PS: Integers problem..

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haidgmat: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Mon Jul 12, 2010 6:32 am

by haidgmat » Sun Sep 05, 2010 5:57 pm

The sum of the first 50 positive even integers is 2,550. What is the sum of the even integers from 102 to 200, inclusive?

a. 5100
b. 7550
c. 10100
d. 15500
e. 20100

Ans- B

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Source: Beat The GMAT — Problem Solving | Sun Sep 05, 2010 5:57 pm

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Sun Sep 05, 2010 6:57 pm

Solution:
We have 2+4+6+8.....100 = 2550.
We need the value of 102+104+106..200 = (100+2)+(100+4)+(100+6)...+(100+100)
= 100*50 + (2+4+6...100) = 5000+2550 = 7550.

The correct answer is hence (B).

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rerika01: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Tue Aug 31, 2010 7:40 am; Thanked: 2 times

by rerika01 » Mon Sep 06, 2010 1:26 am

Another way to approach this problem is by using the average of the set * the number of items in the set. To find the average, just add 200+102=302/2=151. Then to find the number of even numbers: 200-102=98/2(divide by 2 so you only count the even numbers) = 49, then you always add 1 when counting, thus =50. Now you multiply 50*151=7550.

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