Each vote in a certain election went to one of the two candidates, \(X\) or \(Y.\) Candidate \(X\) received \(624\) vote

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

Each vote in a certain election went to one of the two candidates, \(X\) or \(Y.\) Candidate \(X\) received \(624\) vote

by Vincen » Sun Aug 15, 2021 12:33 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.

Answer: B

Source: GMAT Prep

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Source: Beat The GMAT — Data Sufficiency | Sun Aug 15, 2021 12:33 am

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Re: Each vote in a certain election went to one of the two candidates, \(X\) or \(Y.\) Candidate \(X\) received \(624\)

by Brent@GMATPrepNow » Sun Aug 15, 2021 5:41 am

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Vincen wrote: ↑
Sun Aug 15, 2021 12:33 am
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.

Answer: B

Source: GMAT Prep

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