aman88 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%

OA C

Thanks.

Let the total = 100 and let AB = the people who like BOTH candidates.

Only A + Only B + AB = Total A + Total B - AB.
On the lefthand side, AB is ADDED because it is not included among those who like ONLY A and ONLY B.
On the righthand side, AB is SUBTRACTED because TOTAL A = Only A + AB and TOTAL B = Only B + AB, with the result that AB has been double-counted.

Since Total A = 30 and Total B = 48, we get:
Only A + Only B + AB = 30 + 48 - AB
2(AB) = 78 - (Only A + Only B).

Since the percentage who like only ONE CANDIDATE is equal to TWICE the percentage who like BOTH candidates, we get:
Only A + Only B = 2(AB).

Substituting Only A + Only B = 2(AB) into 2AB = 78 - (Only A + Only B), we get:
2(AB) = 78 - 2(AB)
4(AB) = 78
AB = 19.5.

Thus:
Only A + Only B = 2(AB) = 2(19.5) = 39.

Since Only A + Only B + AB + Neither = 100, we get:
Neither = 100 - 39 - 19.5 = 41.5.

The correct answer is C.

aman88 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%

OA C

Thanks.

Total = 100

Let x be the percentage who like both.
The percentage of people who like only A =30-x
The percentage of people who like only B = 48-x

According to the statement

"If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates"
2(x) = 30-x + (48 -x)
x = 19.5
Now let people who like neither be y
Total population 100 = 10.5+ 28.5 + 19.5 + y
y = 41.5

I still didn't understand it properly. I am not very familiar with this topic. Can someone please explain this to me briefly?

I studied this formula:
Total = Set A + Set B + Neither - Both
But there is some variation in this formula in this question. How do I know about that?

Thanks.

Hi,
Can some1 plz explain this using the tabular method?

Thanks,
Shreeraj

aman88 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%

OA C

Thanks.

An alternate approach is to use a GRID.

Let LA = like A, DA = dislike A, LB = like B, DB = dislike B..
Let the total = 100.
It is given that the total LA = 38 and the total LB = 40.
Here's the grid:

______________LA________DA_________T

LB_________________________________48

DB_________________________________52

T_____________30_______70________100

Let:
x = the percentage who LIKE A but DISLIKE B
y = the percentage who LIKE B but DISLIKE A.
Thus, x + y = the percentage who like EXACTLY ONE candidate.

Since the percentage who like one candidate is TWICE the percentage who like both candidates, we get:
x+y = 2(LA and LB)
LA and LB = (x+y)/2.

Inserting these values into the grid, we get:

______________LA________DA_________T

LB__________(x+y)/2_____ y_________48

DB____________x_______52-x________52

T_____________30_______70_________100


Leftmost column:
(x+y)/2 + x = 30
x+y + 2x = 60
3x + y = 60.

Middle column:
y + 52-x = 70
-x + y = 18.

Subtracting the second equation from the first, we get:
4x = 42
x = 10.5.

According to the CENTER BOX, the percentage who like neither A nor B = 52-x.
Thus:
Neither = 52 - 10.5 = 41.5.

The correct answer is C.

Thanks vivek, really liked your approach, reminded me of sets from O-levels days.

@Aman i would advice to go through Arun sharma quants and pictorial representation of this chapter in that book.excellent and you can get a picture of whats being asked