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# A Survey of 100 people revealed that 72 of them had eaten at

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Senior Manager
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A Survey of 100 people revealed that 72 of them had eaten at [#permalink]

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11 Feb 2004, 16:17
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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 surveryed group who had eaten at both P and Q?

a) 20
b)24
c)30
d)50
e)52
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shubhangi

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11 Feb 2004, 16:25
Is the question right..
Which of the following could not be the number of persons in the surveryed group who had eaten at both P and Q?

If its could be...then its 24.If its could not be ....then Im lost

Vivek.
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"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

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Director
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11 Feb 2004, 16:42
Good Question !

Is it A) 20

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SVP
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11 Feb 2004, 16:46

Total = P+Q+neither-Both
Both = P+Q+Neither-Total
72+52+Neither-100 = 24+neither.
Even if Neither=0 Both will be 24. SO minimum no of people eating at botht the restaurants is 24.
A is the choice because A <24

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Director
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11 Feb 2004, 16:48
anandnk wrote:

Total = P+Q+neither-Both
Both = P+Q+Neither-Total
72+52+Neither-100 = 24+neither.
Even if Neither=0 Both will be 24. SO minimum no of people eating at botht the restaurants is 24.
A is the choice because A <24

I need to learn to reason like you!
good explanation!!

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SVP
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11 Feb 2004, 16:49

how did you choose A then? I am curious.

Thanks,
Anand.

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11 Feb 2004, 17:13
Whoopsiedaisy..I interpreted the question in the wrong way..my bad.

Vivek.
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"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

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11 Feb 2004, 19:04
Yes ,it is A. i could not figure it out at first.. did you guys.??
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shubhangi

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14 Feb 2004, 03:18
anandnk wrote:

how did you choose A then? I am curious.

Thanks,
Anand.

This is a very easy question to solve logically. There are 5 answers ranging from 20 to 52. By the type of question asked, the answer must be at one end of the range or another (think about this). Well, the number CAN clearly be 52 so the answer must be at the other extreme 20.

Another way to think of it is "what is the minimum number that can be both"? and the anwers can be found using a Venn Diagram technique but it will take a little longer.
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Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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14 Feb 2004, 03:18
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# A Survey of 100 people revealed that 72 of them had eaten at

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