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OG2015 PS In a certain city

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by lionsshare » Wed Sep 13, 2017 3:23 am
In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?

(A) 50%
(B) 53%
(C) 54%
(D) 55%
(E) 57%

OA: B

Hi, Experts! Please explain how to solve this problem. Many thanks.
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by [email protected] » Wed Sep 13, 2017 6:39 pm
Hi lionsshare,

We're told that 60 percent of the registered voters are Democrats and the rest are Republicans and that 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A. We're asked for the percent of the registered voters who are expected to vote for Candidate A. This question can be solved by TESTing VALUES.

IF.... there are 100 TOTAL voters, then...
60% = 60 are registered Democrats
100 - 60 = 40 are registered Republicans

75% of the 60 Democrats = 45
20% of the 40 Republicans = 8
45 + 8 = 53 of the 100 voters will vote for Candidate A.

Final Answer: B

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by Jay@ManhattanReview » Wed Sep 13, 2017 10:23 pm
lionsshare wrote:In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?

(A) 50%
(B) 53%
(C) 54%
(D) 55%
(E) 57%

OA: B

Hi, Experts! Please explain how to solve this problem. Many thanks.
Percentage of voters that are registered voters for Democrats = 60%
Thus, the percentage of voters that are registered voters for Republicans = 100% - 60% = 40%

Percentage of registered voters for Democrats who voted for Candidate A = 75% of 60% = (75/100) x 60% = (3/4) x 60% = 45%

Percentage of registered voters for Republicans who voted for Candidate A = 20% of 40% = (20/100) x 40% = (1/5) x 40% = 8%

Percentage of total votes expected for Candidate A = 45% + 8% = 53%

The correct answer: B

Hope this helps!

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by Jeff@TargetTestPrep » Tue Sep 19, 2017 2:58 pm
lionsshare wrote:In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?

(A) 50%
(B) 53%
(C) 54%
(D) 55%
(E) 57%

OA: B
We are given that 60% of the voters are Democrats and the rest are Republicans. This means that 40% are Republicans. We also know that 75% of the voters who are Democrats and 20% of the voters who are Republicans are expected to vote for Candidate A.

The easiest way to solve this problem is to assume that the total number of registered voters is 100 (we could use other numbers, but 100 is an easy number to work with in percentage problems).

We know that 60% of the registered voters are Democrat and 40% are Republicans, so there are 60 Democrat registered voters and 40 Republican registered voters.

Now, since 75% of the 60 Democrat registered voters are expected to vote for Candidate A, we know that 0.75 x 60 = 45 Democrats are expected to vote for Candidate A. Similarly, because 20% of the 40 Republican registered voters are expected to vote for Candidate A, we know that 0.2 x 40 = 8 Republicans are expected to vote for Candidate A.

Thus, there are 45 + 8 = 53 voters expected to vote for Candidate A. Remember, we used 100 as the total number of voters, so this means that 53 out of 100, or 53% of the voters, are expected to vote for Candidate A.

Answer: B

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Answer

by prime122 » Tue Apr 17, 2018 8:39 pm
We are given that 60% of the voters are Democrats and the rest are Republicans. This means that 40% are Republicans. We also know that 75% of the voters who are Democrats and 20% of the voters who are Republicans are expected to vote for Candidate A.

The easiest way to solve this problem is to assume that the total number of registered voters is 100 (we could use other numbers, but 100 is an easy number to work with in percentage problems).

We know that 60% of the registered voters are Democrat and 40% are Republicans, so there are 60 Democrat registered voters and 40 Republican registered voters.

Now, since 75% of the 60 Democrat registered voters are expected to vote for Candidate A, we know that 0.75 x 60 = 45 Democrats are expected to vote for Candidate A. Similarly, because 20% of the 40 Republican registered voters are expected to vote for Candidate A, we know that 0.2 x 40 = 8 Republicans are expected to vote for Candidate A.

Thus, there are 45 + 8 = 53 voters expected to vote for Candidate A. Remember, we used 100 as the total number of voters, so this means that 53 out of 100, or 53% of the voters, are expected to vote for Candidate A
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