: 664
Re: p/s sum of integers  [#permalink]

### Show Tags

09 Mar 2011, 16:22

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

sum of 2 , 4 , 6 ....2n = 2[sum(1 2 3....n) ] = 2S
Senior Manager
Joined: 08 Nov 2010
Posts: 341
Re: p/s sum of integers  [#permalink]

### Show Tags

12 Mar 2011, 13:18
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
Joined: 02 Sep 2009
Posts: 50619
Re: p/s sum of integers  [#permalink]

### Show Tags

12 Mar 2011, 13:30
1
144144 wrote:
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?

The sum of the first 5 positive integers is 1+2+3+4+5=15;
The sum of the first 5 positive even integers is 2+4+6+8+10=30=2*15 (so the second sum shouldn't be the sum of the even numbers from the first list as you did).
_________________
Senior Manager
Joined: 08 Nov 2010
Posts: 341
Re: p/s sum of integers  [#permalink]

### Show Tags

12 Mar 2011, 13:53
damn... got confused bc of the S.

thanks!
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8537
Location: Pune, India
Re: p/s sum of integers  [#permalink]

### Show Tags

12 Mar 2011, 19:43
3
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

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Current Student
Joined: 12 Aug 2015
Posts: 2633
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If the sum of the first n positive integers is S, what is  [#permalink]

### Show Tags

09 Jan 2017, 19:02
Intern
Joined: 14 Oct 2016
Posts: 30
Location: India
WE: Sales (Energy and Utilities)
Re: If the sum of the first n positive integers is S, what is  [#permalink]

### Show Tags

08 Sep 2017, 19:52
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

Non-Human User
Joined: 09 Sep 2013
Posts: 8786
Re: If the sum of the first n positive integers is S, what is  [#permalink]

### Show Tags

04 Nov 2018, 09:13
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: If the sum of the first n positive integers is S, what is &nbs [#permalink] 04 Nov 2018, 09:13
Display posts from previous: Sort by