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Each vote in a certain election went to one of the two candi

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by alanforde800Maximus » Wed May 16, 2018 1:27 am

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

1) Candidate X received 50% cast by men
2) Candidate Y received 60% cast by women.

Source: Question Pack-1
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Source: — Data Sufficiency |

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Each vote in a certain election went to one of the two candi

by Brent@GMATPrepNow » Wed May 16, 2018 4:26 am
alanforde800Maximus wrote:Each vote in a certain election went to one of the two candidates, X or Y. Candidate X received 624 votes cast by men and candidate Y received 483 votes cast by women. How many votes did X receive?

1) Candidate X received 50% cast by men
2) Candidate Y received 60% cast by women.

Source: Question Pack-1
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:
Image

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

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


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

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

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

Answer: B

To learn more about the Double Matrix Method , watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Then try these additional practice questions that can be solved using the Double Matrix Method:
- https://www.beatthegmat.com/mba/2011/05 ... question-1
- https://www.beatthegmat.com/mba/2011/05 ... question-2
- https://www.beatthegmat.com/mba/2011/05 ... question-3
- https://www.beatthegmat.com/ds-quest-t187706.html
- https://www.beatthegmat.com/overlapping ... 83320.html
- https://www.beatthegmat.com/finance-maj ... 67425.html
- https://www.beatthegmat.com/ds-french-j ... 22297.html
- https://www.beatthegmat.com/sets-t269449.html#692540
- https://www.beatthegmat.com/in-costume- ... tml#692116

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Jeff@TargetTestPrep » Thu May 17, 2018 5:23 pm
alanforde800Maximus wrote:Each vote in a certain election went to one of the two candidates, X or Y. Candidate X received 624 votes cast by men and candidate Y received 483 votes cast by women. How many votes did X receive?

1) Candidate X received 50% cast by men
2) Candidate Y received 60% cast by women.
We are given that Candidate X received 624 votes cast by men and candidate Y received 483 votes cast by women. We need to determine the number of votes X received.

Statement One Alone:

Candidate X received 50% cast by men.

We can create the equation:

624 = 0.5m

1,248 = m

So we see that the total votes cast by men was 1,248. However, since we don't know the number of votes he received from women, we cannot determine the total number of votes X received.

Statement Two Alone:

Candidate Y received 60% cast by women.

We can create the equation:

483 = 0.6w

805 = w

So we see that the total votes cast by women was 805, so we see that X received 805 - 463 = 342 votes from women. Therefore, X received a total of 624 + 342 = 966 votes.

Answer: B

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by [email protected] » Thu May 17, 2018 6:01 pm
Hi alanforde800Maximus,

We're told that each vote in a certain election went to one of the two candidates, X or Y, Candidate X received 624 votes cast by men and Candidate Y received 483 votes cast by women. We're asked for the total number of votes received by Candidate X. Since we already know how many men voted for X, to answer this question we need to know that number of women who voted for X. This question doesn't actually require much math at all - you can beat it with a bit of logic and paying attention to the details.

1) Candidate X received 50% cast by men

Fact 1 tells us NOTHING about the number of women who voted for X.
Fact 1 is INSUFFICIENT.

2) Candidate Y received 60% cast by women.

With the information from Fact 2, we know that 40% of the women voted for X. Since 60% voted for Y - and that 60% represented 483 votes, we COULD calculate what 40% of the women's votes totaled (using the ratio 60/40 = 483/Z where Z is the number of women who voted for Candidate X). We don't actually have to do that math to know that there would be just ONE answer.
Fact 2 is SUFFICIENT.

Final Answer: B

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