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

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Math Expert
Joined: 02 Sep 2009
Posts: 60727
The population of a city vote for one among 4 political parties, A, B  [#permalink]

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05 Nov 2019, 01:54
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Difficulty:

95% (hard)

Question Stats:

27% (02:54) correct 73% (03:35) wrong based on 41 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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Re: The population of a city vote for one among 4 political parties, A, B  [#permalink]

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05 Nov 2019, 07:27
1
1
Assume total population=LCM(8,10)=40

percent of the male votes will be won by party A= $$\frac{(20-10-2-2)}{(20-2)}*100$$=33.33%

Bunuel 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%

Are You Up For the Challenge: 700 Level Questions

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Joined: 10 Dec 2017
Posts: 177
Location: India
Re: The population of a city vote for one among 4 political parties, A, B  [#permalink]

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05 Nov 2019, 22:26
Bunuel 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%

Are You Up For the Challenge: 700 Level Questions

$$A+B+C+D+F(Fluctuate)=100$$
$$A+25+25+10+10=100$$
$$(AM+AF)+(BM+BF)+(CM+CF)+(DM+DF)+10=100$$
$$AF+BF+CF+DF+F'=50 and AM+BM+CM+DM+F''=50, (F'+F''=10)$$
$$DF=5, DM=5,F'=5, F''=5, BF=0, CM=0$$
$$AF+0+25+5+5=50$$
$$AF=15$$
$$AM+25+0+5+5=50$$
$$AM=15$$
$$A= 30$$
But male voters except those who fluctuate= 15-5=10
male % won by A=$$10/30$$
33.33
D:)
Intern
Joined: 11 Sep 2018
Posts: 11
Re: The population of a city vote for one among 4 political parties, A, B  [#permalink]

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08 Nov 2019, 15:36
nick1816 wrote:
Assume total population=LCM(8,10)=40

percent of the male votes will be won by party A= $$\frac{(20-10-2-2)}{(20-2)}*100$$=33.33%

Bunuel 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%

Are You Up For the Challenge: 700 Level Questions

Can you help me understand how did you arrive at this solution?
Intern
Joined: 24 Aug 2017
Posts: 7
Re: The population of a city vote for one among 4 political parties, A, B  [#permalink]

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09 Nov 2019, 00:41
nick1816 wrote:
Assume total population=LCM(8,10)=40

percent of the male votes will be won by party A= $$\frac{(20-10-2-2)}{(20-2)}*100$$=33.33%

Bunuel 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%

Are You Up For the Challenge: 700 Level Questions

How did you get 40? 8 and 10 came from where?

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Joined: 25 Feb 2019
Posts: 26
GMAT 1: 520 Q43 V20
Re: The population of a city vote for one among 4 political parties, A, B  [#permalink]

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09 Nov 2019, 08:56
satya2029 wrote:
Bunuel 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%

Are You Up For the Challenge: 700 Level Questions

$$A+B+C+D+F(Fluctuate)=100$$
$$A+25+25+10+10=100$$
$$(AM+AF)+(BM+BF)+(CM+CF)+(DM+DF)+10=100$$
$$AF+BF+CF+DF+F'=50 and AM+BM+CM+DM+F''=50, (F'+F''=10)$$
$$DF=5, DM=5,F'=5, F''=5, BF=0, CM=0$$
$$AF+0+25+5+5=50$$
$$AF=15$$
$$AM+25+0+5+5=50$$
$$AM=15$$
$$A= 30$$
But male voters except those who fluctuate= 15-5=10
male % won by A=$$10/30$$
33.33
D:)

Could you please explain why did you subtract 5 from the male voters since the count of 15 already had no fluctuating voters, even i followed the same approach and got the same number except the final answer. Since the question tells to remove the fluctuating voters i found the probability using 15/90 instead it should have been 15/30 where m i going wrong?

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Re: The population of a city vote for one among 4 political parties, A, B  [#permalink]

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11 Nov 2019, 14:40
Bunuel 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%

Are You Up For the Challenge: 700 Level Questions

We can let the total number of voters be 200 (100 male and 100 female). So 50 voters (all of whom are male) are committed to party B, 50 voters (all of whom are female) to party C, and 20 voters (10 male and 10 female) to party D, leaving 20 voters (10 male and 10 female) to fluctuate. Thus, the remaining 30 male and 30 female voters are committed to party A. Since 90 male voters (all except the 10 who fluctuate) will cast their votes, 30/90 = 1/3 = 33.33% of the male votes will be won by party A.

Answer: D
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Re: The population of a city vote for one among 4 political parties, A, B  [#permalink]

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11 Nov 2019, 20:54
Male Female Total
A 15 15 30
B 25 0 25
C 0 25 25
D 5 5 10
Non 5 5 10
100

Hence total male percent =$$\frac{15}{45}*100$$
thus 33.3%
D
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Re: The population of a city vote for one among 4 political parties, A, B   [#permalink] 11 Nov 2019, 20:54
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# The population of a city vote for one among 4 political parties, A, B

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