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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, 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%
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Joined: 02 Sep 2009
Posts: 53065
Re: In a certain city, 60 percent of the registered voters are  [#permalink]

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07 Dec 2012, 04:58
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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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Re: In a certain city, 60 percent of the registered voters are  [#permalink]

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04 Jan 2015, 11:29
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

GMAT assassins aren't born, they're made,
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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Director Joined: 07 Aug 2011 Posts: 529 Concentration: International Business, Technology GMAT 1: 630 Q49 V27 In a certain city, 60 percent of the registered voters are [#permalink] Show Tags 21 Mar 2015, 04:37 1 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 Ryerson (Ted Rogers) Thread Master Joined: 27 Sep 2015 Posts: 57 Location: Canada GMAT 1: 410 Q33 V13 WE: Management Consulting (Computer Software) Re: In a certain city, 60 percent of the registered voters are [#permalink] Show Tags 19 Dec 2015, 08:50 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. _________________ Discipline does not mean control. Discipline means having the sense to do exactly what is needed. Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4955 Location: United States (CA) In a certain city, 60 percent of the registered voters are Democ [#permalink] Show Tags 09 Jun 2016, 12:54 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. _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Senior Manager Joined: 18 Jan 2010 Posts: 251 Re: In a certain city, 60 percent of the registered voters are [#permalink] Show Tags 10 Jun 2016, 01:52 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 Manager Status: On a 600-long battle Joined: 21 Apr 2016 Posts: 136 Location: Hungary Concentration: Accounting, Leadership Schools: Erasmus '19 GMAT 1: 410 Q18 V27 GMAT 2: 490 Q35 V23 Re: In a certain city, 60 percent of the registered voters are [#permalink] Show Tags 07 Apr 2017, 00:56 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: $$\cfrac { w1 }{ w2 } =\cfrac { \left( A2-Avg \right) }{ \left( Avg-A1 \right) } \\ \cfrac { 40 }{ 60 } =\cfrac { \left( 75-Avg \right) }{ \left( Avg-20 \right) } \\ \cfrac { 2 }{ 3 } =\cfrac { \left( 75-Avg \right) }{ \left( Avg-20 \right) } \\ 2\left( Avg-20 \right) =3\left( 75-Avg \right) \\ 2Avg-40=225-3Avg\\ 2Avg+3Aavg=225+40\\ 5Avg=265\\ Avg=\cfrac { 265 }{ 5 } \\ Avg=53$$ _________________ "When the going gets tough, the tough gets going!" |Welcoming tips/suggestions/advices (you name it) to help me achieve a 600| EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13576 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 In a certain city, 60 percent of the registered voters are Democ [#permalink] Show Tags 17 Apr 2017, 10:35 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 _________________ 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 Free
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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, 15:08
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