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If Kelly received 1/3 more votes than Mike in a student

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If Kelly received 1/3 more votes than Mike in a student [#permalink] New post 18 May 2011, 12:08
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

68% (01:53) correct 32% (00:54) wrong based on 114 sessions
If Kelly received 1/3 more votes than Mike in a student election, which of the following could have been the total number of votes cast for the two candidates?

A. 12
B. 13
C. 14
D. 15
E. 16
[Reveal] Spoiler: OA
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Re: From MitDavidDv: Problem Solving Question [#permalink] New post 18 May 2011, 12:25
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MitDavidDv wrote:
If Kelly received 1/3 more votes than Mike in a student election, which of the following could have been the total number of votes cast for the two candidates?
A. 12
B. 13
C. 14
D. 15
E. 16


Question should say: 1/3 TIMES more votes.

K = M + 1/3M
K = (4/3)M
M+K=M+(4/3)M=Total
Total = (7/3)M
M=(3/7)Total

Total must be a multiple of 7 because Mary can't receive fractional numbers of votes.

Only option that is a multiple of 7 is 14.

Ans: "C"
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Re: From MitDavidDv: Problem Solving Question [#permalink] New post 18 May 2011, 17:28
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K = (4/3)M

=> M+K = (7/3)*M

=> M = (3/7)*(M+K)

M+K has to be a multiple of 7.

Only possible option here is 14.

Answer is C.
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Re: From MitDavidDv: Problem Solving Question [#permalink] New post 18 May 2011, 18:37
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MitDavidDv wrote:
If Kelly received 1/3 more votes than Mike in a student election, which of the following could have been the total number of votes cast for the two candidates?
A. 12
B. 13
C. 14
D. 15
E. 16


You can use ratios to solve it too.
Kelly received 1/3 more votes than Mike which means that if Mike got 3 votes, Kelly got 4 votes (1/3 more than Mike). Since votes cannot be fractional, Mike must have got at least 3 votes and Kelly must have got at least 4 votes. They must have got at least 7 votes together. Actual number of votes could be any multiple of 7. The only multiple of 7 in the options is 14.
For more on ratios, check:
http://www.veritasprep.com/blog/2011/03 ... of-ratios/
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Re: From MitDavidDv: Problem Solving Question [#permalink] New post 18 May 2011, 20:28
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7/3 * M = total votes

means total votes/7 = integer.

14 fits
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Re: From MitDavidDv: Problem Solving Question [#permalink] New post 03 Nov 2012, 07:22
It's not clear to whether 1/3 has to be applied to the votes cast to Mike or to the total votes
Please help
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Re: From MitDavidDv: Problem Solving Question [#permalink] New post 03 Nov 2012, 20:37
Expert's post
Ousmane wrote:
It's not clear to whether 1/3 has to be applied to the votes cast to Mike or to the total votes
Please help


The question clearly says "Kelly received 1/3 more votes than Mike"
The comparison of 1/3rd more is with Mike.

So for every 3 votes, Kelly received 1 extra vote i.e. she received 4 votes.
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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink] New post 06 Nov 2012, 14:48
K = 4/3 M
we know M has to be a multiple of 3 in order to get an integer for K + M

plug in a couple values for M:

M = 3 => K = 3 + 1 = 4
M + K = 7 (not in choices)

M = 6 => K = 6 + 2 = 8
M + K = 14 (answer C)
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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink] New post 09 Jan 2015, 11:13
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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink] New post 13 Jan 2015, 21:27
Let votes to Mike = x

Then votes to Kelly \(= x + \frac{x}{3}\)

Total votes \(= 2x + \frac{x}{3} = \frac{7x}{3}\)

\(x = (Total Votes) * \frac{3}{7}\)

Total votes should be divisible by 7, only 14 fits in

Answer = C
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Re: If Kelly received 1/3 more votes than Mike in a student   [#permalink] 13 Jan 2015, 21:27
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