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:
(A) 102 (B) 42
(C) 1 (D) 38
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No. of Students taken Maths as favourite = 2,4,6,8................140 = 70
No. of Students taken Chemistry as favourite = 3,6,9,12............138 = 46
No. of Students taken Physics as favourite = 5,10,15,20.............140 = 28
No. of Students taken Maths and Chemistry as favourite = 6, 12, 18, ......, 138 = 23
No. of Students taken Maths and Physics as favourite = 10, 20, 30, ............140 = 14
No. of Students taken Physics and Chemistry as favourite = 15, 30, 45,..........135 = 9
No. of Students taken Maths, Chemistry and Physics as favourite = 30, 60, 90, 120 = 4
No. of students taken atleast one subject as favourite = 4+19+5+10+18+9+37 = 102
No. of students did not take any favourite subject = 140-102 = 38
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