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Problem Solving

by TheAnuja55 » Sun Oct 07, 2012 5:14 am
  • Hello there,

    Q: 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

    M = mike
    K = Kelly = M+(1/3)M
    Total number of votes = M + (4/3)M =(7/3)M


    ans: (C)

    My question is : why is it C ?
    Why it should be multiple of 7, why not 3 ?
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by GMAT Kolaveri » Sun Oct 07, 2012 5:24 am
TheAnuja55 wrote:
  • M = mike
    K = Kelly = M+(1/3)M
    Total number of votes = M + (4/3)M =(7/3)M


    ans: (C)

    My question is : why is it C ?
    Why it should be multiple of 7, why not 3 ?

Total = (7/3)*M
M = (3/7)*Total

M cannot be a fraction. Hence the total has to be a multiple of 7.
Hope it helps. :)
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by GMATGuruNY » Sun Oct 07, 2012 5:59 am
TheAnuja55 wrote:
  • Hello there,

    Q: 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
Kelly received 1/3 more votes than Mike in a student election.
Thus, if M=3, K = 3 + (1/3)3 = 4.
In other words, M:K = 3:4.
Since the sum of the parts of this ratio = 3+4 = 7, the total number of votes must be a multiple of 7.

To illustrate:
If M=3, then K=4, for a total of 7 votes.
If M=6, then K=8, for a total of 14 votes.
If M=9, then K=12, for a total of 21 votes.
In each case, the total number of votes is a multiple of 7.

Of the answer choices, only C is a multiple of 7.

The correct answer is C.
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