Question

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

Comments

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Answer 1

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