GMAT Kolaveri wrote:In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

25%
27%
34%
43%
49%

Need to know alternate methods of solving this problem in less than 2 min!!

source: https://www.freequestionaday.com/gmat

Let the number of voters in A = 3.
Let the number of voters in B = 1.
The total number of voters in A and B = 3+1 = 4.

Treat the percentages as averages.
Sum in A and B = (number)(average) = 4*52 = 208.
Sum in A = (number)(average) = 3*61 = 183.
Sum in B = 208-183 = 25.
Average in B = sum/number = 25/1 = 25.

The correct answer is A.

GMAT Kolaveri wrote:In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

25%
27%
34%
43%
49%

Need to know alternate methods of solving this problem in less than 2 min!!

Hi!

Almost certainly, the quickest way to solve this type of weighted average problem is by plotting the groups and the total on a number line, like this:

Group 1 -----x------ Total Avg -----y----- Group 2

in which x and y represent the distance between Group 1 and the average and Group 2 and the average.

When you plot the information, you can then construct the following ratio:

Group1/Group2 = y/x

Applying that method to this question, we get:

Group B---------3x---------- 52% -----x------61%

We can see that x=9%, so 3x=27%. Therefore, B = 52% - 27% = 25%... choose A!

Using this approach, you can usually solve these questions in under 30 seconds.

Thank you Mitch and Stuart.

@Mitch,
Could you pls explain "Treat the percentages as averages. " method?

@Stuart,
The method you have used is the alligation method right?

GMAT Kolaveri wrote:Thank you Mitch and Stuart.

@Mitch,
Could you pls explain "Treat the percentages as averages. " method?

This is a weighted average question, no different from the following:

The AVERAGE number of hours worked each week by the residents of Counties A and B, combined, is 52. In County A, the residents work an AVERAGE of 61 hours per week. If the ratio of the population of County A to the population of County B is 3:1, what is the AVERAGE number of hours worked per week by the residents of County B?

One approach is to assign the appropriate WEIGHT to each percentage/average.

Since A:B = 3:1, of every 4 residents, 3 will be from County A and 1 will be from County B.
The total number of hours worked by all 4 residents = 4*52 = 208.
The total number of hours worked by the 3 residents from County A = 3*61 = 183.
Thus, the total number of hours worked by the 1 resident from County B = 208-183 = 25.
Thus, the average number of hours worked per week by the 1 resident from County B = 25/1 = 25.

Smart No. Game

voters raion in two cities = 3/1
lets assume the population be 300 and 100 respectively

over all vote the winner got = 52 %
therefore, 52% of (300+100) people= 208

the winner got 61 % of votes in city with 300 voters(CITY a)
therefore, no of votes he got from that city=183

votes from (city B )= total vote from both cities MINUS votes from city A
= 208-183
=25

(A) wins

25.

I had the same approach as @thevenus.

GMAT Kolaveri wrote:In an election, candidate Smith won 52% of the total vote in Counties A and B. He won 61% of the vote in County A. If the ratio of people who voted in County A to County B is 3:1, what percent of the vote did candidate Smith win in County B ?

25%
27%
34%
43%
49%

We can let the number of votes cast in County B = x and thus the number of votes cast in County A = 3x. We can create the following equation where p = percent of vote candidate Smith won in County B:

0.61(3x) + (p/100)x = .52(3x + x)

61(3x) + px = 52(4x)

183x + px = 208x

183 + p = 208

p = 25

Answer: A