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Question about Set

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patrickgong6688
 Post subject: Question about Set
 Post Posted: Fri Jul 08, 2011 12:06 pm 
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Posts: 10
A survey of 100 person 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 the persons in the surveyed group who had eaten at both P and Q.
A 20 B 24 C 30 D 50 E 52
The answer is A
I don't know why ???Can someone give me a explaination ?
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adrielfrederick
 Post subject: Re: Question about Set
 Post Posted: Mon Jul 11, 2011 1:24 pm 
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Students


Posts: 3
Hi Patrick,

Lets assume that 'x' is the number of people who ate at both P and Q and try to find out the maximum and minimum values of 'x'

The minimum value of 'x' can be calculated by

Only P + Only Q + P &Q = 100
72-x + 52-x + x= 100

which gives x to be 24 (Any number less than this wont add up to 100)

The maximum value of 'x' will be 52 since 52 people ate at restaurant Q and you cannot exceed that anyway

Therefore the range is between 24 and 52 and 20 is the only number out of range.

Do correct me if I am wrong

-Adriel
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jnelson0612
 Post subject: Re: Question about Set
 Post Posted: Thu Jul 14, 2011 12:07 pm 
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ManhattanGMAT Staff


Posts: 1857
That looks great to me!

_________________
Jamie Nelson
ManhattanGMAT Instructor
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