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

Total number of people who play Cricket = 70
Total number of people who play Football = 28
Total number of people who play Basketball = 46

Total number of people who play all three sports (divisible by 2,3 and 5 or divisible by 30) = 44

Total number of people who play both Cricket and Football, but not Basketball = (Roll numbers divisible by both 2 and 5) - Total number of people who play all three sports = 14 - 4 = 10.
Total number of people who play both Football and Basketball, but not Cricket = (Roll numbers divisible by both 3 and 5) - Total number of people who play all three sports = 9 - 4 = 5.
Total number of people who play both Cricket and Basketball, but not Football = (Roll numbers divisible by both 2 and 3) - Total number of people who play all three sports = 23 - 4 = 19

The number of players who do not opt for any of the three sports = $$140-(37+10+9+19+4+5+18)=140-102=38$$ students