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Question

In a class of 120 students numbered from 1 to 120, all even numbered students opt for Physics, those whose numbers are divisible by 5, opt for Chemistry and those whose numbers are divisible by 7, opt for Maths. How many opt for none of the three subjects?

A
19
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B
41
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C
21
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D
26
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Solution

The correct option is B 41
P={2,4,6,,118,120}
C={5,10,15,,115,120}
M={7,14,21,,112,119}
n(P)=60, n(C)=24, n(M)=17
(Here, P= Physics, C= Chemistry, M= Maths)

The elements in PC will be the multiples of LCM (2,5).
So, n(PC)=12
Similarly, n(CM)=3, n(PM)=8
and n(PCM)=1


n(PCM)
=n(P)+n(C)+n(M)n(PC)n(CM) n(PM)+n(PCM)
=60+24+17(12+3+8)+1
=79

Number of students who opt for none of the subjects =12079=41

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