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M18-29

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M18-29  [#permalink]

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New post 16 Sep 2014, 01:04
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A
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  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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Re M18-29  [#permalink]

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New post 16 Sep 2014, 01:04
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.

Answer: D
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Re: M18-29  [#permalink]

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New post 01 Nov 2014, 08:32
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
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Re: M18-29  [#permalink]

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New post 01 Nov 2014, 08:42
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.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M18-29  [#permalink]

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New post 01 Nov 2014, 09:09
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 :-D Good point
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Re: M18-29  [#permalink]

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New post 11 Jul 2017, 07:44
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)
add all of their votes
= 8x+ 36
Since C3 getting 0 votes is a possibility
Put x=0,1,2,3....
and match from the answer list
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Re M18-29  [#permalink]

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New post 26 Oct 2018, 08:17
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?
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Re: M18-29  [#permalink]

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New post 26 Oct 2018, 09:54
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.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M18-29   [#permalink] 26 Oct 2018, 09:54
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