Problem Solving

There are three different cable channels namely Ahead, Luck and Bang. In a survey it was
found that 85% of viewers respond to Bang, 20% to Luck, and 30% to Ahead. 20% of viewers
respond to exactly two channels and 5% to none.

1) What percentage of the viewers responded to all three?
(A) 10
(B) 12
(C) 14
(D) None of these

2) Assuming 20% respond to Ahead and Bang, and 16% respond to Bang and Luck,
what is the percentage of viewers who watch only Luck?
(A) 20
(B) 10
(C) 16
(D) None of these

rahulg83 wrote:There are three different cable channels namely Ahead, Luck and Bang. In a survey it was
found that 85% of viewers respond to Bang, 20% to Luck, and 30% to Ahead. 20% of viewers
respond to exactly two channels and 5% to none.

1) What percentage of the viewers responded to all three?
(A) 10
(B) 12
(C) 14
(D) None of these

2) Assuming 20% respond to Ahead and Bang, and 16% respond to Bang and Luck,
what is the percentage of viewers who watch only Luck?
(A) 20
(B) 10
(C) 16
(D) None of these

You can a. draw or venn diagram or b. use formulas or c. use a table
Using a table is best if you have two options like black and white etc
Otherwise use a. or b like for this question.

I'll solve 1) here. Look at the Venn diagram attached.
Both 20% is in orange.
The total viewers is 100.

Make sure you account for the total viewers and take out the double counts (intersections).

The total viewers are (A U B U L) - 20 - all3 + 5

85 + 20 +30 -20 - all3 + 5 = 100%


120 - all3 = 100
all3 = 20

I'll go with A) for 1.

Someone else can solve 2.

For the first question I get A. or 10pct. For question two I get D. None of these.

Not sure if I am correct.

What is the QA?

ppl,

for 1, if all3 = 20, then how is A i.e. 10% the answer? shouldn't it be 20%?

niraj_a wrote:ppl,

for 1, if all3 = 20, then how is A i.e. 10% the answer? shouldn't it be 20%?

Let total = 100


100 = 85 + 20 + 30 + 5 – 20 – 2(x)
100 = 120 -2x
2x = 20
x = 10

aah i forgot the 2 in the 2x.

Why the 2x.
The formula reads:

AUBUC = A + B + C - {A n B + B n C + C n A} + A n B n C

rahul....can u frame the 2nd quest properly..

I think the answer is D. none because of 20.

Can someone please post OA or confirm without reasonable doubt!

dmateer25 wrote:

niraj_a wrote:ppl,

for 1, if all3 = 20, then how is A i.e. 10% the answer? shouldn't it be 20%?

Let total = 100


100 = 85 + 20 + 30 + 5 – 20 – 2(x)
100 = 120 -2x
2x = 20
x = 10

Yes hes got it right!

niraj_a wrote:aah i forgot the 2 in the 2x.

How did you get the 2x?

Answer 1: Here's my logic based on this diagram:
A+B+C is 30+85+20 = 135
But this is double counting all the orange areas twice - X (once in A and once in L), Y (once in B and once in A) and Z (once in L and once in B) so we have to substract the X+Y+Z once to eliminate the double conting.

W is counted 3 times so we have to take out 2 of these to eliminate the "triple" couting.

Since 5% of the population don't watch any channels at all total is
A+B+C - (X+Y+Z) - 2W = 100-5
X+Y+Z = 20 (given) hence
30+85+20 + 20 - 2w = 100-95
W = 10!

that makes sense, thanks!

srry ppl replying late..
OA for 1st is A
and for 2nd Answer is 4 so its option D

let n(A)=a,n(b)=b,n(c)=c
n(a intersaction b intersaction c intersaction)=h
then n(a intersaction b)=e+h,n(a intersaction c)=f+h,n(b intersaction c)=g+h
100-95=a+b+c-[(e+h)+(f+h)+(g+h)]+h
95=(a+b+c)-[(e+f+g)+3h]+h
95=(85+30+20)-[(20)+3h]+h
95=135-20-2h
2h=20
h=10