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Question

In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :

A
1
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B
102
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C
38
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D
42
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Solution

The correct option is C 38
Let A,B and C be the set of students opted for Mathematics, Physics and Chemistry respectively then,
A={2,4,6,,140} n(A)=70,
B={3,6,9,,138} n(B)=46,
C={5,10,15,,140} n(C)=28,
(AB)={6,12,18,,138}n(AB)=23,
(AC)={10,20,30,,140}n(AC)=14,
(CB)={15,30,45,,135}n(AB)=9,
(ABC)={30,60,90,120}n(AC)=4,

Now,
n(ABC)=Total students n(ABC)
where n(ABC)=n(A)+n(B)+n(C)n(AB)n(AC)n(BC)+n(ABC)
n(ABC)=70+46+2823914+4=102

Hence n(ABC)=140102=38

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