Q. 23

# Mark the correct alternative in the following:

An investigator interviewed 100 students to determine the performance of three drinks: milk, coffee and tea. The investigator reporter that 10 students take all three drinks milk, coffee and tea; 20 students take milk coffee; 25 students take milk and tea; 20 students take coffee and tea; 12 students take milk only; 5 students take coffee only and 8 students take tea only. Then the number of students who did not take any of three drinks is

A. 10

B. 20

C. 25

D. 30

Answer :

Let U be the set of students which are interviewed by investigator

A be the set of students which take milk

B be the set of students which take coffee

C be the set of students which take tea

Then ,n(U)=100 ,n(A)=12, n(B)=5 ,n(C)=8

Also, (A⋂B⋂C) means students who drink all of three=10

(A⋂B) means students who drink milk and coffee =20-10=10

(B⋂C) means students who drink coffee and tea =20-10=10

(A⋂C) means students who drink milk and tea =25-10=15

A⋃B⋃C is the total of above =12+5+8+10+10+15+10=70

The number of students who didn’t take any drink =100-70=30

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