It is currently 23 Jan 2018, 20:03

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

The sum of the first 100 even positive integers – divided by the sum o

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

Hide Tags

1 KUDOS received
Current Student
User avatar
Joined: 12 Aug 2015
Posts: 297
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
The sum of the first 100 even positive integers – divided by the sum o [#permalink]

Show Tags

New post 23 Jan 2016, 06:09
1
This post received
KUDOS
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

60% (01:15) correct 40% (01:07) wrong based on 242 sessions

HideShow timer Statistics

The sum of the first 100 even positive integers – divided by the sum of the next 100 even positive integers – is equal to which of the following?

A. 1/3
B. 101/ 301
C. 51/151
D. 1/2
E. 1
[Reveal] Spoiler: OA

_________________

KUDO me plenty

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 11 Nov 2014
Posts: 358
Location: India
Concentration: Finance, International Business
WE: Project Management (Telecommunications)
GMAT ToolKit User Premium Member
Re: The sum of the first 100 even positive integers – divided by the sum o [#permalink]

Show Tags

New post 23 Jan 2016, 07:40
1
This post received
KUDOS
The first 100 positive numbers are
2, 4, 6, ....198, 200.
If we make 50 pairs made by the first and the last, second and the second last, we get:
2+200 + 4+198 + 6+196 + ... + 100+102
=50*(202)
=10100

same
202 - 400 = 30100

so 101/301

Ans B
Expert Post
1 KUDOS received
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5548
Re: The sum of the first 100 even positive integers – divided by the sum o [#permalink]

Show Tags

New post 23 Jan 2016, 08:03
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
shasadou wrote:
The sum of the first 100 even positive integers – divided by the sum of the next 100 even positive integers – is equal to which of the following?

A. 1/3
B. 101/ 301
C. 51/151
D. 1/2
E. 1


Hi,
i will tell you a simpler way of doing these Qs..

Remember sum of consecutive numbers can eb found by finding average of these numbers * total number..

sum of the first 100 even positive integers= first even integer=2, and 100th even integer=200..
\(sum = \frac{{2+200}}{2}*100=101*100\)..

sum of the next 100 even positive integers= first even integer=202, and 100th even integer=400..
\(sum = \frac{{202+400}}{2}*100=301*100\)..

answer \(=\frac{{101*100}}{{301*100}}= \frac{101}{301}\)

B
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


BANGALORE/-

1 KUDOS received
Intern
Intern
avatar
Joined: 09 Apr 2016
Posts: 35
Re: The sum of the first 100 even positive integers – divided by the sum o [#permalink]

Show Tags

New post 09 Dec 2016, 06:01
1
This post received
KUDOS
Sum of the first even integers: n(n+1)

Sum of the first 100-even integers: 100(101) = 10100
Sum of the first 200-even integers: 200(201) = 40200
Sum of the the even integers between the first 100 and the first 200: 40200-10100 = 30100

--> 10100/30100
2 KUDOS received
Manager
Manager
User avatar
S
Joined: 24 Jan 2017
Posts: 58
Location: Philippines
Concentration: International Business, Social Entrepreneurship
GMAT 1: 760 Q51 V41
GPA: 3.53
WE: Sales (Manufacturing)
The sum of the first 100 even positive integers – divided by the sum o [#permalink]

Show Tags

New post 28 Jul 2017, 19:27
2
This post received
KUDOS
First 100 even integers: 2...200
Sum of first 100 even integers: (a1+an)n/2 = (2+200)*100/2=202*50
Next 100 even integers: 202~400
Sum of next 100 even integers: (a1+an)n/2 = (202+400)*100/2=602*50
Ratio of the sums: 202/402 = 101/301
1 KUDOS received
Director
Director
User avatar
P
Joined: 13 Mar 2017
Posts: 561
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: The sum of the first 100 even positive integers – divided by the sum o [#permalink]

Show Tags

New post 28 Jul 2017, 21:52
1
This post received
KUDOS
shasadou wrote:
The sum of the first 100 even positive integers – divided by the sum of the next 100 even positive integers – is equal to which of the following?

