M22-14

Question

Out of 320 people surveyed, 75% like Talk-Show A. Of those who like Talk-Show A, 65% also like Talk-Show B. If there are no people who like Talk-Show B but do not like Talk-Show A, how many of the 320 people do not like Talk-Show B?

A. 72
B. 84
C. 120
D. 156
E. 164

Show Answer

Official Answer

E

A. 72
B. 84
C. 120
D. 156
E. 164

Bunuel · Answer

Official Solution:

Out of 320 people surveyed, 75% like Talk-Show A. Of those who like Talk-Show A, 65% also like Talk-Show B. If there are no people who like Talk-Show B but do not like Talk-Show A, how many of the 320 people do not like Talk-Show B?

A. 72
B. 84
C. 120
D. 156
E. 164

Show Answer

Official Answer

E

A. 72
B. 84
C. 120
D. 156
E. 164

People who like Talk-Show A = 75% of 320 = 240.
 
People who like both A and B = 65% of 240 = 156. Given that there are no people who like Talk-Show B but do not like Talk-Show A, those 156 people are the total who like Talk-Show B. Essentially, "there are no people who like Talk-Show B but do not like Talk-Show A" implies that B is a subset of A.
 
Therefore, people who don't like Talk-Show B = Total - People who like Talk-Show B = 320 - 156 = 164.

Answer: E

shelrod007 · Answer

Out of 320 people, 75% like talk-show 1 and 65% of the people who like talk-show 1 also like talk-show 2. If there are no people who like talk-show 2 but do not like talk-show 1, how many of the 320 people do not like talk-show 2

@Bunnel : I am not sure of my understanding but does the question ask to find X + 84 ?

Talk show 2 and Talk show 1 = 320*0.75*0.65 = 156.

Does this statement ' If there are no people who like talk-show 2 but do not like talk-show 1' mean people only liking talk show 2 = 0 ?

Bunuel · Answer

Check below:

RenanBragion · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Akshay1298 · Answer

As per the Q-stem,

People who doesn't like Talk-show A - 80;
People who doesn't like Talk-show B - 84;

Therefore 80+84 = 164;

Is this a right approach or a wrong approach?

Bunuel · Answer

I'm not sure how you're getting this. The question specifically asks, "How many of the 320 people do not like Talk-Show B?" You already wrote, "People who don't like Talk-Show B = 84," so why are you summing this with 80? Also, how did you even get 84 there?

Akshay1298 · Answer

Bunuel · Answer

No, your approach is incorrect. If the number of people who like Talk-Show B is 156, then the number who do not like Talk-Show B is not A - 156 = 84; it's the total minus 156, which is 320 - 156 = 164. Please review the official solution and the discussion above carefully for more context.

bumpbot · Answer

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M22-14

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