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TheAnuja55: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Wed Jul 27, 2011 12:35 amFollowed by: 2 members

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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Source: Beat The GMAT — Problem Solving | Sun Oct 07, 2012 5:14 am

GMAT Kolaveri: Master | Next Rank: 500 Posts; Posts: 287; Joined: Fri Mar 23, 2012 12:33 amFollowed by: 6 members; Location: Pune,India; Thanked: 60 times

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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Vinoth@GMAT Kolaveri
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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