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A survey of 100 people revealed that 72 of them had eaten at restauran

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A survey of 100 people revealed that 72 of them had eaten at restauran [#permalink]

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New post 01 Feb 2018, 22:38
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A survey of 100 people revealed that 72 of them had eaten at restaurant P and that 52 of them had eaten at restaurant Q. Which of the following could not be the number of persons in the surveyed group who had eaten at both P and Q ?

(A) 20

(B) 24

(C) 30

(D) 50

(E) 52
[Reveal] Spoiler: OA

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Re: A survey of 100 people revealed that 72 of them had eaten at restauran [#permalink]

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New post 01 Feb 2018, 23:24
Bunuel wrote:
A survey of 100 people revealed that 72 of them had eaten at restaurant P and that 52 of them had eaten at restaurant Q. Which of the following could not be the number of persons in the surveyed group who had eaten at both P and Q ?

(A) 20

(B) 24

(C) 30

(D) 50

(E) 52


The maximum number of students who have eaten at both restaurants = 52

The Minimum number of students who have eaten at both restaurants = 72+52-100 = 24

Hence the number of students eating at both restaurants may vary from 24 to 52 hence

Answer: Option A
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Re: A survey of 100 people revealed that 72 of them had eaten at restauran [#permalink]

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New post 02 Feb 2018, 01:33
100-N=124-Both
Both - N=24
So both can't be 20
A

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Re: A survey of 100 people revealed that 72 of them had eaten at restauran [#permalink]

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New post 02 Feb 2018, 05:27
The number of people who have eaten at the both restaurant should be 24. I do not understand how the answer is A

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Re: A survey of 100 people revealed that 72 of them had eaten at restauran [#permalink]

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New post 05 Feb 2018, 09:16
Bunuel wrote:
A survey of 100 people revealed that 72 of them had eaten at restaurant P and that 52 of them had eaten at restaurant Q. Which of the following could not be the number of persons in the surveyed group who had eaten at both P and Q ?

(A) 20

(B) 24

(C) 30

(D) 50

(E) 52


We can create the equation:

100 = 72 + 52 - both + neither

both - neither = 24

Since “neither” is at least 0, then “both” must be a number at least 24; thus, “both” can’t be 20.

Answer: A
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Re: A survey of 100 people revealed that 72 of them had eaten at restauran   [#permalink] 05 Feb 2018, 09:16
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