If Kelly received 1/3 more votes than Mike in a student : Problem Solving (PS)

MitDavidDv

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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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A

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69% (01:25) correct

31% (01:39) wrong

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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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KarishmaB

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

Updated on: 08 Oct 2022, 02:39

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Expert Reply

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.
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Originally posted by KarishmaB on 18 May 2011, 19:37.
Last edited by KarishmaB on 08 Oct 2022, 02:39, edited 1 time in total.

fluke

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Re: If Kelly received 1/3 more votes than Mike in a student [#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"

Spidy001

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Re: If Kelly received 1/3 more votes than Mike in a student [#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: If Kelly received 1/3 more votes than Mike in a student [#permalink]

18 May 2011, 21:28

1

Kudos

7/3 * M = total votes

means total votes/7 = integer.

14 fits

Ousmane

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Posts: 35

Re: If Kelly received 1/3 more votes than Mike in a student [#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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KarishmaB

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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink]

03 Nov 2012, 21:37

Expert Reply

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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watwazdaquestion

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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)

PareshGmat

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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink]

13 Jan 2015, 22:27

1

Kudos

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

Answer = C

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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink]

10 May 2017, 12:33

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Expert Reply

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.

Answer: C
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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink]

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
Answer = C
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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink]

22 Jun 2018, 08:16

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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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink]

12 Nov 2018, 00:02

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.

Answer C

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abhishekdadarwal2009

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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink]

13 Jan 2019, 10:04

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

let mike got x votes, then Kelly got (x+1/3x) votes

thus total votes=x+(x+1/3x)=(7/3)x.

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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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink]

14 Jan 2020, 11:01

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 no of votes Mike got be 3 , So Kelly received 4 votes

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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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink]

16 Jan 2020, 07:22

Expert Reply

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.

Answer: C

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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink]

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Re: If Kelly received 1/3 more votes than Mike in a student [#permalink]

30 Nov 2023, 20:30

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