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16 Sep 2014, 01:04
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In a certain club election for chairman, each member voted for one of the three candidates. If candidate 1 received three times as many votes as the other two candidates combined, and candidate 2 received nine more votes than candidate 3, which of the following could be the number of members in the club?
A. 24
B. 30
C. 32
D. 36
E. 40
A. 24
B. 30
C. 32
D. 36
E. 40
16 Sep 2014, 01:04
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Official Solution:
In a certain club election for chairman, each member voted for one of the three candidates. If candidate 1 received three times as many votes as the other two candidates combined, and candidate 2 received nine more votes than candidate 3, which of the following could be the number of members in the club?
A. 24
B. 30
C. 32
D. 36
E. 40
Let \(x\) represent 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 given information states that \(x = 3(y + z)\) and \(y = z + 9\). The total number of club members equals the total number of votes, which is \(x + y + z =3(y + z) + y + z =4(y + z) = 4(2z + 9) = 8z + 36\). Since \(z\) must be a non-negative integer, the club can have 36, 44, 52, ... members. Among the given choices, only choice D fits.
Answer: D
In a certain club election for chairman, each member voted for one of the three candidates. If candidate 1 received three times as many votes as the other two candidates combined, and candidate 2 received nine more votes than candidate 3, which of the following could be the number of members in the club?
A. 24
B. 30
C. 32
D. 36
E. 40
Let \(x\) represent 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 given information states that \(x = 3(y + z)\) and \(y = z + 9\). The total number of club members equals the total number of votes, which is \(x + y + z =3(y + z) + y + z =4(y + z) = 4(2z + 9) = 8z + 36\). Since \(z\) must be a non-negative integer, the club can have 36, 44, 52, ... members. Among the given choices, only choice D fits.
Answer: D
01 Nov 2014, 08:32
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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
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
Good point 
