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

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

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New post 27 Dec 2015, 10:01
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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%

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

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New post 02 Jan 2016, 18:44
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Hi All,

This question can be solved by TESTing VALUES.

We're given a series of facts to work with:
1) In an election, candidate Smith won 52 percent of the total vote in Counties A and B.
2) He won 61 percent of the vote in County A.
3) The ratio of people who voted in County A to County B is 3:1

We're asked for the PERCENT of the vote that he won in County B.

Let's TEST VALUES....

Since the ratio of the people who voted is 3:1, let's TEST...
300 people voted in County A
100 people voted in County B

He won 52% of the TOTAL vote...
(.52)(400) = 208 votes

He won 61% of County A....
(.61)(300) = 183 votes

208 - 183 = 25 votes won in County B (out of the 100 votes that were cast).

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

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New post 12 Apr 2016, 08:03
Bunuel 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%

given voters in ratio 3:1
let A has 300 voters & B has 100 voters
for A 61% voted means 61*300=183 votes
combined for A & B has 400 voters and voted 52% so total votes =208

balance votes=208-183=25
As B has 100 voters so 25 votes means 25% of votes required

Ans A
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Re: In an election, candidate Smith won 52 percent of the total vote in Co  [#permalink]

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New post 12 Apr 2016, 10:33
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1
Bunuel 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%


Another way to do these type of Q, which involve AVERAGES is WEIGHTED average method or Allegation..

\(A:B = 3:1\)...
A = 61% and AVG = 52%..
so \(B = 52 - \frac{3}{1}( 61-52)\)..
=> 52-3*9 = 52-27 = 25%
A
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Re: In an election, candidate Smith won 52 percent of the total vote in Co  [#permalink]

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New post 12 May 2016, 10:04
Bunuel 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%

Can be done with weighted avg. method also....
w1/w2=(a2-avg)/(avg-a1)
let a2=vote win in country B=x then
3/1=(x-52)/52-61)
x=25%
Ans A
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In an election, candidate Smith won 52 percent of the total vote in Co  [#permalink]

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New post 31 Jan 2018, 23:17
Bunuel 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%


\(a = 3b\)
\(\frac{52(a+b)}{100} = \frac{61a}{100} + \frac{nb}{100}\)
\(n = 25\)
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In an election, candidate Smith won 52 percent of the total vote in Co &nbs [#permalink] 31 Jan 2018, 23:17
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