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Vein Diagram-how to attack these questions..

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Vein Diagram-how to attack these questions..

by rahulg83 » Tue Dec 09, 2008 7:22 pm
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
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Re: Vein Diagram-how to attack these questions..

by canuckclint » Tue Dec 09, 2008 10:31 pm
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.
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venn.jpg
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by jnellaz » Thu Dec 11, 2008 8:18 am
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?
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by niraj_a » Thu Dec 11, 2008 12:34 pm
ppl,

for 1, if all3 = 20, then how is A i.e. 10% the answer? shouldn't it be 20%?
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by dmateer25 » Thu Dec 11, 2008 12:40 pm
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
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by niraj_a » Thu Dec 11, 2008 1:05 pm
aah i forgot the 2 in the 2x.
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by canuckclint » Fri Dec 12, 2008 10:44 am
Why the 2x.
The formula reads:

AUBUC = A + B + C - {A n B + B n C + C n A} + A n B n C
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by willbeatthegmat » Fri Dec 12, 2008 12:22 pm
rahul....can u frame the 2nd quest properly..
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by canuckclint » Fri Dec 12, 2008 3:18 pm
I think the answer is D. none because of 20.

Can someone please post OA or confirm without reasonable doubt!
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by canuckclint » Fri Dec 12, 2008 11:16 pm
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!
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by tritrantran » Sat Dec 13, 2008 8:29 am
niraj_a wrote:aah i forgot the 2 in the 2x.
How did you get the 2x?
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by adilka » Sat Dec 13, 2008 1:24 pm
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!
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venn_192.jpg
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by tritrantran » Sat Dec 13, 2008 5:41 pm
that makes sense, thanks!
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by rahulg83 » Sat Dec 13, 2008 10:45 pm
srry ppl replying late..
OA for 1st is A
and for 2nd Answer is 4 so its option D
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by polkhol8 » Sat Apr 09, 2011 4:20 am
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
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