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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]

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New post 07 Dec 2012, 05:53
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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%
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Re: In a certain city, 60 percent of the registered voters are  [#permalink]

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New post 07 Dec 2012, 05:58
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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]

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New post 04 Jan 2015, 12:29
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:

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In a certain city, 60 percent of the registered voters are  [#permalink]

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New post 21 Mar 2015, 05:37
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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%



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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Re: In a certain city, 60 percent of the registered voters are  [#permalink]

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New post 19 Dec 2015, 09:50
Plugin 100 as total register voters
D are 60% of 100 are 60 voters
R are 40% of 100 are 40 voters

75% of 60 D register voters are 45
20% of 40 R register voter are 8

Total voter vote for Candidate A is 53 or 53% of 100.
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In a certain city, 60 percent of the registered voters are Democ  [#permalink]

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New post 09 Jun 2016, 13:54
banksy 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%


Solution:

We are given that 60 percent of the voters are Democrats and the rest are Republicans. This means that 40 percent 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 initially 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 is B.
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Re: In a certain city, 60 percent of the registered voters are  [#permalink]

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New post 10 Jun 2016, 02:52
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 total voters are x

Democrats: 0.6 x
Republicans: 0.4x

Voters: (0.75 of 0.6x)+(0.2 of 0.4x) = 0.45x+0.08x = 0.53x = 53 % voted.

B is the answer
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Re: In a certain city, 60 percent of the registered voters are  [#permalink]

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New post 07 Apr 2017, 01:56
These type of problems always give me troubles. But, after a while, I manage to solve it.

Initially, by putting the information into a double-set matrix (I know, it takes time to build it, but it helps me see things more clearly).

Total number of registered voters = R
Registered and Democrats = \(\cfrac { 3 }{ 5 } R\)
Registered Republicans = \(\cfrac { 2 }{ 5 } R\)
75% of Registered Democrats = \(\cfrac { 3 }{ 4 } \left( \cfrac { 3 }{ 5 } R \right)\)
20% of the Registered Republicans = \(\cfrac { 1 }{ 5 } \left( \cfrac { 2 }{ 5 } R \right)\)

\(\cfrac { \cfrac { 3 }{ 4 } \left( \cfrac { 3 }{ 5 } R \right) +\cfrac { 1 }{ 5 } \left( \cfrac { 2 }{ 5 } R \right) }{ R } \\ \cfrac { \cfrac { 9 }{ 20 } R+\cfrac { 2 }{ 25 } R }{ R } \\ \cfrac { \cfrac { 45 }{ 100 } R+\cfrac { 8 }{ 100 } R }{ R } \\ \cfrac { \cfrac { 53 }{ 100 } R }{ R } \\ \cfrac { 53 }{ 100 } R\ast \cfrac { 1 }{ R } \\ \cfrac { 53 }{ 100 } =53%\)

2nd method: Weighted averages:

\(\cfrac { w1 }{ w2 } =\cfrac { \left( A2-Avg \right) }{ \left( Avg-A1 \right) } \\ \cfrac { 40 }{ 60 } =\cfrac { \left( 75-Avg \right) }{ \left( Avg-20 \right) } \\ \cfrac { 2 }{ 3 } =\cfrac { \left( 75-Avg \right) }{ \left( Avg-20 \right) } \\ 2\left( Avg-20 \right) =3\left( 75-Avg \right) \\ 2Avg-40=225-3Avg\\ 2Avg+3Aavg=225+40\\ 5Avg=265\\ Avg=\cfrac { 265 }{ 5 } \\ Avg=53\)
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In a certain city, 60 percent of the registered voters are Democ  [#permalink]

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New post 17 Apr 2017, 11:35
1
Hi All,

This question is perfect for TESTing VALUES (the approach that rxs0005 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:

GMAT assassins aren't born, they're made,
Rich
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Re: In a certain city, 60 percent of the registered voters are  [#permalink]

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Re: In a certain city, 60 percent of the registered voters are   [#permalink] 02 Oct 2018, 16:08
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