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# Presidential Candidates

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Presidential Candidates [#permalink]  14 Jun 2011, 13:29
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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%
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Re: Presidential Candidates [#permalink]  14 Jun 2011, 14:08
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

T=A only+B only+Both+Neither
100=30-19.5+48-19.5+19.5+N
100=78-19.5+N
N=100-78+19.5=22+19.5=41.5

Ans: "C"
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Re: Presidential Candidates [#permalink]  14 Jun 2011, 16:12
Spot on as always Fluke !!!
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Re: Presidential Candidates [#permalink]  13 Jul 2011, 20:17
fluke 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%

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

T=A only+B only+Both+Neither
100=30-19.5+48-19.5+19.5+N
100=78-19.5+N
N=100-78+19.5=22+19.5=41.5

Ans: "C"

Isn't the formula for overlapping sets

T = A only + B only - Both + Neither?
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Re: Presidential Candidates [#permalink]  07 Sep 2011, 12:30
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".
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Re: Presidential Candidates [#permalink]  07 Sep 2011, 14:45
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] 07 Sep 2011, 14:45
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