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

[BTGmoderatorDC]

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


OA E

Source: Official Guide

[Jay@ManhattanReview]

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

OA E

Source: Official Guide

You would note that the 101st term is 100 greater than the 1st term; the 102nd term is 100 greater than the 2nd term; the 103rd term is 100 greater than the 3rd term; and similarly, the 200th term is 100 greater than the 100th term.

So, the sum of the first 200 positive integers = the sum of the first 100 positive integers + the sum of the 100 positive integers, starting from 101st integer to 200th integer

= 5050 + ( = the sum of the first 100 positive integers + 100 x 100);
= 5050 + (5050 + 10,000)
= 20,100

The correct answer: E

Hope this helps!

-Jay
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[Brent@GMATPrepNow]

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

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@GMATPrepNow]

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

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

[[email protected]]

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: E

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

[Scott@TargetTestPrep]

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


OA E

Source: Official Guide

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