The Sum of first N consecutive odd integers is N^2. What is : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 23 Jan 2017, 18:02

### 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 June
Open Detailed Calendar

# The Sum of first N consecutive odd integers is N^2. What is

Author Message
TAGS:

### Hide Tags

Manager
Joined: 21 Jul 2006
Posts: 83
Followers: 1

Kudos [?]: 24 [4] , given: 0

The Sum of first N consecutive odd integers is N^2. What is [#permalink]

### Show Tags

02 Aug 2006, 16:34
4
KUDOS
20
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:36) correct 34% (01:48) wrong based on 556 sessions

### HideShow timer Statistics

The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 39 inclusive.

A. 351
B. 364
C. 410
D. 424
E. 450
[Reveal] Spoiler: OA
Manager
Joined: 25 Jul 2006
Posts: 99
Followers: 1

Kudos [?]: 11 [0], given: 0

### Show Tags

02 Aug 2006, 16:40
B....

1- 11 are the first 6 odd intergers; sum = 6^2 = 36

1- 39 are the first 20 odd intergers; sum = 400

sum of odd nos frm 13- 39 = 400-36 = 364
Manager
Joined: 09 Apr 2006
Posts: 173
Location: Somewhere in Wisconsin!
Followers: 1

Kudos [?]: 3 [0], given: 0

### Show Tags

02 Aug 2006, 18:44
Use AP and you woudn't need the supplied formula:

a(1) = 13; a(n) = a(1) + (n-1)d = 39 (where d =2).
Sum = n/2[a(1) + a(n)] = 364, where n = 14
_________________

Thanks,
Zooroopa

SVP
Joined: 30 Mar 2006
Posts: 1737
Followers: 1

Kudos [?]: 78 [0], given: 0

### Show Tags

02 Aug 2006, 22:24
Number of odd numbers from 1-39 = 39+1/2 = 20
Sum = 400

Number of odd numbers between = 1-12 = (12 - 1 +1)/2 = 6
sum = 36

Sum between 13-39 inclusive = 400 - 36 = 364
Manager
Joined: 26 Jun 2006
Posts: 152
Followers: 1

Kudos [?]: 6 [0], given: 0

### Show Tags

03 Aug 2006, 08:03
I also used AP without using N^2 condition. For me, sometimes, it is easeir to just stick to basics and do the calcs. This way, at least, I know I will arrive at the correct answer sooner or later...
Director
Joined: 28 Dec 2005
Posts: 755
Followers: 1

Kudos [?]: 14 [0], given: 0

### Show Tags

03 Aug 2006, 23:41
I would suggest using the formula, for the simple reason that instead of an AP the problem might refer to some fancy formula for an unknown sequence of numbers.

Anyway here we go...

For odd integers till 39, number of integers = 20
Sum = 20^2 = 400
For odd integers till (but not including 13), number of integers = 6
Sum = 6^2 = 36
Difference = 364 = B
VP
Joined: 29 Dec 2005
Posts: 1348
Followers: 10

Kudos [?]: 60 [0], given: 0

Re: PS : Number Prop. [#permalink]

### Show Tags

04 Aug 2006, 05:43
ghantark wrote:
The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 39 inclusive.

351
364
410
424
450

OA later

i never knew this formulea that sum of n consecutive odd integers = n^2.
however, we can use regular formula:
the sum of consecutive odd integers from 13-39 = n (L-s)/2 = [{(39-13)/2} +1][39-13] = 14 x 26 = 364
Manager
Joined: 09 Apr 2006
Posts: 173
Location: Somewhere in Wisconsin!
Followers: 1

Kudos [?]: 3 [0], given: 0

Re: PS : Number Prop. [#permalink]

### Show Tags

05 Aug 2006, 00:03
Professor wrote:
ghantark wrote:
The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 39 inclusive.

