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

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Joined: 28 Jan 2011
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Question Stats:

68% (01:53) correct 32% (00:55) wrong based on 130 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]  18 May 2011, 12:25
2
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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, 17:28
1
KUDOS
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.

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Re: From MitDavidDv: Problem Solving Question [#permalink]  18 May 2011, 18:37
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Expert's post
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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews VP Status: There is always something new !! Affiliations: PMI,QAI Global,eXampleCG Joined: 08 May 2009 Posts: 1356 Followers: 14 Kudos [?]: 178 [1] , given: 10 Re: From MitDavidDv: Problem Solving Question [#permalink] 18 May 2011, 20:28 1 This post received KUDOS 7/3 * M = total votes means total votes/7 = integer. 14 fits _________________ Visit -- http://www.sustainable-sphere.com/ Promote Green Business,Sustainable Living and Green Earth !! Intern Joined: 11 Jul 2012 Posts: 46 Followers: 0 Kudos [?]: 1 [0], given: 0 Re: From MitDavidDv: Problem Solving Question [#permalink] 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 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5866 Location: Pune, India Followers: 1481 Kudos [?]: 7979 [0], given: 190 Re: From MitDavidDv: Problem Solving Question [#permalink] 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink]  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]  09 Jan 2015, 11:13
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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink]  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

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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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