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

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Manager
Joined: 28 Jan 2011
Posts: 76
Location: Tennessee
Schools: Belmont University

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18 May 2011, 13:08
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Difficulty:

25% (medium)

Question Stats:

64% (01:58) correct 36% (01:04) wrong based on 254 sessions

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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
[Reveal] Spoiler: OA
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Joined: 20 Dec 2010
Posts: 2010
Re: From MitDavidDv: Problem Solving Question [#permalink]

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18 May 2011, 13:25
4
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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]

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18 May 2011, 18:28
1
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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.

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

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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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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: 1326 Re: From MitDavidDv: Problem Solving Question [#permalink] ### Show Tags 18 May 2011, 21:28 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 Re: From MitDavidDv: Problem Solving Question [#permalink] ### Show Tags 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 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7446 Location: Pune, India Re: From MitDavidDv: Problem Solving Question [#permalink] ### Show Tags 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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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)
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09 Jan 2015, 12:13
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13 Jan 2015, 22:27
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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04 Feb 2016, 00:05
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01 May 2017, 20:27
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10 May 2017, 12:33
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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

If we let k = the number of votes Mike received, then (4/3)k = the number of votes Kelly received. Thus, they received a total of k + 4k/3 = 3k/3 + 4k/3 = 7k/3 votes.

Since 7k/3 has to be an integer, k can be any multiple of 3.

When k is 3, the total number of votes is 7(3)/3 = 7.

When k is 6, the total number of votes is 7(6)/3 = 14.

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19 May 2017, 12:33
Let votes to Mike = x
Total votes =2x+x/3=7x/3= hence answer should be multiple of 7 thats 14 - option C
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Re: If Kelly received 1/3 more votes than Mike in a student   [#permalink] 19 May 2017, 12:33
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