Sets and Probability Question -Arco Master GRE /CAT

[Deep79]

1Ques :
A survey of 100 persons revealed that 72 of them had eaten at restaurant P. and 52 at restaurant Q.
Which of the followig could not be the numbr of persons in surveyed group who had eaten at both P & Q restaurants.
Options :

A- 20
B-24
C-30
D-50
E-52

Ans: In the book, answer is 20/A and pencil -corrected to B by some reader(its library book,someone used it before).

I also think answer is B -24.

For A/20 answer-Books logic is-
total people 100 ,
People who ate at P or Q=72 +52=124( more than total )
Hence
Some people who must have eaten at both restuarents= (72+52)-100=24


24 is the minimum number of persons who have eaten at both.
24 to 52=could have eaten at both

So
Num of people who have eaten at both rest "CANNOT BE" less than 24 that is 20/A.


What is the right answer.

[Riyad Mohammad]

the ans is B.