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

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

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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
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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
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
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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
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
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