Percentage question(voters problem)

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hemant_rajput: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 22, 2012 7:13 amFollowed by: 13 members; Thanked: 46 times; GMAT Score:700

by hemant_rajput » Fri Jan 18, 2013 8:38 am

Q47 . In an assembly election at X, the total turnout was 80% out of which 16% of the total voters on the voting list were declared invalid. Find which of the following can be the percentage votes got by the winner of election if the candidate who came second got 20% of the total voters on the voting list. (There were only 3 contestants, only one winner and the total number of voters on the voters' list was 20000).
a. 44.8%
b. 46.6%
c. 48%
d. None of these

[spoiler]oa:a[/spoiler]

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Source: Beat The GMAT — Problem Solving | Fri Jan 18, 2013 8:38 am

adthedaddy: Master | Next Rank: 500 Posts; Posts: 167; Joined: Fri Mar 09, 2012 8:35 pmFollowed by: 3 members; Thanked: 39 times

by adthedaddy » Sun Jan 20, 2013 6:25 am

Of the total voters, 80% turned out for voting;
Of the total voters, 16% voters were declared invalid.
Remaining voters = 80-16 = 64%
20% votes were received by the 2nd person.
Thus, the winning voter gets votes between 20.01 - 44%

Overhere, as there is an option of "None of these" this is a bit ambiguous as an option of 44.8 is given as opt.(a)
We get an answer near to (a) but not exactly. Hence ans can be (a) or (d).

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Jan 20, 2013 7:47 am

Phewww, that's a tough question to interpret! The first sentence is already quite confusing and ambiguous.

hemant_rajput wrote:Q47 . In an assembly election at X, the total turnout was 80% out of which 16% of the total voters on the voting list were declared invalid.

The total turnout was 80%....: Presumably, this mean that 80% of the 20,000 people on the voters' list showed up. So, 16,000 people turned up to vote.

....out of which 16% of the total voters on the voting list were declared invalid.
"Out of which" suggests that 16% of the 16,000 people who turned up to vote were declared invalid.
"of the total voters on the voting list" suggests that 16% of the 20,000 people on the voters' list were declared invalid.

Next there's "the candidate who came second got 20% of the total voters on the voting list"
Including the invalid votes?

Given this ambiguity (and only 4 answer choices), this could never be an official GMAT question.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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ritind: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Wed Nov 21, 2012 10:40 pm; Thanked: 4 times

by ritind » Mon Jan 21, 2013 11:44 pm

Here's my approach:

Total no. of voters on voting list - 20000 (Lets call it vov)

turnout - 80% of vov = 16000

invalid - 16% of vov = 3200

Candidate who came second got - 20% of vov = 4000

no of votes left = 16000 - 3200 - 4000 = 8800

Lets say that candidate who came first got all the remaining votes = 8800

% of votes won by winning candidate = 8800/20000 * 100 = 44%

Therefore the answer should be D

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