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# In an election, candidate Smith won 52% of the total vote in

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In an election, candidate Smith won 52% of the total vote in  [#permalink]

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25 Sep 2012, 05:35
10
00:00

Difficulty:

35% (medium)

Question Stats:

73% (02:03) correct 27% (02:11) wrong based on 370 sessions

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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 ?

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

Hint:-Choose smart Numbers

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Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

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25 Sep 2012, 05:41
1
(61%)*3x + (y%)*x = (52%)*4x
y = 25%
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Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

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25 Sep 2012, 06:00
2
1
thevenus 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 ?

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

Hint:-Choose smart Numbers

Use the property of weighted averages:
at-a-certain-company-average-arithmetic-mean-number-of-137851.html#p1115917

$$b$$ - percent of the vote that candidate Smith win in County B
In our case: $$\frac{A}{B}=\frac{3}{1}=\frac{52-b}{61-52}$$, from which $$b = 25%.$$

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Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

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10 Jan 2014, 03:27
A : B : Total
3 : 1 : 4

Say there are a total of 100 votes. 100/4 = 25. Three parts of the 100 are in country A. So 75. Rest is in country B. Thus 25, A.

Wasn't quite sure, so this was an elevated guess, does this work? Or was it luck? :D
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In an election, candidate Smith won 52% of the total vote in  [#permalink]

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24 Feb 2015, 02:27
unceldolan wrote:
A : B : Total
3 : 1 : 4

Say there are a total of 100 votes. 100/4 = 25. Three parts of the 100 are in country A. So 75. Rest is in country B. Thus 25, A.

Wasn't quite sure, so this was an elevated guess, does this work? Or was it luck? :D

I think it should work. It sort of uses the unknown multiplier.

In this sense, since we have 4 parts, 1/4 (which is B) is 25%.

We could for example do this:

3x+1x=100 (if we pick 100 as a smart number)
4x=100
x=25.

Then 1*25=25, so B=25.

Nice way!
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Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

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24 Feb 2015, 02:34
EvaJager wrote:
thevenus 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 ?

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

Hint:-Choose smart Numbers

Use the property of weighted averages:
at-a-certain-company-average-arithmetic-mean-number-of-137851.html#p1115917

$$b$$ - percent of the vote that candidate Smith win in County B
In our case: $$\frac{A}{B}=\frac{3}{1}=\frac{52-b}{61-52}$$, from which $$b = 25%.$$

Sounds reasonable. I couldn't quite get the denominator 61-52 for B. 61% is only the votes in A. 52% are total votes. So, if we subtract 52% (the total votes) from 61% (only votes from A) we should remain with votes from B?
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Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

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28 Feb 2015, 10:31
1
2
thevenus 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 ?

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

Hint:-Choose smart Numbers

Let total votes in County A = 3x.
Let total votes in County B = x.
Hence total votes in Count A & B together = 4x

Given that, 0.52(4x) = 0.61(3x) + n(x)
So, 2.08x = 1.83x + nx
So, n = 0.25 = 25%
Hence option A

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In an election, candidate Smith won 52% of the total vote in  [#permalink]

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20 Nov 2017, 17:30
thevenus 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 ?

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

Hint:-Choose smart Numbers

$$\frac{A}{B}=\frac{3}{1}$$

I just used those numbers, as you would in a mixture problem.

Let A = 3
Let B = 1
Resultant percentage = .52(A + B) = .52(4)
Let x = percent of vote won in B

.61(3) + x(1) = .52(4)
1.83 + x = 2.08
x = 2.08 - 1.83
x = .25 * 100 = 25 percent

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Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

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21 Nov 2017, 02:47
1
thevenus 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 ?

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

Hint:-Choose smart Numbers

hi

lets think this way

the voters, the weights, in country A and B are in the ratio of 3 : 1

now, set the weighted average equation

61 * 3 + 1 * b
____________ = 52
4

solving for b, we get the desired result: 25%
thanks

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Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

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22 Nov 2017, 11:13
thevenus 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 ?

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

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Re: In an election, candidate Smith won 52% of the total vote in  [#permalink]

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08 Oct 2018, 07:48
To find the percent of votes won in County B, we need to recognize that the total votes won is the sum of the votes in the 2 counties and that the number of votes won in each county is the percentage won multiplied by the number of voters. If we let x% be the percent won in County B, we can write this equation: (61% of County A voters) + (x% of County B voters) = 52% of all voters, or 0.61(County A voters) + (x/100) (County B voters) = 0.52(all voters).

We don't know the number of voters, but we do know that the ratio of County A voters to County B voters is 3:1. Thus, 3/4 of the voters are in County A and 1/4 are in County B. Now suppose that V is the total number of voters, meaning that we have V voters in County A and V voters in County B. So, our original equation becomes 0.61*(3/4) v + (x/100) (1/4) v = 0.52v.

Notice that V appears in each term, so it can be cancelled out. In other words, since we know the proportion of voters in each county, we don't need to know the actual number of voters. In fact, we can simply think of the overall percentage won, 52%, as the weighted average of the percentages won in each county, where the weights are each county's fraction of the total voters.

To solve for x, let's get rid of the fractions by multiplying both sides by 400. This gives us 0.61(300) + x = 208, 183 + x = 208, or x = 208 - 183 = 25. The percent of the voters voting for candidate Smith was 25%. Choice (A) is correct.
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Re: In an election, candidate Smith won 52% of the total vote in   [#permalink] 08 Oct 2018, 07:48
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