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:

Step-by-step solution

From the given 140 students, all even numbered students opted Mathematics M , hence, the number of students opted Mathematics is M ≡ 140 2 = 70 , where x denotes the greatest integer function of x . Similarly, the students who opted Physics are P ≡ 140 3 = 46 And, the students who opted Chemistry are C ≡ 140 5 = 28 Similarly, the students who opted Mathematics and Physics are the numbers which are divisible by both 2   &   3 i.e. 6 , and their number is 140 6 = 23 The students who op