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sohaib_iba: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Wed Feb 24, 2010 7:09 am

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by sohaib_iba » Wed Jun 02, 2010 12:48 am

In an election 4% of the votes cast are invalid. A candidate gets 55% of the valid votes and wins the election by 240 valid votes. Find the total number of votes cast?

A) 2500
B) 2000
C) 1250
D) 3500

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Source: Beat The GMAT — Problem Solving | Wed Jun 02, 2010 12:48 am

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

by Rahul@gurome » Wed Jun 02, 2010 1:14 am

The candidate gets 55% of valid votes.
So the other candidates get (100-55)% or 45% of valid votes.
The candidate wins by (55-45)% or 10% of valid votes.
Now 10% of valid votes is 240.
So total no. of valid votes is 240/(10%) which is 2400.
Also 4% of total votes is invalid.
So (100-4)% or 96% of total votes is valid.
So 96% of total votes is 2400.
So total number of votes is 2400/(96%) = 2500.
The correct answer is (A).

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selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 am; Thanked: 135 times; Followed by:7 members

by selango » Wed Jun 02, 2010 2:27 am

Let the number of votes cast be x.

Valid votes =96/100*x=y

Winning candidate gets 55% of valid votes and wins the election by 240 votes-->

The other candidate gets 45% of votes.

-->55/100*y=45/100*y+240

y=2400

96/100*x=2400

x=2500

option A