351
364
410
424
450

OA later

i never knew this formulea that sum of n consecutive odd integers = n^2.
however, we can use regular formula:
the sum of consecutive odd integers from 13-39 = n (L-s)/2 = [{(39-13)/2} +1][39-13] = 14 x 26 = 364

It can be derived from the regular formula for A.P.

1+3+5+....=n/2[2.1+(n-1).2] = n^^2 !!
_________________

Thanks,
Zooroopa

Manager
Joined: 20 Mar 2006
Posts: 200
Followers: 1

Kudos [?]: 3 [0], given: 0

Re: PS : Number Prop. [#permalink]

### Show Tags

05 Aug 2006, 14:37
ghantark wrote:
The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 39 inclusive.

351
364
410
424
450

OA later

Sum of odd integers from 1 to 39 inclusive = 20^2=400
sum of odd integers from 1 to 11 inclusive = 6^2 = 36
therfore sum of odd integers between 13 and 39 incl = 400 -36 = 364

Hence B

Heman
Senior Manager
Joined: 23 Oct 2010
Posts: 386
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 21

Kudos [?]: 326 [1] , given: 73

Re: The Sum of first N consecutive odd integers is N^2. What is [#permalink]

### Show Tags

07 Jun 2012, 00:58
1
KUDOS
I method -
the sum of odd numbers till 39(inclusive) =n^2=20^2

the sum of odd numbers till 11 (inclusive) =n^2=6^2

20^2 -6^2=(20-6)(20+6)=26*14=364

================

II method
n* (a1+an)/2
n=((39-13)/2)+1=14

(39+13)/2* 14=26*14=364
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 98
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
Followers: 0

Kudos [?]: 21 [0], given: 144

Re: The Sum of first N consecutive odd integers is N^2. What is [#permalink]

### Show Tags

21 Jan 2015, 17:44
ghantark wrote:
The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 39 inclusive.

A. 351
B. 364
C. 410
D. 424
E. 450

from the question I see that it ask about the sum of odd numbers between 13 and 39 not from 13 to 39 therefore, 13 and 39 are not includes in the sum.So, there are 20 odd numbers from 1 to 39 so 20^2 = 400 and from 1 to 13 there are 7 odd numbers so it will be 7^2=49
400-49=351

if I am no right what will be the answer if the question was ask about the sum of odd numbers from 13 to 39
_________________

Click +1 Kudos if my post helped

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 8336
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 382

Kudos [?]: 2473 [0], given: 163

Re: The Sum of first N consecutive odd integers is N^2. What is [#permalink]

### Show Tags

21 Jan 2015, 18:59
Expert's post
3
This post was
BOOKMARKED
Hi All,

These types of "sum of a sequence" questions can be approached in a number of different ways - you can use various formulas or you can approach this prompt by pattern-matching and minimizing the math that you have to do. For this question, you can use "bunching"....

We're dealing with a sequence of CONSECUTIVE ODD INTEGERS: 13 to 39, inclusive. We're asked for the SUM of this group.

1) Start with the sum of the smallest and the biggest: 13 + 39 = 52
2) Now look at the 'next smallest' and the 'next biggest': 15 + 37 = 52

From this, you can see that you're just going to be adding up a bunch of 52s. We DO have to check to see if there's a "middle" term in this sequence that doesn't get "bunched" though. To determine if that middle term exists, we just have find the last few 52s in the group....

21 and 31
23 and 29
25 and 27

Now we have proof that there is no middle term. We have 7 bunches of 52.

