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M22-14

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Bunuel
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M22-14 [#permalink] New post   16 Sep 2014, 01:16
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E

Difficulty:

45% (medium)

Question Stats:

69% (02:32) correct 31% (02:44) wrong based on 134 sessions
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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
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E
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Bunuel
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Re M22-14 [#permalink] New post   16 Sep 2014, 01:16
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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


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
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shelrod007
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Re: M22-14 [#permalink] New post   26 Jan 2015, 20:01
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 ?
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Bunuel
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Re: M22-14 [#permalink] New post   27 Jan 2015, 02:59
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shelrod007 wrote:
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 ?


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spetznaz
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Re: M22-14 [#permalink] New post   11 Jan 2018, 10:12
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+1 for option E
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RenanBragion
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Re: M22-14 [#permalink] New post   07 Jun 2020, 06:20
I think this is a high-quality question and I agree with explanation.
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Bunuel
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Re: M22-14 [#permalink] New post   16 Oct 2023, 00:45
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M22-14 [#permalink]
16 Oct 2023, 00:45
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