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 numbers is divisible by 5 opted chemistry course. Then number of students who did not opted any of these courses.

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answer is 38.

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Detailed Solution

$n (S) - n (A \cup B \cup C) = n (S) - (n (A) + n (B) + n (C) - n (A \cap B - n (B \cap C) - n (C \cap A) + n (A \cap B \cap C) = 140 - (70 + 46 + 28 - 23 - 9 - 14 + 4 = 140 - (144 - 46 + 4) = 38$

140-(70+46+28-23-9--14+4)

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