Find all School-related info fast with the new School-Specific MBA Forum

It is currently 10 Feb 2016, 01:36
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The sum of the first k positive integers is equal to k(k+1)/

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Director
Director
User avatar
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 649
Followers: 37

Kudos [?]: 530 [2] , given: 39

The sum of the first k positive integers is equal to k(k+1)/ [#permalink] New post 19 Jan 2012, 10:16
2
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

53% (02:44) correct 47% (01:33) wrong based on 159 sessions
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)/2 - (n+1)(n+2)/2
B. m(m+1)/2 - n(n+1)/2
C. m(m+1)/2 - (n-1)n/2
D. (m-1)m/2 - (n+1)(n+2)/2
E. (m-1)m/2 - n(n+1)/2

I got Answer B.
But OA is different.
[Reveal] Spoiler: OA

_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 31291
Followers: 5354

Kudos [?]: 62302 [0], given: 9453

Re: The sum of the first k positive integers is equal to k(k+1)/ [#permalink] New post 19 Jan 2012, 10:28
Expert's post
5
This post was
BOOKMARKED
Baten80 wrote:
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)/2 - (n+1)(n+2)/2
B. m(m+1)/2 - n(n+1)/2
C. m(m+1)/2 - (n-1)n/2
D. (m-1)m/2 - (n+1)(n+2)/2
E. (m-1)m/2 - n(n+1)/2

I got Answer B.
But OA is different.


The sum of the integers from n to m, inclusive, will be the sum of the first m positive integers minus the sum of the first n-1 integers: \(\frac{m(m+1)}{2}-\frac{(n-1)(n-1+1)}{2}=\frac{m(m+1)}{2}-\frac{(n-1)n}{2}\).

Answer: C.
_________________

New to the Math Forum?
Please read this: 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

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 31291
Followers: 5354

Kudos [?]: 62302 [2] , given: 9453

Re: The sum of the first k positive integers is equal to k(k+1)/ [#permalink] New post 19 Jan 2012, 10:34
2
This post received
KUDOS
Expert's post
Baten80 wrote:
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)/2 - (n+1)(n+2)/2
B. m(m+1)/2 - n(n+1)/2
C. m(m+1)/2 - (n-1)n/2
D. (m-1)m/2 - (n+1)(n+2)/2
E. (m-1)m/2 - n(n+1)/2

I got Answer B.
But OA is different.


Or try plug-in method: let m=4 and n=3 --> then m+n=7. Let see which option yields 7.
A. m(m+1)/2 - (n+1)(n+2)/2 = 10-10=0;
B. m(m+1)/2 - n(n+1)/2 = 10-6=4;
C. m(m+1)/2 - (n-1)n/2 = 10-3=7 --> OK;
D. (m-1)m/2 - (n+1)(n+2)/2 = 6-10=-4;
E. (m-1)m/2 - n(n+1)/2 = 6-6=0.

Answer: C.
_________________

New to the Math Forum?
Please read this: 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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 8204
Followers: 417

Kudos [?]: 111 [0], given: 0

Top 10 in overall
Re: The sum of the first k positive integers is equal to k(k+1)/ [#permalink] New post 03 Jul 2014, 01:09
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

Current Student
avatar
Joined: 03 Apr 2015
Posts: 26
Schools: ISB '16 (A)
Followers: 0

Kudos [?]: 5 [0], given: 6

Re: The sum of the first k positive integers is equal to k(k+1)/ [#permalink] New post 19 Jul 2015, 05:05
Can also be solved by using Sum of A.P formula from n to m. (A bit lengthy though)
Intern
Intern
avatar
Joined: 03 Jul 2015
Posts: 36
Followers: 0

Kudos [?]: 5 [0], given: 26

Re: The sum of the first k positive integers is equal to k(k+1)/ [#permalink] New post 13 Sep 2015, 19:04
1
This post was
BOOKMARKED
Bunuel wrote:
Baten80 wrote:
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)/2 - (n+1)(n+2)/2
B. m(m+1)/2 - n(n+1)/2
C. m(m+1)/2 - (n-1)n/2
D. (m-1)m/2 - (n+1)(n+2)/2
E. (m-1)m/2 - n(n+1)/2

I got Answer B.
But OA is different.


The sum of the integers from n to m, inclusive, will be the sum of the first m positive integers minus the sum of the first n-1 integers: \(\frac{m(m+1)}{2}-\frac{(n-1)(n-1+1)}{2}=\frac{m(m+1)}{2}-\frac{(n-1)n}{2}\).

Answer: C.

this is very effective technique to solve quickly but would you please explain this method since i can not understand this method. thnx in advance
Intern
Intern
avatar
Joined: 07 Jan 2015
Posts: 39
GPA: 3.31
WE: Science (Other)
Followers: 0

Kudos [?]: 4 [0], given: 410

The sum of the first k positive integers is equal to k(k+1)/ [#permalink] New post 16 Sep 2015, 20:52
Baten80 wrote:
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)/2 - (n+1)(n+2)/2
B. m(m+1)/2 - n(n+1)/2
C. m(m+1)/2 - (n-1)n/2
D. (m-1)m/2 - (n+1)(n+2)/2
E. (m-1)m/2 - n(n+1)/2

I got Answer B.
But OA is different.


I think this question can be solved easily by picking numbers.

Let n = 1 and m = 2

Sum of 1 integer is 1;
Sum of 2 integers is 3

So, Sum of the integers from 1 to 2 must be 3. Let's pluck N and M in the choices

A. \(\frac{2(2+1)}{2}\) - \(\frac{(1+1)(1+2)}{2}\) \(= 3 - 3 = 0\)

B. \(\frac{2(2+1)}{2}\) - \(\frac{1(1+1)}{2}\) \(= 3 - 1 = 2\)

C. \(\frac{2(2+1)}{2}\) - \(\frac{(1-1)1}{2}\) \(= 3 - 0 = 3\) Bingo!

D. \(\frac{(2-1)2}{2}\) - \(\frac{(1+1)(1+2)}{2}\) \(= 1 - 3 = -2\)

E. \(\frac{(2-1)2}{2}\) - \(\frac{1(1+1)}{2}\) \(= 1 - 1 = 0\)

Correct me if I'm wrong pls
VP
VP
avatar
Joined: 17 Jul 2014
Posts: 1054
Location: United States
GMAT 1: 550 Q39 V27
GMAT 2: 560 Q42 V26
GMAT 3: 560 Q43 V24
GPA: 3.56
Followers: 8

Kudos [?]: 112 [0], given: 82

GMAT ToolKit User Top 10 in overall CAT Tests
Re: The sum of the first k positive integers is equal to k(k+1)/ [#permalink] New post 20 Dec 2015, 17:08
I solved by picking numbers.
n=12
m=15.

only answer choice C yields a valid result.
Manager
Manager
avatar
Joined: 12 Nov 2015
Posts: 53
Followers: 0

Kudos [?]: 1 [0], given: 21

Re: The sum of the first k positive integers is equal to k(k+1)/ [#permalink] New post 20 Dec 2015, 21:14
The only thing to trick here is that we need the sum of (n-1) integers to be subtracted from the sum of m integers.
Re: The sum of the first k positive integers is equal to k(k+1)/   [#permalink] 20 Dec 2015, 21:14
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic If the sum of the first k positive integers is equal to, k(k+1)/2, Wha MathRevolution 2 25 Jan 2016, 16:40
56 Experts publish their posts in the topic The sum of all the digits of the positive integer q is equal enigma123 20 21 Jan 2012, 15:02
The sum of the first 50 positive integers is 2550 siddhans 1 17 Jul 2011, 23:54
18 Experts publish their posts in the topic If the sum of the first n positive integers is S, what is Lolaergasheva 10 08 Mar 2011, 05:07
23 Experts publish their posts in the topic The sum of the squares of the first 15 positive integers ctrlaltdel 13 15 Nov 2009, 21:34
Display posts from previous: Sort by

The sum of the first k positive integers is equal to k(k+1)/

  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 and phpBB SEO

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®.