How many natural numbers up to 2001 are divisible by 3,4 but not by 5

How many natural numbers up to 2001 are divisible by 3,4 but not by 5?

a) 768

b) 801

c) 934

d) 1067

Sol:

Divisible by 3 till 2001 = 667

Divisible by 4 till 2001 = 500

Divisible by 12 till 2001 = 166 ⇒ Divisible by 3, 4 = 667 + 500 – 166 = 1001