GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 23 Jan 2020, 11:00

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 the first 100 positive integers is 5,050. What is the sum

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
S
Joined: 26 Nov 2018
Posts: 96
Location: Bangladesh
Concentration: Technology, Entrepreneurship
GPA: 3.3
WE: Manufacturing and Production (Manufacturing)
GMAT ToolKit User
The sum of the first 100 positive integers is 5,050. What is the sum  [#permalink]

Show Tags

New post Updated on: 21 Sep 2019, 03:47
2
7
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

76% (01:09) correct 24% (01:27) wrong based on 148 sessions

HideShow timer Statistics

The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?

A. 10,000
B. 10,200
C. 15,050
D. 20,050
E. 20,100

PS85402.01

Originally posted by Rashed12 on 11 Mar 2019, 03:13.
Last edited by Bunuel on 21 Sep 2019, 03:47, edited 2 times in total.
Renamed the topic and edited the question.
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8335
Re: The sum of the first 100 positive integers is 5,050. What is the sum  [#permalink]

Show Tags

New post 11 Mar 2019, 04:32
3
1
Rashed12 wrote:
If the sum of the first 100 positive integers is 5050 then what is the sum of the first 200 positive integers?

A. 10,000
B. 10,200
C. 15,050
D. 20,050
E. 20,100



Various ways..
1) making use of the info in the question..
Sum of first 100 positive integers =5050. Now 101 to 200, each term will be 100 more than a certain term in 1 to 100. For example, 101 is 100 more than 1, 102 is again 100 more than 2... And so on till 200 is 100 more than 100.... Thus, Sum of 101 to 200 will be sum of 1 to 100+100*100=5050+10000=15050..
Sum of all 1 to 200 = 5050+15050=20,100.
2) Average
Average of 1 to 200 is middle of 100 and 101, so 100.50, thus sum = 200*100.50=20,100.
3) Sum = \(200*\frac{1+200}{2}\)=200*100.50=20,100.

E
_________________
Intern
Intern
avatar
B
Joined: 06 Dec 2017
Posts: 14
GMAT ToolKit User
Re: The sum of the first 100 positive integers is 5,050. What is the sum  [#permalink]

Show Tags

New post 13 Mar 2019, 10:50
1
Sum of first n consecutive numbers, = n/2(n+1)
SUm of first 10 consecutive numbers = 5*11 = 55
SUm of first 100 consecutive numbers = 50*101 = 5050 (Given)
SUm of first 200 consecutive numbers = 100*201 = 20,100 (Option E)
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4226
Location: Canada
Re: The sum of the first 100 positive integers is 5,050. What is the sum  [#permalink]

Show Tags

New post 09 Dec 2019, 11:07
1
Top Contributor
Rashed12 wrote:
The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?

A. 10,000
B. 10,200
C. 15,050
D. 20,050
E. 20,100

PS85402.01


GIVEN: 1 + 2 + 3 + 4 + 5 + .....+ 99 + 100 = 5050

We want to find the sum 1 + 2 + 3 + 4 + 5 + .....+ 199 + 200
Notice that 1 + 2 + 3 + 4 + 5 + .....+ 199 + 200 = 1 + 2 + 3 + 4 + 5 + .....+ 99 + 100 + (100 + 1) + (100 + 2) + (100 + 3) + (100 + 4) + . . . (100 + 99) + (100 + 100)
= (1 + 2 + 3 + 4 + 5 + .....+ 99 + 100) + (1 + 2 + 3 + 4 + 5 + .....+ 99 + 100) + (100 + 100 + 100 + 100 + ...100 + 100) [ note that there are one hundred 100's in the sum]
= (5050) + (5050) + (100)(100)
= 10,100 + 10,000
= 20,100

Answer: E

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4226
Location: Canada
Re: The sum of the first 100 positive integers is 5,050. What is the sum  [#permalink]

Show Tags

New post 09 Dec 2019, 11:09
Top Contributor
Rashed12 wrote:
The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?

A. 10,000
B. 10,200
C. 15,050
D. 20,050
E. 20,100

PS85402.01


Another approach is to use the formula for the sum of the first positive n integers.
1 + 2 + 3 + 4 + .... + n = (n)(n+1)/2

So, the sum of the first 200 positive integers = (200)(200+1)/2
= (200)(201)/2
= (100)(201)
= 20,100

Answer: E

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15965
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The sum of the first 100 positive integers is 5,050. What is the sum  [#permalink]

Show Tags

New post 09 Dec 2019, 17:56
Hi All,

We're told that the sum of the first 100 positive integers is 5,050. We're asked for the sum of the first 200 positive integers. This question can be approached in a number of different ways - and since we're dealing with the sum of CONSECUTIVE integers, this question can be solved rather easily by BUNCHING.

To start, since we're dealing with the first 200 positive integers, we can form 100 'groups of 2'.... Let's start by adding the smallest and largest numbers....

1+200 = 201

Then the next smallest and next largest and so on...

2+199 = 201
3+198 = 201
Etc.

We'll end up with 100 'pairs' that equal 201, thus, the overall sum of all 200 numbers is (100)(201) = 20,100

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9105
Location: United States (CA)
Re: The sum of the first 100 positive integers is 5,050. What is the sum  [#permalink]

Show Tags

New post 17 Dec 2019, 20:44
Rashed12 wrote:
The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?

A. 10,000
B. 10,200
C. 15,050
D. 20,050
E. 20,100

PS85402.01


We can use the formula: average x number = sum. To find the average, we add the first and last numbers and divide by 2. Thus, the sum of the first 200 integers is:

(1 + 200)/2 x 200 = 201 x 100 = 20,100

Alternate solution:

Since the sum of the first 100 positive integers (i.e., 1 to 100) is 5,050 and each of the next 100 positive integers (i.e., 101 to 200) is 100 more than its counterpart in the first 100 integers (101 is 100 more than 1, 102 is 100 more than 2, etc.), then the sum of the integers from 101 to 200 (inclusive) is 100 x 100 = 10,000 more than 5,050, i.e., 15,050. Therefore, the sum of the first 200 positive integers (i.e., 1 to 200) is 5,050 + 15,050 = 20,100.

Answer: E
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
181 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.

Intern
Intern
avatar
Joined: 03 Jan 2020
Posts: 17
Location: United States
GMAT 1: 720 Q56 V40
Re: The sum of the first 100 positive integers is 5,050. What is the sum  [#permalink]

Show Tags

New post 03 Jan 2020, 17:34
MBA HOUSE KEY CONCEPT: Summation of an arithmetic progression

Formula: (a1 + an) n / 2

a1 = first term = 1

an = last term = 200

n number of terms = 200

(1 + 200) 200 / 2 = 20100

E :)
GMAT Club Bot
Re: The sum of the first 100 positive integers is 5,050. What is the sum   [#permalink] 03 Jan 2020, 17:34
Display posts from previous: Sort by

The sum of the first 100 positive integers is 5,050. What is the sum

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





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