BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 1223
Joined: Sat Feb 15, 2020 2:23 pm
Followed by:1 members

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

by BTGModeratorVI » Tue Jul 07, 2020 6:28 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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


Answer: E
Source: Official guide
Top
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

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

by Brent@GMATPrepNow » Tue Jul 07, 2020 7:41 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

BTGModeratorVI wrote: ↑
Tue Jul 07, 2020 6:28 am
 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


Answer: E
Source: Official guide
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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

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

by Brent@GMATPrepNow » Tue Jul 07, 2020 7:42 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

BTGModeratorVI wrote: ↑
Tue Jul 07, 2020 6:28 am
 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


Answer: E
Source: Official guide
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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1