How many numbers are there from 200 to 800 which are neither divisible by 5 nor by 7?

Total numbers = (800 - 200) + 1  = 601

Number of terms which divide by 5

l = 800

a = 200

Common difference(d) = 5

l = a + (n-1)d

800 = 200 + (n - 1)5

n-1 = 120

n = 121

Number of terms which divide by 7

l = 798

a = 203

Common difference(d) = 7

l = a + (n-1)d

798 = 203 + (n - 1)7

n-1 = 85

n = 86

Number of terms which divide by 5 and 7

l = 770

a = 210

Common difference(d) = 35

l = a + (n-1)d

770 = 210 + (n - 1)35

n-1 = 16

n = 17

Number of terms which divide by either 5 or 7 = 121 + 86 - 17 = 190

Number of terms which divide by neither 5 nor 7 = 601 - 190 = 411