no of integer divisible by 3 in rangeof (1, 500) = floor( 500 / 3) = 166
no of integer divisible by 5 in rangeof(1, 500) = floor( 500 / 5) = 100
no of integer divisible by 7 in rageof(1, 500) = floor( 500 / 7) = 71
no of integer by 3 and 5 = floor{ 500 / L.C.M(3, 5)} = 33
no of integer by 5 and 7 = floor{ 500 / L.C.M(5, 7)} = 14
no of integer by 3 and 7 = floor{ 500 / L.C.M(3,7) } = 23
no of integer by 3 and 5 and 7 = floor{ 500 / L.C.M(3,5,7)} = 4
so, total no of integer divisible by 3 or 5 or 7 in rageof(1, 500) =
no of integer by 3 + no of integer by 5 + no of integer by 7 - { (no of integer by 3 and 5) - (no of integer by 5 and 7) - (no of integer by 3 and 7) + (no of integer by 3 and 5 and 7)
= 166 + 100 + 71 - 33 - 14 -23 + 4 = 271
So, "C is Correct"