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

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Math Expert
Joined: 02 Sep 2009
Posts: 45244
In an election, candidate Smith won 52 percent of the total vote in Co [#permalink]

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27 Dec 2015, 10:01
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Difficulty:

35% (medium)

Question Stats:

73% (01:35) correct 27% (01:46) wrong based on 113 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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02 Jan 2016, 18:44
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Expert's post
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...

He won 61% of County A....

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

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Joined: 05 Mar 2015
Posts: 960
Re: In an election, candidate Smith won 52 percent of the total vote in Co [#permalink]

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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

As B has 100 voters so 25 votes means 25% of votes required

Ans A
Math Expert
Joined: 02 Aug 2009
Posts: 5779
Re: In an election, candidate Smith won 52 percent of the total vote in Co [#permalink]

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12 Apr 2016, 10:33
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Expert's post
1
This post was
BOOKMARKED
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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Director
Joined: 05 Mar 2015
Posts: 960
Re: In an election, candidate Smith won 52 percent of the total vote in Co [#permalink]

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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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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   [#permalink] 31 Jan 2018, 23:17
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