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The population of a city vote for one among 4 political parties, A, B 05 Nov 2019, 01:54
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95% (hard)

Question Stats:

42% (03:27) correct 58% (03:35) wrong based on 347 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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D
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The population of a city vote for one among 4 political parties, A, B 05 Nov 2019, 07:27
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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
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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The population of a city vote for one among 4 political parties, A, B 05 Nov 2019, 22:26
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Bunuel
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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\(A+B+C+D+F(Fluctuate)=100\)
\(A+25+25+10+10=100\)
\((AM+AF)+(BM+BF)+(CM+CF)+(DM+DF)+10=100\)
\(AF+BF+CF+DF+F'=50 and AM+BM+CM+DM+F''=50, (F'+F''=10)\)
\(DF=5, DM=5,F'=5, F''=5, BF=0, CM=0\)
\(AF+0+25+5+5=50\)
\(AF=15\)
\(AM+25+0+5+5=50\)
\(AM=15\)
\(A= 30\)
But male voters except those who fluctuate= 15-5=10
male % won by A=\(10/30\)
33.33
D:)
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The population of a city vote for one among 4 political parties, A, B 08 Nov 2019, 15:36
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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
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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Can you help me understand how did you arrive at this solution?
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The population of a city vote for one among 4 political parties, A, B 09 Nov 2019, 00:41
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nick1816
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
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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How did you get 40? 8 and 10 came from where?

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The population of a city vote for one among 4 political parties, A, B 09 Nov 2019, 08:56
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satya2029
Bunuel
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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\(A+B+C+D+F(Fluctuate)=100\)
\(A+25+25+10+10=100\)
\((AM+AF)+(BM+BF)+(CM+CF)+(DM+DF)+10=100\)
\(AF+BF+CF+DF+F'=50 and AM+BM+CM+DM+F''=50, (F'+F''=10)\)
\(DF=5, DM=5,F'=5, F''=5, BF=0, CM=0\)
\(AF+0+25+5+5=50\)
\(AF=15\)
\(AM+25+0+5+5=50\)
\(AM=15\)
\(A= 30\)
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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The population of a city vote for one among 4 political parties, A, B 11 Nov 2019, 14:40
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Bunuel
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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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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The population of a city vote for one among 4 political parties, A, B 11 Nov 2019, 20:54
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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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The population of a city vote for one among 4 political parties, A, B 14 Apr 2020, 04:42
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globaldesi
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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Why the 5 male voters who fluctuate should not be included?

The stimulus says clearly "what percent of the male votes will be won by party A"
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The population of a city vote for one among 4 political parties, A, B 09 Nov 2020, 08:53
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jcgomezlv
globaldesi
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
Why the 5 male voters who fluctuate should not be included?

The stimulus says clearly "what percent of the male votes will be won by party A"
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Hi jcgomezlv,

The question statement clearly states that the voters who fluctuate DID NOT vote.
Since, they did not vote, we cannot possibly count them in.
Hence, we explicitly subtract 5 from the total number of male voters (50) and this gives us the total number of male voters = 45

Hope that helps!
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The population of a city vote for one among 4 political parties, A, B 01 May 2023, 10:38
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porwal1

satya2029 is incorrect in the final piece of logic, and you are correct. We do not need to subtract 5 from 15. Rather we need to subtract 5 from 50.

Total male voters - Fluctuating male voters = 50 - 5 = 45

Total Male A / Total Male who will actually vote = 15 / 45 = 33.33%
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The population of a city vote for one among 4 political parties, A, B 19 Sep 2025, 21:37
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