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

Redeem

integers

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 124
Joined: Mon May 19, 2008 1:12 pm
Thanked: 3 times

integers

by Nycgrl » Sat Aug 02, 2008 2:42 pm
The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?
(A) 10,100
(B) 10,200
(C) 15,050
(D) 20,050
(E) 20,100
Top
Source: — Problem Solving |
Legendary Member
Posts: 661
Joined: Tue Jul 08, 2008 12:58 pm
Location: France
Thanked: 48 times

by pepeprepa » Sat Aug 02, 2008 2:59 pm
I would use a sum formula, that's very common, you can find it in all maths reviews:
"The sum of the k for k=1 to k=n"=(n*(n+1))/2

"The sum of the k for k=1 to k=200"=(200*201)/2
=20100
Top
Senior | Next Rank: 100 Posts
Posts: 82
Joined: Wed Jun 18, 2008 4:26 pm
Thanked: 10 times

by newera » Sat Aug 02, 2008 4:40 pm
another way is:

a) find the number of terms. last number - first number + 1. so 200-0+1=201
b) find the average. add the first and last number and divide by two. so, (200+0)/2=100.
c) multiply. 201*100=20,100
Top
Master | Next Rank: 500 Posts
Posts: 222
Joined: Fri Jan 04, 2008 8:10 pm
Thanked: 15 times

by sibbineni » Sat Aug 02, 2008 5:10 pm
The terms are in Arithmatic progression

so sum to n terms =n/2(2a+(n-1)d)

n=no of terms
a= first term
d= common difference

here
a=1
n=200
d=1

then sum to 200 terms is==>200/2(2*1+(200-1))
===>100(2+199)
===>100(201)
===>20100

so E
Top
Senior | Next Rank: 100 Posts
Posts: 58
Joined: Fri Jul 18, 2008 12:26 pm
Thanked: 2 times

by malolakrupa » Sat Aug 02, 2008 7:07 pm
sum of first 200 numbers = sum of first 100 numbers + (101+ 102....+ 200)

This equals sum of first 100 numbers + 100* 100 + sum of first 100 numbers

Hence the answer is 2* 5050 + 10000 = 20100
Top
Senior | Next Rank: 100 Posts
Posts: 88
Joined: Tue Jul 15, 2008 1:43 am
Thanked: 3 times
Followed by:1 members
GMAT Score:590

by eccentric » Sun Aug 03, 2008 10:43 am
I use the formula n + (n(n-1)/2)
the value for 100 is irrelevant just substitute n = 200 in the above formula...
the ans is 20100
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Fri Dec 13, 2019 1:02 pm
Nycgrl wrote:The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?
(A) 10,100
(B) 10,200
(C) 15,050
(D) 20,050
(E) 20,100

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
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1