A. 1/3
B. 101/ 301
C. 51/151
D. 1/2
E. 1


Sum of first 100 even positive integers = 2 + 4 +6 +8 +.... + 200 = 2(1+2+3+4+..... +100) = 2* (100*101/2) = 100*101
Sum of next 100 even positive integers = 202 + 204 +206 +..... +400 = 2 (101 + 102 + ... + 200) = 2 ((1+2+3+.....+200)-(1+2+3+...+100))
= 2 [200* 201/2 - 100*101/2] = 200*201 - 100*101

Ratio = 100*101/ (200*201 - 100*101)= 101/(402 - 101) = 101/301

Answer B
_________________

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

Intern
Intern
avatar
B
Joined: 30 May 2013
Posts: 29
GMAT 1: 600 Q50 V21
Reviews Badge
Re: The sum of the first 100 even positive integers – divided by the sum o [#permalink]

Show Tags

New post 28 Jul 2017, 22:25
shasadou wrote:
The sum of the first 100 even positive integers – divided by the sum of the next 100 even positive integers – is equal to which of the following?

A. 1/3
B. 101/ 301
C. 51/151
D. 1/2
E. 1


Ans(B) 101/301

Given that, p = (2+4+6.....+200 ) [First 100 Terms] / (202+204....+400) [Next 100 Terms]
p= 2(1+2+...+100) / 2 ( 101+ 102+200)
P= (1+2+....+100) / (101+102+...+200) ( Cancelling out 2)
After this we can, we can solve this using 2 methods.
Method1:
To calculate the sum of a continuous series, with a same difference between any two continuous numbers, simply take the average of first & last number and multiple it by the number of terms. For ex : 4+7+10+13= (average of 13&4, multiplied by 4) = 8.5*4 = 34
Now in the original problem,
p = Average of (1&100)*100 / Average of (101&200)*100
p=(1+100)/(101+200) (Cancelling out 2, not shown here)
p=101/301 Answer.

Method2: [This is a formula dependent approach and lengthy one also]
For Equation, P= (1+2+....+100) / (101+102+...+200)
We can use the formula for the sum of first "n" natural numbers : S= n(n+1)/2. But this formula works when the series starts from 1.
So, using this formula, we can calculate the sum for the numerator part of the above equation.
But for denominator, first we need to calculate the some of 200 numbers and then subtract the sum of first 100.
And this double calculation makes this approach slightly lengthy.

Thanks!
Manager
Manager
User avatar
B
Joined: 30 Apr 2017
Posts: 88
Re: The sum of the first 100 even positive integers – divided by the sum o [#permalink]

Show Tags

New post 02 Nov 2017, 13:55
paidlukkha wrote:
The first 100 positive numbers are
2, 4, 6, ....198, 200.
If we make 50 pairs made by the first and the last, second and the second last, we get:
2+200 + 4+198 + 6+196 + ... + 100+102
=50*(202)
=10100

same
202 - 400 = 30100

so 101/301

Ans B



why don't we use 0?
isn't it even integer??
Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43380
Re: The sum of the first 100 even positive integers – divided by the sum o [#permalink]

Show Tags

New post 02 Nov 2017, 20:28
2
This post received
KUDOS
Expert's post
soodia wrote:
paidlukkha wrote:
The first 100 positive numbers are
2, 4, 6, ....198, 200.
If we make 50 pairs made by the first and the last, second and the second last, we get:
2+200 + 4+198 + 6+196 + ... + 100+102
=50*(202)
=10100

same
202 - 400 = 30100

so 101/301

Ans B



why don't we use 0?
isn't it even integer??


"The sum of the first 100 even positive integers..."

Yes, 0 is an even integer but it's neither positive nor negative.
_________________

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

Re: The sum of the first 100 even positive integers – divided by the sum o   [#permalink] 02 Nov 2017, 20:28
Display posts from previous: Sort by

The sum of the first 100 even positive integers – divided by the sum o

  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®.