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Math Expert V
Joined: 02 Sep 2009
Posts: 53770

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Difficulty:   45% (medium)

Question Stats: 71% (01:46) correct 29% (02:10) wrong based on 228 sessions

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When members of a certain club elected a chairman, each member voted for one of the three candidates. If candidate 1 received three times as many votes as the other two candidates together and candidate 2 received nine more votes than candidate 3, which of the following can be the number of members in the club?

A. 24
B. 30
C. 32
D. 36
E. 40

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Math Expert V
Joined: 02 Sep 2009
Posts: 53770

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Official Solution:

When members of a certain club elected a chairman, each member voted for one of the three candidates. If candidate 1 received three times as many votes as the other two candidates together and candidate 2 received nine more votes than candidate 3, which of the following can be the number of members in the club?

A. 24
B. 30
C. 32
D. 36
E. 40

Let $$x$$ denote the number of votes for candidate 1, $$y$$ the number of votes for candidate 2, and $$z$$ the number of votes for candidate 3. The stem gives that $$x = 3(y + z)$$ and $$y = z + 9$$. The number of club members $$= x + y + z = 4(y + z) = 4(2z + 9) = 8z + 36$$. Because $$z$$ must be a non-negative integer, the club can contain 36, 44, 52, ... members. Among the listed choices only choice D fits.

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Intern  Status: PhD Student
Joined: 21 May 2014
Posts: 43
WE: Account Management (Manufacturing)

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1
This question looks doubtful to me,
Lets see both the equations first, without going into further calculations

x=3(y+z)

y=z+9

This means y is greater than z and x is greater than both of other numbers. GMAT has some hidden rules about these type of questions. one of them is VOTE can not be negative and other is vote can not be in fraction.

Lets look at by putting simple numbers
If smallest number z is 1 then y=10 and x=33
by adding them we will get 44 minimum, or else Votes will go in fractions.

need expert's opinion
Math Expert V
Joined: 02 Sep 2009
Posts: 53770

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awal_786@hotmail.com wrote:
This question looks doubtful to me,
Lets see both the equations first, without going into further calculations

x=3(y+z)

y=z+9

This means y is greater than z and x is greater than both of other numbers. GMAT has some hidden rules about these type of questions. one of them is VOTE can not be negative and other is vote can not be in fraction.

Lets look at by putting simple numbers
If smallest number z is 1 then y=10 and x=33
by adding them we will get 44 minimum, or else Votes will go in fractions.

need expert's opinion

What if z = 0? It's possible isn't it? A candidate CAN receive 0 votes.
_________________
Intern  Status: PhD Student
Joined: 21 May 2014
Posts: 43
WE: Account Management (Manufacturing)

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Bunuel wrote:
awal_786@hotmail.com wrote:
This question looks doubtful to me,
Lets see both the equations first, without going into further calculations

x=3(y+z)

y=z+9

This means y is greater than z and x is greater than both of other numbers. GMAT has some hidden rules about these type of questions. one of them is VOTE can not be negative and other is vote can not be in fraction.

Lets look at by putting simple numbers
If smallest number z is 1 then y=10 and x=33
by adding them we will get 44 minimum, or else Votes will go in fractions.

need expert's opinion

What if z = 0? It's possible isn't it? A candidate CAN receive 0 votes.

That makes the solution even easier Good point
Intern  B
Joined: 23 Jun 2017
Posts: 10

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Let candidates be C1,C2 and C3
and let C3 -- x votes
so C2 gets---- x+9 votes
and hence C3 gets--- 3(2x+9)
= 8x+ 36
Since C3 getting 0 votes is a possibility
Put x=0,1,2,3....
and match from the answer list
Intern  B
Joined: 05 Sep 2017
Posts: 2

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I think this is a poor-quality question and I don't agree with the explanation. The question states that "each candidate voted for one of the three candidates", thus how is it possible that z=0?
Math Expert V
Joined: 02 Sep 2009
Posts: 53770

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LET wrote:
I think this is a poor-quality question and I don't agree with the explanation. The question states that "each candidate voted for one of the three candidates", thus how is it possible that z=0?

Each member voted for one of the three candidates, does not mean that one of the candidates cannot get 0 votes. For example, all could have given votes to only two of the candidates, ignoring the third one.
_________________ Re: M18-29   [#permalink] 26 Oct 2018, 09:54
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# M18-29

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