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# The population of a city vote for one among 4 political parties

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Manager
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Posts: 245
The population of a city vote for one among 4 political parties  [#permalink]

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17 Apr 2017, 08:19
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Difficulty:

95% (hard)

Question Stats:

50% (03:01) correct 50% (03:04) wrong based on 70 sessions

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The population of a city vote for one among 4 political parties, A, B, C and D. 25% of the voters are committed to party B, 25% to party C and 10% to party D. 10% of the total voters fluctuate and can vote for any party. 50% of the voters are female and 50% of the voters committed to party D are male. Of the voters who fluctuate, half are female. Party B does not have any committed female voters while party C does not have any committed male voters. If all the voters except those who fluctuate cast their votes, what percent of the male votes will be won by party A?

A. 16.66%
B. 25%
C. 30%
D. 33.33%
E. 35%

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Manager
Joined: 18 Jan 2017
Posts: 81
Location: India
Concentration: Finance, Economics
GMAT 1: 700 Q50 V34
Re: The population of a city vote for one among 4 political parties  [#permalink]

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17 Apr 2017, 16:50
The population of a city vote for one among 4 political parties, A, B, C and D- Let the total no of voters be 100

50% of the voters are female- Therefore Male voters= 50 and Female Voters=50

25% of the voters are committed to party B and Party B does not have any committed female voters- Thus all 25 Voters who voted for party B are Male

25% to party C and party C does not have any committed male voters- Thus all 25 Voters who voted for party B are Female

10% to party D and 50% of the voters committed to party D are male- 5 Male voters and 5 Female voters

10% of the total voters fluctuate and can vote for any party and Of the voters who fluctuate, half are female - 5 Male voters and 5 Female voters

Thus No of committed Male Voters who voted for A= Total Male voters - Fluctuating Male Voters- Committed Male voters for B,C,D
= 50-5-(25+0+5)= 15

If all the voters except those who fluctuate cast their votes, what percent of the male votes will be won by party A= 15/45%=33.33%
Math Expert
Joined: 02 Aug 2009
Posts: 7025
The population of a city vote for one among 4 political parties  [#permalink]

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17 Apr 2017, 19:13
14101992 wrote:
The population of a city vote for one among 4 political parties, A, B, C and D. 25% of the voters are committed to party B, 25% to party C and 10% to party D. 10% of the total voters fluctuate and can vote for any party. 50% of the voters are female and 50% of the voters committed to party D are male. Of the voters who fluctuate, half are female. Party B does not have any committed female voters while party C does not have any committed male voters. If all the voters except those who fluctuate cast their votes, what percent of the male votes will be won by party A?

A. 16.66%
B. 25%
C. 30%
D. 33.33%
E. 35%

Let the votes be 100, so % can be taken as numbers..

Now concentrate ONLY on male votes..
There are 50 male voters..
1) actually voted is 50-5=45..
As it is given 10 are fluctuating of which HALF are females
2) 5 of these voted for D, so left 45-5=40
As only 10 voted for D, of which HALF are male.
3) 25 of these voted for B, so left 40-25=15
4) none voted for C..

So 15 voted out of 45 for A..
%=15/45=$$33\frac{1}{3}$$%

D
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Manager
Joined: 22 Jun 2016
Posts: 245
Re: The population of a city vote for one among 4 political parties  [#permalink]

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18 Apr 2017, 01:00
The above 2 answers are correct. For easier and faster solution, one can try making a table like this to solve.

Suppose the total number of voters is 400. Let F denote those people who fluctuate. From the given information, we can tabulate the number of male and female voters for each party as follows:
M F Total
A 60 60 120
B 100 — 100
C — 100 100
D 20 20 40
F 20 20 40
-----------------------
Tot 200 200 400

Since only 180 males cast their votes and party A receives 60 male votes, the required percentage is 60/180 = 33.33%.

Hence, D is the correct choice.
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Re: The population of a city vote for one among 4 political parties  [#permalink]

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23 Oct 2017, 09:53
1
14101992 wrote:
The population of a city vote for one among 4 political parties, A, B, C and D. 25% of the voters are committed to party B, 25% to party C and 10% to party D. 10% of the total voters fluctuate and can vote for any party. 50% of the voters are female and 50% of the voters committed to party D are male. Of the voters who fluctuate, half are female. Party B does not have any committed female voters while party C does not have any committed male voters. If all the voters except those who fluctuate cast their votes, what percent of the male votes will be won by party A?

A. 16.66%
B. 25%
C. 30%
D. 33.33%
E. 35%

Please see the following attachment. Data of orange cell have been derived.
Attachment:

Capture.PNG [ 4.41 KiB | Viewed 494 times ]

Total number of male voters who voted = Total number of male - Total number of male voters who did not vote
$$=>50-5=45$$

Out of 45, voted for A = 45 - voted for B, C and D = 45-(25+0+5) = 15

$$\frac{15}{45}*100=33.33$$%
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Hasan Mahmud

Re: The population of a city vote for one among 4 political parties &nbs [#permalink] 23 Oct 2017, 09:53
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