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In a survey about potential presidential candidates A and B, [#permalink]
14 Jun 2011, 12:29

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Difficulty:

45% (medium)

Question Stats:

63% (03:42) correct
37% (02:59) wrong based on 97 sessions

In a survey about potential presidential candidates A and B, 30% of the public likes A and 48% liked B.If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that liked neither.

Re: Presidential Candidates [#permalink]
14 Jun 2011, 13:08

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IEsailor wrote:

In a survey about potential presidential candidates A and B, 30% of the public likes A and 48% liked B.If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that liked neither.

a.) 27.5 % b.) 35.5 % c.) 41.5 % d.) 22% e.) 67%

T=100 A=30 B=48 Both=x A only=30-x B only=48-x N=Neither

Given: A only+B only=2*Both 30-x+48-x=2x 78=4x x=19.5

In a survey about potential presidential candidates A and B, 30% of the public likes A and 48% liked B.If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that liked neither.

a.) 27.5 % b.) 35.5 % c.) 41.5 % d.) 22% e.) 67%

T=100 A=30 B=48 Both=x A only=30-x B only=48-x N=Neither

Given: A only+B only=2*Both 30-x+48-x=2x 78=4x x=19.5

no, my friend, you're mistaken. the only reason we subtract "both" is because "A=A only+both" and "B=B only+both". "A+B = A only + B only + 2*both" and, therefore, we subtract "both".
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MGMAT recommends using a small table when dealing with overlapping sets with only 2 variables. So if i try to use it in this problem, it doesn't work.

Like A Don't like A TOTAL Like B x 48-x 48 Don't like B 30-x N 52 TOTAl 30 70 100

Everything is the same as in Fluke's answer except I also calculated total for Don't like A =70 and Don't like B =52. Then if try to get to N i use N=52-30-x N= 2.5 Why is this approach wrong?

Re: Presidential Candidates [#permalink]
17 Aug 2013, 11:52

MBAhereIcome wrote:

gijoedude wrote:

Isn't the formula for overlapping sets

T = A only + B only - Both + Neither?

no, my friend, you're mistaken. the only reason we subtract "both" is because "A=A only+both" and "B=B only+both". "A+B = A only + B only + 2*both" and, therefore, we subtract "both".

So why don't we use T = A only + B only + 2*both + Neither? Don't understand this part. Why we add the "both" part I mean

Re: In a survey about potential presidential candidates A and B, [#permalink]
18 Aug 2013, 16:12

IEsailor wrote:

In a survey about potential presidential candidates A and B, 30% of the public likes A and 48% liked B.If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that liked neither.

A. 27.5 % B. 35.5 % C. 41.5 % D. 22% E. 67%

i think fraction can't be answer here .........

Solution:

Like both = x So like only one = 2x Like Only A = 30-2x Like Only B = 48-2x

Like neither= 100 – [(30-2x) + (48-2x) + x ] = 100 – [78-3x] = 22 + 3x

From this equation we can back solve. And only 67% satisfies the Answer. [If, 22+3x = 67 or, 3x = 45 or, x =15 ] [So like both 15 %, like only A = 0 %, like only B=18% and neither = 67%] {total = 0+18+15+67 = 100 }

Re: In a survey about potential presidential candidates A and B, [#permalink]
25 Nov 2013, 20:39

One more thing, we can take x = 100 of above & solve it Also, we are calculating in terms of percentage, so answer may be in decimal. (Here we dont know the exact number of people surveyed)
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Re: In a survey about potential presidential candidates A and B, [#permalink]
25 Nov 2013, 23:09

Expert's post

IEsailor wrote:

In a survey about potential presidential candidates A and B, 30% of the public likes A and 48% liked B.If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that liked neither.

A. 27.5 % B. 35.5 % C. 41.5 % D. 22% E. 67%

Number of people who like both = x Number of people who like only 1 but not both = 2x Number of people who like at least 1 candidate = x + 2x = 3x

3x = 30 + 48 - x (the 3x does not include the ones who don't line either candidate. Rest of the formula is the standard overlapping sets formula. The 3x gives the number of people in the overlapping circles) x = 19.5%

Re: In a survey about potential presidential candidates A and B, [#permalink]
25 Nov 2013, 23:12

Expert's post

Asifpirlo wrote:

IEsailor wrote:

In a survey about potential presidential candidates A and B, 30% of the public likes A and 48% liked B.If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that liked neither.

A. 27.5 % B. 35.5 % C. 41.5 % D. 22% E. 67%

i think fraction can't be answer here .........

Also, fraction as the answer is not a problem. If you get that 41.5% people don't like either candidate, it just means that there are at least 200 total people such that 41.5% of 200 is 83 people. You can certainly have 83 people not liking either candidate.
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