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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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Question Stats:

75% (02:17) correct 25% (02:33) wrong based on 124 sessions

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

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New post 26 Aug 2019, 03:25
3 methods:

1) scale

x---52---61
--3--:--1--

means 9=x –>52-3x=52-27=25

2) table

61*3
x*1
52*(1+3)

183+x=208 –> x=25

3) Allegation

(52-x)/(61-52)=3/1
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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 Sep 2019, 19:05
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%



We can create the equation:

0.61A + nB = 0.52(A + B)

0.61A + nB = 0.52A + 0.52B

0.09A = 0.52B - nB

and

A/B = 3/1

A = 3B

Substituting, we have:

0.09(3B) = 0.52B - nB

0.27B = 0.52B - nB

nB = 0.25B

n = 0.25 = 25%

Alternate Solution:

Let’s assume that 400 people voted. This means that 300 were in County A and 100 were in County B.

Smith won 52% of the 400 votes, which is 400 x 0.52 = 208 total votes.
He also won 61% of the vote in County A, which is 300 x 0.61 = 183 votes.

This means that his County B vote total is 208 - 183 = 25, which is 25% of the 100 votes cast in County B.

Answer: A
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Re: In an election, candidate Smith won 52 percent of the total vote in Co   [#permalink] 02 Sep 2019, 19:05
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