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# In an election between two candidates, 75% of the voters cast their

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Math Expert
Joined: 02 Sep 2009
Posts: 59631
In an election between two candidates, 75% of the voters cast their  [#permalink]

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Updated on: 15 Oct 2018, 00:58
00:00

Difficulty:

15% (low)

Question Stats:

88% (02:52) correct 12% (02:43) wrong based on 76 sessions

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In an election between two candidates, 75% of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of voters enrolled in that election.

A. 16800
B. 32019
C. 23000
D. 21413
E. 31527

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Originally posted by Bunuel on 13 Apr 2017, 01:40.
Last edited by Bunuel on 15 Oct 2018, 00:58, edited 1 time in total.
Edited the question.
Marshall & McDonough Moderator
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Re: In an election between two candidates, 75% of the voters cast their  [#permalink]

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13 Apr 2017, 03:28
2
1
75% of valid votes = 9261
Valid votes = (9261 * 4)/3 = 3087 * 4 = 12348

(75% - 1.5% = approx. 75%) of Total voters = 12348
Total voters = (12348 * 4)/3 = 4116 * 4 = Close to 16000

Senior Manager
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Re: In an election between two candidates, 75% of the voters cast their  [#permalink]

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14 Apr 2017, 05:20
Total number of the enrolled voters=x

x*(0.75)*(0.98)*(0.75)=9261

x=16800

Intern
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Re: In an election between two candidates, 75% of the voters cast their  [#permalink]

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14 Apr 2017, 11:22
1
1
In an election between two candidates, 75% of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.

As it seems 75% of the voters cast their votes I believe the ans X=(9261*100*100)/(98*75)=12600 Note - the question is total number of votes enrolled in election

If the question was total number of voters then ans X=(12600*100)/75=16800
VP
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Re: In an election between two candidates, 75% of the voters cast their  [#permalink]

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14 Apr 2017, 11:47
hello, i want to ask a question. So, basically, the voting system work based on the US ballot system? In other word, 1 person is only able to cast one vote?
VP
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Re: In an election between two candidates, 75% of the voters cast their  [#permalink]

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14 Apr 2017, 11:56
Vyshak wrote:
75% of valid votes = 9261
Valid votes = (9261 * 4)/3 = 3087 * 4 = 12348

(75% - 1.5% = approx. 75%) of Total voters = 12348
Total voters = (12348 * 4)/3 = 4116 * 4 = Close to 16000

your answer is still unconvincing, it is because if the right answer is either C or D, there is no way to choose the answer using your method of calculation
Manager
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Re: In an election between two candidates, 75% of the voters cast their  [#permalink]

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14 Apr 2017, 12:31
Assuming total voters enrolled to be 100.

out of which 2% is invalid ..$$\frac{75*2}{100}$$ = 1.5.. total valid votes are 75-1.5=73.5

Now for 73.5 votes 75% are valid .
By general cross method

100 - 73.5*75%
? - 9261

=>$$\frac{(9261*100)}{(75 \%*73.5 )}$$
=>$$\frac{(9261*100*100)}{(75*73.5)}$$
dividing by 25(100 & 75) and 7(9261 & 73.5) and then simplifying gives 16800
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In an election between two candidates, 75% of the voters cast their  [#permalink]

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22 Apr 2017, 17:39
1
chesstitans, yes, in the U.S. the system is SUPPOSED to be one person, one vote.

I think there is a typo in the question. I think the question needs to ask about total voteRs, not votes. See sreenu7464 's post.

Bunuel?
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Re: In an election between two candidates, 75% of the voters cast their  [#permalink]

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15 Oct 2018, 01:00
1
generis wrote:
chesstitans, yes, in the U.S. the system is SUPPOSED to be one person, one vote.

I think there is a typo in the question. I think the question needs to ask about total voteRs, not votes. See sreenu7464 's post.

Bunuel?

______________________
Fixed the typo. Thank you.
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Manager
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Re: In an election between two candidates, 75% of the voters cast their  [#permalink]

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24 Apr 2019, 11:31
My method is a bit long if there is a better method I am open to it
We are solving for X which is the total number of votes
We know 3/4*73.5/100*x=9261
So x= 16800
IMO A

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Re: In an election between two candidates, 75% of the voters cast their  [#permalink]

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27 Apr 2019, 02:47
Bunuel wrote:
In an election between two candidates, 75% of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of voters enrolled in that election.

A. 16800
B. 32019
C. 23000
D. 21413
E. 31527

given
0.73*0.75*x = 9261
solve for x
we get ~ 16800
IMO A
Re: In an election between two candidates, 75% of the voters cast their   [#permalink] 27 Apr 2019, 02:47
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