It is currently 24 Feb 2018, 00:23

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

Which of the following is the sum of all the even numbers between 1 an

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

Hide Tags

Intern
Intern
avatar
Joined: 15 Feb 2015
Posts: 20
Location: United States
Concentration: General Management, Technology
GPA: 3
WE: Business Development (Manufacturing)
Which of the following is the sum of all the even numbers between 1 an [#permalink]

Show Tags

New post 12 Sep 2015, 10:16
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

78% (01:06) correct 22% (01:17) wrong based on 96 sessions

HideShow timer Statistics

Which of the following is the sum of all the even numbers between 1 and 99, inclusive?

A. 2550

B. 2450

C. 2600

D. 2499

E. 2652
[Reveal] Spoiler: OA
1 KUDOS received
Current Student
avatar
S
Joined: 20 Mar 2014
Posts: 2683
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Which of the following is the sum of all the even numbers between 1 an [#permalink]

Show Tags

New post 12 Sep 2015, 13:27
1
This post received
KUDOS
hiteshahire22 wrote:
Which of the following is the sum of all the even numbers between 1 and 99, inclusive?

A. 2550

B. 2450

C. 2600

D. 2499

E. 2652


Sum of an arithmetic series = Sn = \(\frac{n(2a+(n-1)d)}{2}\), where n = number of terms = number of even numbers between 1 and 99 = 49, d = difference between 2 consecutive even terms = 2, a = 1st term of the series = 2.

Thus Sn = \(\frac{49(2*2+(49-1)2)}{2}\) = 49*50 = a bit less than 50*50 = a bit less than 50*50 but with 0 as the unit's digit =B is the only option satisfying this.

B , 2450 is the correct answer.
Expert Post
2 KUDOS received
EMPOWERgmat Instructor
User avatar
D
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11069
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: Which of the following is the sum of all the even numbers between 1 an [#permalink]

Show Tags

New post 12 Sep 2015, 14:35
2
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
Hi hiteshahire22,

This question can be solved with "bunching."

We're asked for the SUM of all of the EVEN integers from 1 to 99, so we really want the sum of 2, 4, 6, 8.....98.

If you take the smallest and biggest numbers, you have...
2+98 = 100

If you take the next smallest and next biggest numbers, you have...
4+96 = 100

This pattern will continue on, so we're going to have a bunch of 100s, BUT we have to be careful to make sure that we don't miss a number if it's "in the middle" and doesn't get paired up. Since we know that the sum of each pair is 100, we can 'jump ahead' to find the last few pairs...

44+56 = 100
46+54 = 100
48+52 = 100
There IS a middle number: 50; this number does NOT get paired up.

Since 48 is the 24th even integer, we know there are twenty-four 100s + one 50. 2400+50 = 2450

Final Answer:
[Reveal] Spoiler:
B


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

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

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

Manager
Manager
User avatar
G
Joined: 13 Jun 2012
Posts: 185
Location: United States
WE: Supply Chain Management (Computer Hardware)
GMAT ToolKit User
Re: Which of the following is the sum of all the even numbers between 1 an [#permalink]

Show Tags

New post 12 Sep 2015, 16:07
1
This post was
BOOKMARKED
We need to find two things- Number of even terms and then Sum of all the terms.

Number of even terms= last even number - 1st even number/ spacing between two even numbers + 1. so, 98-2/2+1 = 49. now Sum of all the terms = Number of even terms * last number + 1st / 2 which is 49*99+1/2 = 2450
Intern
Intern
avatar
B
Joined: 14 Oct 2016
Posts: 30
Location: India
WE: Sales (Energy and Utilities)
Premium Member
Re: Which of the following is the sum of all the even numbers between 1 an [#permalink]

Show Tags

New post 08 Sep 2017, 23:18
There are 2 Formulas we need to know

1 Sum of even numbers <=n where n is a natural number

in case N is odd then sum is given by {(n-1)(n+1)/4}

in case N is even then sum is given by n(n+2)/4

So in our case since n=99 is odd we have (98*100/4)= 2450
_________________

Abhimanyu

Senior Manager
Senior Manager
User avatar
G
Joined: 02 Mar 2017
Posts: 271
Location: India
Concentration: Finance, Marketing
Re: Which of the following is the sum of all the even numbers between 1 an [#permalink]

Show Tags

New post 08 Sep 2017, 23:27
49*2=98
---->49 Numbers
n/2(a1+an)

49(2+98)/2
4900/2
2450
_________________

Kudos-----> If my post was Helpful

Re: Which of the following is the sum of all the even numbers between 1 an   [#permalink] 08 Sep 2017, 23:27
Display posts from previous: Sort by

Which of the following is the sum of all the even numbers between 1 an

  new topic 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®.