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In a class of 28 students, one student is to be elected as class

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In a class of 28 students, one student is to be elected as class  [#permalink]

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New post Updated on: 20 May 2017, 05:43
1
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A
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E

Difficulty:

  25% (medium)

Question Stats:

73% (01:11) correct 27% (01:15) wrong based on 139 sessions

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In a class of 28 students, one student is to be elected as class representative. Three of the 28 students are running for the position. The three candidates may not vote, but all the other students must vote. What is the smallest percent of votes with which a candidate could win, if winning is defined as receiving a plurality of votes (more votes than any other candidate)?

(A) 25%
(B) 33.34%
(C) 34%
(D) 36%
(E) 50.1%

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Originally posted by hazelnut on 20 May 2017, 05:38.
Last edited by Bunuel on 20 May 2017, 05:43, edited 1 time in total.
Renamed the topic and edited the question.
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Re: In a class of 28 students, one student is to be elected as class  [#permalink]

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New post 20 May 2017, 07:29
So 25 people (28-3) are voting for 3 people.
If we divide 25 by 3, we get
25 = (3*8 +1)

So 3 people can each get 8 votes and the candidate who gets 1 remaining vote can be the winner.
So minimum votes required to win = 9.
Required percent = 9/25 * 100 = 36%

Hence D
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Re: In a class of 28 students, one student is to be elected as class  [#permalink]

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New post 20 May 2017, 13:34
1
In a class of 28 students, one student is to be elected as class representative. Three of the 28 students are running for the position. The three candidates may not vote, but all the other students must vote. What is the smallest percent of votes with which a candidate could win, if winning is defined as receiving a plurality of votes (more votes than any other candidate)?
(A) 25%
(B) 33.34%
(C) 34%
(D) 36%
(E) 50.1%

Total number of Students = 28
Number of Students running for class representative position = 3
Candidates/Students may not vote = 3
Therefore Total number of students who must vote = 28 - 3 = 25
Required fraction = \(\frac{25}{3}\) = 8.333
ie; each of three candidates can get 8 equal votes.
8 x 3 = 24, thus 1 vote remains.
Candidate who gets 1 more vote could win. Therefore winning candidate would get 9 votes.
Required Percentage = \(\frac{9}{25}\) x 100 = 36%
Answer D...

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Re: In a class of 28 students, one student is to be elected as class  [#permalink]

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New post 18 Jun 2017, 03:52
Total votes = 28-3 = 25
To win by the smallest margin, one of the candidates needs just a little over \(\frac{1}{3}\) of total votes = \(\frac{1}{3}\)*25 \(\approx{9}\)

Percentage of the votes = \(\frac{9}{25}\)*100 = 36%
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Re: In a class of 28 students, one student is to be elected as class  [#permalink]

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New post 27 Jan 2018, 13:30
Hi All,

Based on how the answer choices are written, and the 'design' of the prompt, there's a big logic 'shortcut' that you can use to avoid most of the 'math work.' Since there are only 25 voters who must vote, each voter represents 4% of the total. The answer to the given question will be based on the number of voters who vote for a particular student, but the percentage equivalent MUST be a multiple of 4%.

There's only one answer that fits that restriction (the correct one):

It's unlikely that you would come across this exact shortcut on Test Day though (the GMAT question writers wouldn't make it this easy for you to bypass all of the wrong answers).

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Re: In a class of 28 students, one student is to be elected as class &nbs [#permalink] 27 Jan 2018, 13:30
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