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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
102
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B
42
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C
1
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D
38
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Solution

The correct option is D 38
Let n(A)= number of students opted Mathematics =70,
n(B)= number of students opted Physics =46,
n(C)= number of students opted Chemistry =28,
n(AB)=23,
n(BC)=9,
n(AC)=14,
n(ABC)=4,
Now n(ABC)
=n(A)+n(B)+n(C)n(AB)n(BC)n(AC)+n(ABC)
=70+46+2823914+4=102
Si number of students not opted for any course = Total n(ABC)
=140102=38.

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