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## Each of people voted once in an election, X

tagged by: Brent@GMATPrepNow

This topic has 3 expert replies and 3 member replies
canbtg Senior | Next Rank: 100 Posts
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#### Each of people voted once in an election, X

Sat Nov 02, 2013 6:31 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
Each of people voted once in an election, X got 483 from male voters, Y got 433 from female voters. How many votes did X get?
1) X got votes from 50% of male voters
2) Y got votes from 60% of female voters

OAB

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Brent@GMATPrepNow GMAT Instructor
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Sat Nov 02, 2013 8:06 am
canbtg wrote:
Each of people voted once in an election, X got 483 from male voters, Y got 433 from female voters. How many votes did X get?

1) X got votes from 50% of male voters
2) Y got votes from 60% of female voters
We can use the Double Matrix Method here to help us arrange our information. The Double Matrix can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of voters, and the two characteristics are:
- male or female
- voted for X or voted for Y

So, we can set up out diagram as follows:

X got 483 from male voters, Y got 433 from female voters.
We can add that information as follows:

Target question: How many votes did X get?
Notice that the two blue boxes represent the males and females who voted for X.

So, our goal here is to find the sum of these two boxes.

Statement 1: X got votes from 50% of male voters
The two highlighted boxes represent the male voters. If 50% of them voted for X, then the other 50% voted for Y.

So, 483 of the males also voted for Y...

We can now see that we don't have enough information to find the sum of the values in the 2 blue boxes

As such, statement 1 is NOT SUFFICIENT

Statement 2: Y got votes from 60% of female voters
The two highlighted boxes represent the female voters.

Let's let F = the total number of female voters.
If 60% of the females voted for Y, then we can write 0.6F = 433
If we wanted to, we COULD solve this equation for F, at which point we COULD ALSO determine the number of females who voted for X.
Since we COULD determine the number of females who voted for X, then we COULD ALSO find the total number of people who voted for X

Since we could easily answer the target question with certainty, statement 2 is SUFFICIENT

Aside: This question has a slight issue in that the numbers don't work very well. If we were to solve for the number of female voters, we'd get a fractional answer, and a true GMAT question would never allow for this.

Then try these additional practice questions that can be solved using the Double Matrix Method:
- http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1
- http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2
- http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3
- http://www.beatthegmat.com/ds-quest-t187706.html
- http://www.beatthegmat.com/overlapping-sets-questions-t183320.html
- http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html
- http://www.beatthegmat.com/ds-french-japanese-t222297.html
- http://www.beatthegmat.com/sets-t269449.html#692540
- http://www.beatthegmat.com/in-costume-for-halloween-t269355.html#692116

Cheers,
Brent

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canbtg Senior | Next Rank: 100 Posts
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Sat Nov 02, 2013 8:18 am
thanks Brent . The question is from GMATPREP QP .

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Brent@GMATPrepNow GMAT Instructor
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Sat Nov 02, 2013 8:42 am
canbtg wrote:
thanks Brent . The question is from GMATPREP QP .
Hmmm, if it's an official GMATPrep question then either I'm missing something totally basic, or the question was not transcribed correctly. Here's why:

Let's let F = the total number of female voters.
It is given that 433 of the females voted for Y
Statement 2 say that 60% of the females voted for Y.
This mean that we can write 0.6F = 433
So, F = 433/0.6 = 721 2/3
This doesn't make any sense. We can't have 721 2/3 females.

Cheers,
Brent

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canbtg Senior | Next Rank: 100 Posts
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Sat Nov 02, 2013 3:01 pm
Brent@GMATPrepNow wrote:
canbtg wrote:
thanks Brent . The question is from GMATPREP QP .
Hmmm, if it's an official GMATPrep question then either I'm missing something totally basic, or the question was not transcribed correctly. Here's why:

Let's let F = the total number of female voters.
It is given that 433 of the females voted for Y
Statement 2 say that 60% of the females voted for Y.
This mean that we can write 0.6F = 433
So, F = 433/0.6 = 721 2/3
This doesn't make any sense. We can't have 721 2/3 females.

Cheers,
Brent
I get your point . This is from some online resource tagged with GMATPREP Question (totally , misleading) . SO , I am sorry for creating a confusion .

I could Actually trace the original GMAT question :

Each vote in a certain election went to one of the two candidates, X or Y. Candidate X received 624 of the votes cast by men , and candidate Y received 483 of the votes cast by women , how many votes did X receive?
A. Candidate X got 50% of the votes cast by men.
B. Candidate Y got 60% of the votes cast by women.

OA
B

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Brent@GMATPrepNow GMAT Instructor
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Sat Nov 02, 2013 3:48 pm
Good work.
483 works much better.

Cheers,
Brent

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nikhilgmat31 Legendary Member
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Thu Oct 08, 2015 10:06 pm
Does the new statements mean

1. Candidate X got 50% of the votes cast by men. = x got 50% of votes from men
2. Candidate Y got 60% of the votes cast by women. = y got 60 % of votes from women

1- In this case X got 624 votes from men so total votes X got = 624 * 2 = 1248 - SUFFICIENT

2. In this case Y got 483 votes from women so 60% of Y = 483 gives Y = 805 - NOT SUFFICIENT.

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