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# In a survey about potential presidential candidates A and B,

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In a survey about potential presidential candidates A and B, [#permalink]

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14 Jun 2011, 12:29
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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%
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Aug 2013, 01:37, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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Re: Presidential Candidates [#permalink]

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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

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]

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14 Jun 2011, 15:12
Spot on as always Fluke !!!

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Re: Presidential Candidates [#permalink]

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13 Jul 2011, 19:17
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]

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07 Sep 2011, 11:30
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]

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07 Sep 2011, 13:45
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?

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Re: Presidential Candidates [#permalink]

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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

Thanx

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Re: In a survey about potential presidential candidates A and B, [#permalink]

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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 }

I think the Answer is (E)

Bunuel should check it…………………….
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Re: In a survey about potential presidential candidates A and B, [#permalink]

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25 Nov 2013, 20:31
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Solved using overlapping sets, kindly refer sketch below:
Attachments

rer.JPG [ 63.68 KiB | Viewed 2654 times ]

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Re: In a survey about potential presidential candidates A and B, [#permalink]

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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]

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25 Nov 2013, 23:09
Expert's post
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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%

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%

Total = 100 = 30 + 48 - 19.5 + Neither
Neither = 41.5%

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Re: In a survey about potential presidential candidates A and B, [#permalink]

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

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30 Dec 2013, 06:04
A=30
B=48

Let,
a= A only
b= B only
c= A and B

T= A+B -(A and B) + N.....(1)

A+B = 30+48 = 78 = a+b+2c....(2)
Given,
a+b=2c....(3)

Sub (3) in (2),

4c=78. So, c=19.5

Therefore,
T(100) = 30+48 - 19.5 + N = > N= 100-78+19.5=41.5

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Re: In a survey about potential presidential candidates A and B, [#permalink]

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Re: In a survey about potential presidential candidates A and B, [#permalink]

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Re: In a survey about potential presidential candidates A and B, [#permalink]

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16 Oct 2016, 06:11
olivite wrote:
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?

N=52-(30-z) =>N=52-30+x=22+x = 22+19.5 = 41.5%

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Re: In a survey about potential presidential candidates A and B,   [#permalink] 16 Oct 2016, 06:11
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