In a class, students are assigned roll numbers from 1 to 140. All students with even roll numbers opted for cricket, all those whose roll numbers are divisible by 5 opted for football, and all those whose roll numbers are divisible by 3 opted for basketball. 'The number of students who did not opt for any of the three sports is
Explanation:
Number of students who opted for cricket = Number of number which are divisible by 2 = Quotient of 140/2 = 70. Number of students who opted for football = Number of number which are divisible by 5 = Quotient of 140/5 = 28. Number of students who opted for basketball = Number of number which are divisible by 3 = Quotient of 140/3 = 46.
Number of students who opted for cricket and football = Number of number which are divisible by 2 and 5 = Quotient of 140/10 = 14. Number of students who opted for basketball and football = Number of number which are divisible by 3 and 5 = Quotient of 140/15 = 9. Number of students who opted for cricket and basketball = Number of number which are divisible by 2 and 3 = Quotient of 140/6 = 23.
Number of students who opted for cricket and football and basketball = Number of number which are divisible by 2, 5 and 3 = Quotient of 140/30 = 4.
∴ C ∪ F ∪ B = C + F + B - C ∩ F - F ∩ B - B ∩ C + C ∩ F ∩ B
⇒ C ∪ F ∪ B = 70 + 28 + 46 - (14 + 9 + 23) + 4
⇒ C ∪ F ∪ B = 144 - 46 + 4 = 102
∴ Number of students who opted for none of the three sports = 140 - 102 = 38.
Hence, option (b).
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