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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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18 May 2011, 12:08
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Difficulty:

35% (medium)

Question Stats:

67% (01:02) correct 33% (01:04) wrong based on 444 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
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18 May 2011, 18:37
5
3
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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18 May 2011, 12:25
4
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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18 May 2011, 17:28
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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18 May 2011, 20:28
1
7/3 * M = total votes

14 fits
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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
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03 Nov 2012, 20:37
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

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

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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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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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10 May 2017, 11:33
1
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, 11:33
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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22 Jun 2018, 07:16
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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11 Nov 2018, 23:02
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.

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13 Jan 2019, 09:04
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.
Re: If Kelly received 1/3 more votes than Mike in a student &nbs [#permalink] 13 Jan 2019, 09:04
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