Question

In a class of 120 students numbered 1 to 120, all even number students opt for physics, whose number are divisible by 5 opt for chemistry & those whose no are divisible by 7 opt for math. How many opt for none of these subjects?

Answer 1

welcome to OS :)

Answer 2

student at even
2 4 6 8 10 ........120
total=60

Answer 3

for 5 10 15 20 .....at these position
total=24

Answer 4

at 7 14 21 28.....these position
total=17

Answer 5

total student who took the subject=60+24+17=101

Answer 6

but in this
we counted few student 2 times or 3 times
like 10 20 30 40 50 60 70 80 90 100 110 120 are counted for both even and divisible by 5

Answer 7

similarly
14 28 42 56 70 84 98 are counted in both even and divisible by 7

Answer 8

and 35 70 105 are counted for both divisible by 7 and 5

Answer 9

70 is counted in all 3 even divisible by 5 and 7

Answer 10

so decrease all these from 101 ..so that we can get exact number of student whoo took q subject

Answer 11

22 number are these
so 101-22=79 but we subtracted 1ll 70 which are included so no 70 in our calculation

Answer 12

so we will add one to include 70
so total who took the subject =79+1=80
so who didnt took any sub=120-80