In a survey about potential presidential candidates A and B,

Question

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%

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

fluke · Accepted Answer

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"

IEsailor · Answer

Spot on as always Fluke !!!

gijoedude · Answer

Isn't the formula for overlapping sets

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

MBAhereIcome · Answer

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".

olivite · Answer

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?

jjack0310 · Answer

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

Asifpirlo · Answer

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 –   = 100 –   = 22 + 3x
 
From this equation we can back solve. And only 67% satisfies the Answer.

{total = 0+18+15+67 = 100 }

I think the Answer is (E)

Bunuel should check it…………………….

PareshGmat · Answer

Solved using overlapping sets, kindly refer sketch below:

PareshGmat · Answer

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)

KarishmaB · Answer

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%

Answer (C)

KarishmaB · Answer

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.

vinayak4u · Answer

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

niksaqua · Answer

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

FarhinR · Answer

Is there any way to solve this using matrix like the Manhattan book?

Posted from my mobile device

shubhamagarwal44 · Answer

@  ScottTargetTestPrep   can you please solve this using the matrix method described in TTP?

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In a survey about potential presidential candidates A and B,

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