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

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

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.

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.

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

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

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:

\(\cfrac { w1 }{ w2 } =\cfrac { \left( A2-Avg \right) }{ \left( Avg-A1 \right) } \\ \cfrac { 40 }{ 60 } =\cfrac { \left( 75-Avg \right) }{ \left( Avg-20 \right) } \\ \cfrac { 2 }{ 3 } =\cfrac { \left( 75-Avg \right) }{ \left( Avg-20 \right) } \\ 2\left( Avg-20 \right) =3\left( 75-Avg \right) \\ 2Avg-40=225-3Avg\\ 2Avg+3Aavg=225+40\\ 5Avg=265\\ Avg=\cfrac { 265 }{ 5 } \\ Avg=53\)

Imo B
.60*.75+.40*.20=.53

Sent from my ONE E1003 using GMAT Club Forum mobile app

To calculate the percentage of registered voters expected to vote for Candidate A, we need to consider the proportions of Democrats and Republicans who are expected to vote for Candidate A.

Given:
Percentage of registered voters who are Democrats = 60%
Percentage of registered voters who are Republicans = 100% - 60% = 40%

Percentage of Democrats expected to vote for Candidate A = 75%
Percentage of Republicans expected to vote for Candidate A = 20%

To find the overall percentage of registered voters expected to vote for Candidate A, we calculate the weighted average of the two proportions using the percentages of Democrats and Republicans:

Percentage of registered voters expected to vote for Candidate A = (Percentage of Democrats * Percentage of Democrats expected to vote for Candidate A) + (Percentage of Republicans * Percentage of Republicans expected to vote for Candidate A)

Percentage of registered voters expected to vote for Candidate A = (60% * 75%) + (40% * 20%) = 45% + 8% = 53%

Therefore, it is expected that 53% of the registered voters will vote for Candidate A, which corresponds to option (B) in the given choices.