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In a class of 120 students numbered 1 to 120, all even number students opt for physics, whose number are divisible by 5 opt for chemistry & those whose no are divisible by 7 opt for math. How many opt for none of these subjects?

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johnkellock

41 opt for none of these subjects

60 even numbers between 1 and 120

24 numbers are divisible by 5 between 1 and 120.
(however 12 of them end in 0 and are even numbers therefore ruled out)
12 multiples are left

17 multiples of 5 between 1 and 120
however 8 of them are multiples of 2 and 2 are multiples of 5
7 multiples are left 

60 + 12 + 7 = 79

120 - 79 = 41

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