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

Options

A. 38
B. 102
C. 1
D. 42

Answer

A

Explanation

Number of students opted for Mathematics = 70 = M (Even numbers)
Number of students opted for Physics = 46 = P (Divisible by 3)
Number of students opted for Chemistry = 28 = C (Divisible by 5)
M=70
P=46
C=28
`McapP=[140//6]=23`
`PcapC=[140//15]=9`
`McapC=[140//10]=4`
`n(McupPcupC)=M+P+C-(McapP)-(PcapC)-(McapC)+(McapPcapC)`
`=70+46+28-23-9-4+4=102`
Number of students who did NOT opt for any course.
For any course = `140-102=38`