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In an election, candidate Smith won 52 percent of the total

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by BTGmoderatorAT » Wed Jan 31, 2018 10:00 pm
In an election, candidate Smith won 52 percent of the total vote in Counties A and B. He won 61 percent 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?

A. 25%
B. 27%
C. 34%
D. 43%
E. 49%

Is there a strategic approach to this question? Can any experts show?
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by karthishanky » Wed Jan 31, 2018 11:40 pm
County A+ County B ration - 52:48
County A ratio - 61:39
Population of County A : Population of County B - 3x:1x

Assume the Population to be 100
Total Population of county A and B - 400

C-A : C-B - 208:192
C-A ratio - 183:117

Difference between whole ratio and Ratio of A = 208 - 183 = 25

25 is what percent of 100 --> 25%
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by GMATGuruNY » Thu Feb 01, 2018 5:03 am
ardz24 wrote:In an election, candidate Smith won 52 percent of the total vote in Counties A and B. He won 61 percent 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?

A. 25%
B. 27%
C. 34%
D. 43%
E. 49%
Since A:B = 3:1, let A=300 and B=100, for a total of 400 votes.

Since Smith won 52% of the 400 votes in A and B, the total number of votes won = (52/100)(400) = 208.
Since Smith won 61% of the 300 votes in A, the number of votes won in A = (61/100)(300) = 183.
Thus, the number of votes won in B = (total votes won in A and B) - (votes won in A) = 208-183 = 25.
Since Smith won 25 of the 100 votes in B, the percent won in B = 25/100 = 25%.

The correct answer is A.
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by DrMaths » Thu Feb 01, 2018 9:22 am
Convert the given facts into equations:
S = 0.52(A+B) = 0.61A + vB (where v = % win in B)
A=3B
Substitute A:
0.52(3B+B) = 0.61*3B + vB
0.52(4B) = 0.61*3B + vB
2.08 = 1.83 + v
v = 2.08-1.83 = 0.25 = 25%
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by Scott@TargetTestPrep » Fri Feb 02, 2018 11:29 am
ardz24 wrote:In an election, candidate Smith won 52 percent of the total vote in Counties A and B. He won 61 percent 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?

A. 25%
B. 27%
C. 34%
D. 43%
E. 49%
We can let the number of people in County A = A and in County B = B, thus:

A/B = 3/1

A = 3B

Let's create a weighted average equation where x is the percentage (in decimal form) of the votes in County B for Smith:


(0.61A + xB)/(A + B) = 0.52

[0.61(3B) + xB]/(3B + B) = 0.52

1.83B + xB = 0.52(4B)

1.83 + x = 2.08

x = 0.25 = 25%

Answer: A

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