How many of the whole numbers from 1 to 200 are divisible by neither 2 nor 5?

Explanation

1. 01

   Divisible by 2: 100 numbers. