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

It is currently 23 May 2019, 07:01

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

The sum of all the integers k such that −26 < k < 24 is

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55266
The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 20 Oct 2015, 02:58
6
27
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

72% (00:50) correct 28% (00:56) wrong based on 1270 sessions

HideShow timer Statistics

Most Helpful Expert Reply
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6206
Location: United States (CA)
Re: The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 25 Oct 2016, 17:05
6
4
Bunuel wrote:
The sum of all the integers k such that −26 < k < 24 is

(A) 0
(B) −2
(C) −25
(D) −49
(E) −51


We must determine the sum of the consecutive integers from -25 to 23, inclusive. To determine the sum we can use the formula sum = average x quantity.

To determine quantity, the number of consecutive integers, we compute the following:

quantity = largest number – smallest number + 1

quantity = 23 – (-25) + 1 = 23 + 25 + 1 = 49

Next we must determine the average. Since we have a set of evenly-spaced integers we can determine the average using the formula:

average = (largest number + smallest number)/2.

average = (-25 + 23)/2 = -2/2 = -1

Finally we can determine the sum:

sum = quantity x average

sum = 49 x -1 = -49.

Alternate solution:

We must determine the sum of the consecutive integers from -25 to 23 inclusive. However, if we add -23 and 23, the sum will be 0, and so will be the sum of -22 and 22, -21 and 21, and so on. Therefore, the sum of each of these pairs of numbers (as long as they are opposites) is 0. The only numbers left that are not paired with their opposites are -25, -24 and 0. So the sum of all the integers from -25 to 23, inclusive, is the same as the sum of -25, -24 and 0, which is (-25) + (-24) + 0 = -49.

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Most Helpful Community Reply
Intern
Intern
avatar
Joined: 29 Aug 2015
Posts: 12
Re: The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 20 Oct 2015, 07:57
4
1
The range of k is from -25 to +23. The range includes 23 pairs of opposite numbers which nullify each other and we are left with just -24 & -25, the sum of which is -49.

Answer choice D
General Discussion
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2931
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 20 Oct 2015, 05:31
3
4
Bunuel wrote:
The sum of all the integers k such that −26 < k < 24 is

(A) 0
(B) −2
(C) −25
(D) −49
(E) −51

Kudos for a correct solution.


Bunuel: I guess I have seen this question on Forum
the-sum-of-all-the-integers-k-such-that-26-k-24-is-72685.html

The sum of all the integers k such that −26 < k < 24 = SUm of all Integers from -25 to 23

SUM = (-25)+(-24)+------+(23) = (-25)+(-24)+(-23)+(-22)+------(22)+(23) = (-49)+(0) = -49

Answer: option D
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern
Intern
User avatar
Status: GMAT1:520 Q44 V18
Joined: 03 Sep 2015
Posts: 10
Location: United States
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
Re: The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 20 Oct 2015, 09:15
2
Range is given as -26<k<24 => where -26 and 24 are excluded
We can say that -23 to +23 in the range would be cancelled out..
R = {-25,-24,-23 .................+22,+23} => This would give us -25 - 24 = -49.
Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 837
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User
Re: The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 20 Oct 2015, 09:42
2
Bunuel wrote:
The sum of all the integers k such that −26 < k < 24 is

(A) 0
(B) −2
(C) −25
(D) −49
(E) −51

Kudos for a correct solution.


Since k defines a range between −26 < k < 24 we can set 0 as the reference point for the negative values and positive values.

The negative values will range from -25 to 0 whereas the positive values will range from 0-23.

We can conclude that for all but -25 and -24 the number pairs will add to 0. So we have left -25 - 24 = -49.

Answer D.
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.
Manager
Manager
User avatar
S
Joined: 30 Dec 2015
Posts: 84
GPA: 3.92
WE: Engineering (Aerospace and Defense)
Premium Member
Re: The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 09 Oct 2016, 13:05
Bunuel wrote:
The sum of all the integers k such that −26 < k < 24 is

(A) 0
(B) −2
(C) −25
(D) −49
(E) −51

Kudos for a correct solution.


a little lengthy, but prevents counting errors:

\(Sum = \frac{[25-(-23)+1]}{2} * (25 - 23) = \frac{49}{2} * (-2) = -49\)
_________________
If you analyze enough data, you can predict the future.....its calculating probability, nothing more!
Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4486
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User CAT Tests
Re: The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 24 Oct 2016, 10:59
1
Bunuel wrote:
The sum of all the integers k such that −26 < k < 24 is

(A) 0
(B) −2
(C) −25
(D) −49
(E) −51

Kudos for a correct solution.

−26 < k < 24

= -25 , -24 , -23........ k ...........23

Only -25 & - 24 will remain , all gets cancelled...


Hence answer will be -49

Answer will be (D) - 49
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 372
Re: The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 26 Oct 2016, 19:05
2
Question can be solved using sum/# = avg equation:

We know that the total number (#) is 23-(-25)+1 = 49
We also know that since 49 is odd we can pull the 25th number in the sequence and that will be the average

Thus, the equation becomes SUM/49 = -1 --> Manipulating this you will find SUM = -49
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55266
Re: The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 13 Apr 2017, 12:09
2
1
Bunuel wrote:
The sum of all the integers k such that −26 < k < 24 is

(A) 0
(B) −2
(C) −25
(D) −49
(E) −51

Kudos for a correct solution.


