It is currently 22 Nov 2017, 22:52

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the sum of the first k positive integers is equal to, k(k+1)/2, Wha

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

Hide Tags

Expert Post
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4352

Kudos [?]: 3057 [0], given: 0

GPA: 3.82
Premium Member CAT Tests
If the sum of the first k positive integers is equal to, k(k+1)/2, Wha [#permalink]

Show Tags

New post 25 Jan 2016, 17:40
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

49% (01:37) correct 51% (00:53) wrong based on 68 sessions

HideShow timer Statistics

If the sum of the first k positive integers is equal to, k(k+1)/2, What is the sum of the integers from n to m, inclusive, where 0<n<m?

A. (m(m+1)-(n-1)n)/2
B. (m(m+1)-(n+1)n)/2
C. (m(m-1)-(n-1)n)/2
D. (m(m-1)-(n+1)n)/2
E. (m(m+1)-(n-1)n)/4


* A solution will be posted in two days.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-sum-of-t ... 26289.html
[Reveal] Spoiler: OA

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo


Last edited by Bunuel on 27 Sep 2017, 03:21, edited 3 times in total.
Added the OA.

Kudos [?]: 3057 [0], given: 0

Manager
Manager
avatar
S
Joined: 12 Mar 2015
Posts: 103

Kudos [?]: 27 [0], given: 92

Concentration: Leadership, Finance
GPA: 3.9
WE: Information Technology (Computer Software)
Re: If the sum of the first k positive integers is equal to, k(k+1)/2, Wha [#permalink]

Show Tags

New post 26 Jan 2016, 01:06
MathRevolution wrote:
If the sum of the first k positive integers is equal to, k(k+1)/2, What is the sum of the integers from n to m, inclusive, where 0<n<m?

A. (m(m+1)-(n-1)n)/2
B. (m(m+1)-(n+1)n)/2
C. (m(m-1)-(n-1)n)/2
D. (m(m-1)-(n+1)n)/2
E. (m(m+1)-(n-1)n)/4


* A solution will be posted in two days.



1+2+3+4..+n+...+m

m(m+1)/2 - (n-1)(n-1+1)/2
= (m(m+1) - (n-1)(n))/2

Answer A

Kudos [?]: 27 [0], given: 92

Expert Post
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4352

Kudos [?]: 3057 [0], given: 0

GPA: 3.82
Premium Member CAT Tests
Re: If the sum of the first k positive integers is equal to, k(k+1)/2, Wha [#permalink]

Show Tags

New post 27 Jan 2016, 18:23
If the sum of the first k positive integers is equal to, k(k+1)/2, What is the sum of the integers from n to m, inclusive, where 0<n<m?

A. (m(m+1)-(n-1)n)/2
B. (m(m+1)-(n+1)n)/2
C. (m(m-1)-(n-1)n)/2
D. (m(m-1)-(n+1)n)/2
E. (m(m+1)-(n-1)n)/4


==> n+(n+1)+…….+(m-1)+m={1+2+…+(n-1)+n+(n+1)+…+(m-1)+m}-{1+2+…+(n-1)}=m(m+1)/2-n(n-1)/2.

Therefore, the answer is A.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 3057 [0], given: 0

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15546

Kudos [?]: 283 [0], given: 0

Premium Member
Re: If the sum of the first k positive integers is equal to, k(k+1)/2, Wha [#permalink]

Show Tags

New post 25 Aug 2017, 07:19
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

1 KUDOS received
Director
Director
avatar
P
Joined: 22 May 2016
Posts: 999

Kudos [?]: 347 [1], given: 594

Re: If the sum of the first k positive integers is equal to, k(k+1)/2, Wha [#permalink]

Show Tags

New post 26 Aug 2017, 12:01
1
This post received
KUDOS
MathRevolution wrote:
If the sum of the first k positive integers is equal to, k(k+1)/2, What is the sum of the integers from n to m, inclusive, where 0<n<m?

A. (m(m+1)-(n-1)n)/2
B. (m(m+1)-(n+1)n)/2
C. (m(m-1)-(n-1)n)/2
D. (m(m-1)-(n+1)n)/2
E. (m(m+1)-(n-1)n)/4


* A solution will be posted in two days.

If you don't know how to manipulate that particular formula, or if the manipulation takes too long, choose values.

Let n = 2 and m = 4

Find the sum of the integers from n to m, inclusive. Either

1) 2 + 3 + 4 = 9, or

2) [IF you choose numbers too far apart]: (average) * (# of terms) is

\(\frac{(2+4)}{2}\) * 3 = 9

Check answer choices with n = 2, m = 4. The one that yields 9 as the answer is correct.

The arithmetic with these numbers is quick.

Answer A. (m(m+1)-(n-1)n)/2
(4*5 - 1*2)/2 = 18/2 = 9. MATCH

I checked the others, quickly.

B. (m(m+1)-(n+1)n)/2
(20 - 6)/2 = 7. NOT a match

C. (m(m-1)-(n-1)n)/2
(12 - 1) = 11 won't work as a numerator. Move on. NOT a match

D. (m(m-1)-(n+1)n)/2
(12 - 6) = 6, already too small without division. Move on. NOT a match.

E. (m(m+1)-(n-1)n)/4
(20 - 1) = 19 won't work as a numerator. Move on. NOT a match

Answer A

Kudos [?]: 347 [1], given: 594

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133079 [0], given: 12403

Re: If the sum of the first k positive integers is equal to, k(k+1)/2, Wha [#permalink]

Show Tags

New post 27 Sep 2017, 03:21
MathRevolution wrote:
If the sum of the first k positive integers is equal to, k(k+1)/2, What is the sum of the integers from n to m, inclusive, where 0<n<m?

A. (m(m+1)-(n-1)n)/2
B. (m(m+1)-(n+1)n)/2
C. (m(m-1)-(n-1)n)/2
D. (m(m-1)-(n+1)n)/2
E. (m(m+1)-(n-1)n)/4


* A solution will be posted in two days.


OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-sum-of-t ... 26289.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 133079 [0], given: 12403

Re: If the sum of the first k positive integers is equal to, k(k+1)/2, Wha   [#permalink] 27 Sep 2017, 03:21
Display posts from previous: Sort by

If the sum of the first k positive integers is equal to, k(k+1)/2, Wha

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.