In a Class of 120 students numbered 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 Math. How many opt for none of the three subject ?

A 19
B 41
C 43
D 51

Correct Answer: 41

Physics takes = 120/2 = 60Chemistry takes = 120/5 = 24Mathematics takes = 120/7 = 17Physics and chemistry = 120/10 = 12Physics andmathematics = 120/14 = 8Chemistry and mathematics = 120/35 = 3Physics,  Chemistry and mathematics = 120/70 = 1So,  Only physics and chemistry = 12 - 1 = 11Only physics and mathematics = 8 - 1 = 7Only Chemistry and mathematics = 3 - 1 = 2Now, Only physics = 60 - 11 - 7 = 41Only Chemistry = 24 - 11 - 2 - 1 = 10Only mathematics = 17 - 7 - 2 - 1 = 7Shortcut not taken none ofthe three = 120 - (41 + 10 + 7 + 11 + 7 + 2 + 1) = 12 - 79 = 41 
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