The sum will be: (-25)+(-24)+(-23)+...+(-1)+0+1+..+23 --> the sum of pairs -23 and 23, -22 and 22 and so on is 0 and we are left only with -25+(-24)=-49.

Or: as we have evenly spaced set: the sum will be average of the first and the last terms multiplied be the # of terms: \(\frac{-25+23}{2}*49=-49\).

Answer: D.

Hope it's clear.
_________________
Intern
Intern
avatar
B
Joined: 10 Mar 2013
Posts: 6
Re: The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 02 Jun 2017, 02:26
to find the sum of a series in AP, sum= [(1st term + last term)/2]* no. of terms

now, to find the last term of a series in AP: tn=an+(n-1)*d
where, an=1st term, n=no. of terms and d=common difference
−26 < k < 24
in this case, tn=23 an=-25 and d=1
hence n=49
sum= [(first term+last term)/2]*no. of terms=[(-25+23)/2]49=-49
Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4486
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User CAT Tests
Re: The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 02 Jun 2017, 09:18
1
Bunuel wrote:
The sum of all the integers k such that −26 < k < 24 is

(A) 0
(B) −2
(C) −25
(D) −49
(E) −51

Kudos for a correct solution.


\(−26 < k < 24\)

So, \(−26 < k < 24\) = \(−25,−24 ,−23,−22, −21..................21, 22 , 23\)

Thus, answer must be (D) −49
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern
Intern
avatar
B
Joined: 03 May 2014
Posts: 16
Re: The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 14 Jun 2017, 07:30
For me I had difficulty translating the question into meaning. The way the question is phrased implies that k is the sum of a set of integers, the value of which falls in the range of integers between -26 to 24 not that k was the range of integers itself.
Manager
Manager
User avatar
S
Joined: 21 Jul 2017
Posts: 190
Location: India
Concentration: Social Entrepreneurship, Leadership
GMAT 1: 660 Q47 V34
GPA: 4
WE: Project Management (Education)
Premium Member Reviews Badge
Re: The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 13 Sep 2017, 09:43
Sum = [(First term + Last term)/2]*total number of terms
Here first term is -25
Last term is 23
Total number of terms are 49
Intern
Intern
avatar
B
Joined: 28 Jul 2016
Posts: 8
Location: India
Concentration: Technology, International Business
WE: Project Management (Computer Hardware)
Re: The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 06 Nov 2017, 01:21
Bunuel wrote:
The sum of all the integers k such that −26 < k < 24 is

(A) 0
(B) −2
(C) −25
(D) −49
(E) −51

Kudos for a correct solution.




solved using (b-a)-1:
= (-26 - 24) - 1
= (-50)-1
= -49
Intern
Intern
avatar
B
Joined: 14 Nov 2016
Posts: 9
WE: Consulting (Consulting)
GMAT ToolKit User
Re: The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 23 Apr 2018, 20:50
I can't stop laughing on seeing a silly mistake on question like this.
Intern
Intern
avatar
Joined: 13 Feb 2019
Posts: 1
The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 11 May 2019, 15:03
We must determine the sum of the consecutive integers from -25 to -1 and from 1 to 23, then we add them together.

-25-24-23-22-21........-1 is -1( 25+24+23+22+21......2+1) or -1(1+2......+21+22+23+24+25)

Now,we have the famous formula for the sum of consecutives integers :n(n+1)/2

So, (1+2......+21+22+23+24+25)= 25(25+1)/2=325

-1* (1+2......+21+22+23+24+25)= -1* [ 25(25+1)/2]= -325 (1)

The same for:

(1+2.......+20+21+22+23)= 23(23+1)/2=276 (2)


The sum of all the integers k such that −26 < k < 24 is: (1)+ (2)

-1* [ 25(25+1)/2]+23(23+1)/2= -325+276= -49

Alternate solution:

Sum= Average*Number

average = (largest number + smallest number)/2.
Number= largest number – smallest number + 1

Sum=[23-25/2]*[23-(-25)+1]= -1*49=-49
Manager
Manager
avatar
B
Joined: 25 Sep 2018
Posts: 58
The sum of all the integers k such that −26 < k < 24 is  [#permalink]

Show Tags

New post 11 May 2019, 22:42
Bunuel wrote:
The sum of all the integers k such that −26 < k < 24 is

(A) 0
(B) −2
(C) −25
(D) −49
(E) −51

Kudos for a correct solution.


Here,
Summation from -25 to +23 is as follows:

From -23 to +23=0
-24 & -25 are left

So, the summation of (-25)+(-24)=-49

Answer is D

Posted from my mobile device
GMAT Club Bot
The sum of all the integers k such that −26 < k < 24 is   [#permalink] 11 May 2019, 22:42
Display posts from previous: Sort by

The sum of all the integers k such that −26 < k < 24 is

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.