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]

18 May 2011, 13:08

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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

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Re: From MitDavidDv: Problem Solving Question [#permalink]

18 May 2011, 13:25

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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]

18 May 2011, 18:28

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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]

18 May 2011, 19:37

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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]

18 May 2011, 21:28

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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]

03 Nov 2012, 08:22

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]

03 Nov 2012, 21:37

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]

06 Nov 2012, 15:48

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)

Re: If Kelly received 1/3 more votes than Mike in a student [#permalink] 06 Nov 2012, 15:48

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

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