7(52) = 364

[Reveal] Spoiler:
B

GMAT assassins aren't born, they're made,
Rich
_________________

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1858 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 47 Kudos [?]: 1937 [1] , given: 193 Re: The Sum of first N consecutive odd integers is N^2. What is [#permalink] ### Show Tags 22 Jan 2015, 02:13 1 This post received KUDOS 23a2012 wrote: ghantark wrote: The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 39 inclusive. A. 351 B. 364 C. 410 D. 424 E. 450 from the question I see that it ask about the sum of odd numbers between 13 and 39 not from 13 to 39 therefore, 13 and 39 are not includes in the sum.So, there are 20 odd numbers from 1 to 39 so 20^2 = 400 and from 1 to 13 there are 7 odd numbers so it will be 7^2=49 400-49=351 if I am no right what will be the answer if the question was ask about the sum of odd numbers from 13 to 39 Its asking sum of odd integers between 13 and 39 inclusive, so we require to minus sum of odd integers up to 11 inclusive $$= 20^2 - 6^2 = 26 * 14 = 364$$ Answer = B _________________ Kindly press "+1 Kudos" to appreciate Manager Status: Kitchener Joined: 03 Oct 2013 Posts: 98 Location: Canada Concentration: Finance, Finance GPA: 2.9 WE: Education (Education) Followers: 0 Kudos [?]: 21 [0], given: 144 Re: The Sum of first N consecutive odd integers is N^2. What is [#permalink] ### Show Tags 22 Jan 2015, 15:23 ghantark wrote: The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 39 inclusive. A. 351 B. 364 C. 410 D. 424 E. 450 Thank you for EMPOWERgmatRichC and PareshGmat But I still do not understand what will be the answer if the question was ask about the sum of odd numbers from 13 to 39 and why we do not includ 13? _________________ Click +1 Kudos if my post helped EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8336 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 382 Kudos [?]: 2473 [0], given: 163 Re: The Sum of first N consecutive odd integers is N^2. What is [#permalink] ### Show Tags 22 Jan 2015, 16:37 Hi 23a2012, My explanation (and everyone else's too) includes 13 and 39 in the sum. The prompt uses the phrase "ALL odd integers between 13 and 39, INCLUSIVE." This means that we have to INCLUDE 13 and 39 and all of the explanations do that. GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13526
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: The Sum of first N consecutive odd integers is N^2. What is [#permalink]

### Show Tags

24 Apr 2016, 00:23
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.
_________________
Senior Manager
Joined: 23 Apr 2015
Posts: 339
Location: United States
WE: Engineering (Consulting)
Followers: 5

Kudos [?]: 70 [0], given: 36

Re: The Sum of first N consecutive odd integers is N^2. What is [#permalink]

### Show Tags

23 Aug 2016, 20:27
ghantark wrote:
The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 39 inclusive.

A. 351
B. 364
C. 410
D. 424
E. 450

The numbers to be added are 13,15,...39. These are in Arithmetic progression with difference as 2.

a1 (first term) = 13
d = 2
N (number of terms)= $$\frac{(39-13)}{2} + 1 = 14$$
Sum = $$\frac{N}{2} *(2*a1 + (N-1)*d)$$
= $$\frac{14}{2} *(2*13 + (14-1)2)$$
= 364

+1 for Kudos
Intern
Joined: 30 Mar 2015
Posts: 7
Followers: 0

Kudos [?]: 0 [0], given: 2

Re: The Sum of first N consecutive odd integers is N^2. What is [#permalink]

### Show Tags

18 Sep 2016, 10:54
what if the question was exlusive instead of inclusive ?
can you please show me the difference ?
I have tried to do it but i got confused should i remove 1 and 39 or just one of them
Thank you :D
Re: The Sum of first N consecutive odd integers is N^2. What is   [#permalink] 18 Sep 2016, 10:54
Similar topics Replies Last post
Similar
Topics:
7 If n is a positive integer and (n+1)(n+3) is odd, then (n+2)(n+4) must 3 21 Jul 2016, 11:45
7 If the sum of the first n positive odd integers is n^2, what is the su 3 02 Dec 2015, 04:27
16 What is the value of n if the sum of the consecutive odd 6 05 Nov 2013, 03:15
32 If the sum of the first n positive integers is S, what is 11 08 Mar 2011, 05:07
16 If the sum of n consecutive positive integers is 33, what of 12 10 Dec 2010, 06:58
Display posts from previous: Sort by