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

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07 Dec 2012, 05:58
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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%

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.

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

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21 Mar 2015, 05:37
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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%

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 Democ [#permalink]

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17 Apr 2017, 11:35
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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

[Reveal] Spoiler:
B

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** GMAT Club Legend Joined: 09 Sep 2013 Posts: 15457 Followers: 649 Kudos [?]: 209 [0], given: 0 Re: In a certain city, 60 percent of the registered voters are [#permalink] ### Show Tags 04 Jan 2015, 10:41 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 9120 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 445 Kudos [?]: 2873 [0], given: 169 Re: In a certain city, 60 percent of the registered voters are [#permalink] ### Show Tags 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: [Reveal] Spoiler: B GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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

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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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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.

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

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10 Jun 2016, 02:52
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.

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

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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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Re: In a certain city, 60 percent of the registered voters are   [#permalink] 07 Apr 2017, 01:56
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