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Manager  Joined: 28 Jan 2011
Posts: 73
Location: Tennessee
Schools: Belmont University

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Difficulty:   35% (medium)

Question Stats: 67% (01:26) correct 33% (01:35) wrong based on 396 sessions

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If Kelly received 1/3 times 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
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10011
Location: Pune, India

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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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Karishma
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5
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"
##### General Discussion
Director  Joined: 01 Feb 2011
Posts: 528

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1
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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1
7/3 * M = total votes

14 fits
Intern  Joined: 11 Jul 2012
Posts: 39

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It's not clear to whether 1/3 has to be applied to the votes cast to Mike or to the total votes
Veritas Prep GMAT Instructor V
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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

The comparison of 1/3rd more is with Mike.

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Karishma
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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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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

Target Test Prep Representative V
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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

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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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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Let the number of votes for Mike and Kelly be M and K respectively. As per the statement K=(4/3)*M. K/M=4/3. The sum has to be a multiple of 7. The total number of votes need to be a multiple of 7. Only 14 or option C fits the bill.

Option C it is !!
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MitDavidDv wrote:
If Kelly received 1/3 times 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

Let the vote received by Mike be M.
Vote Received by Kelly is 1/3 more than the votes of Mike = (1/3)M +M = (4/3)M
Ratio of votes of Kelly to Mike = 4/3

Since votes should be a natural number. So it must be a multiple of 4+3 = 7. Only Option C i.e. 14 is a multiple of 7.

Director  P
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If Kelly received 1/3 times 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

so x=(3*total votes)/7. since the votes have to be integer then we have to pick a nunber which is divisible by 7 to make x as an integer.

only option c is divisivle by 7 and thus x=6 and Kelly got 8 votes.=14

C is correct.
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MitDavidDv wrote:
If Kelly received 1/3 times 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

Consideriing Total No of votes polled = Total No of Students = 7

Thus, Total no of students must be a multiple of 7 , among the given options only (C) 14 fits, hence thats the correct Answer!!!
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Target Test Prep Representative V
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MitDavidDv wrote:
If Kelly received 1/3 times 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

We can let K = the number of votes received by Kelly, M = the number of votes received by Mike and T = the total number of votes received by the two candidates. We can create the equation:

K = 4M/3

and

T = K + M

Thus, T = K + M = 4M/3 + M = 4M/3 = 3M/3 = 7M/3.

We see that T must be a multiple of 7. So 14 is the only possible answer among the given choices for the total number of votes cast.

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# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If Kelly received 1/3 more votes than Mike in a student   [#permalink] 16 Jan 2020, 07:22
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