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!!
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Let the number of voters in A = 3.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 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.
Last edited by GMATGuruNY on Wed Apr 18, 2012 3:39 am, edited 1 time in total.
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Hi!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!!
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.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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- GMAT Kolaveri
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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?
@Mitch,
Could you pls explain "Treat the percentages as averages. " method?
@Stuart,
The method you have used is the alligation method right?
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This is a weighted average question, no different from the following:GMAT Kolaveri wrote:Thank you Mitch and Stuart.
@Mitch,
Could you pls explain "Treat the percentages as averages. " method?
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.
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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
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
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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: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%
0.61(3x) + (p/100)x = .52(3x + x)
61(3x) + px = 52(4x)
183x + px = 208x
183 + p = 208
p = 25
Answer: A
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