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In a certain city, 60 percent of the registered voters are

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In a certain city, 60 percent of the registered voters are [#permalink] New post 07 Dec 2012, 04:53
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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%
[Reveal] Spoiler: OA
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Re: In a certain city, 60 percent of the registered voters are [#permalink] New post 07 Dec 2012, 04:58
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Walkabout 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%


Say there are total of 100 registered voters in that city. Thus 60 are Democrats and 40 are Republicans.

60*0.75=45 Democrats are expected to vote for Candidate A;
40*0.20=8 Republicans are expected to vote for Candidate A.

Thus total of 45+8=53 registered voters are expected to vote for Candidate A, which is 53% of the total number of registered voters.

Answer: B.
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Re: In a certain city, 60 percent of the registered voters are [#permalink] New post 04 Jan 2015, 09:41
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Re: In a certain city, 60 percent of the registered voters are [#permalink] New post 04 Jan 2015, 11:29
Expert's post
Hi All,

This question is perfect for TESTing VALUES (the approach that Bunuel used). It can also be solved with arithmetic/algebra:

We're told that 60% of voters are Democrats and 40% are Republicans

X = Total Voters
.6X = Democrats
.4X = Republicans

Next, we're told that 75% of the Democrats and 20% of the Republicans are expected to vote for Candidate A...

(.6X)(.75) = .45X
(.4X)(.2) = .08X

The question asks what percent of the voters are expected to vote for Candidate A:

.45X + .08X = .53X = 53% of voters

Final Answer:
[Reveal] Spoiler:
B


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In a certain city, 60 percent of the registered voters are [#permalink] New post 21 Mar 2015, 04:37
Walkabout 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%



weighted average question :

D:R
3:2
so we know weighted average will be 2 units far from the D and 3 units far from R .

so 5X= 75-20 ; X =11 ;
hence w.avg = 75 - 2*11 = 53
or
20 + 3*11 = 53

alternately
(0*40 + 55*60)/100 = 33 so W.Avg= 33+20 = 53
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In a certain city, 60 percent of the registered voters are   [#permalink] 21 Mar 2015, 04:37
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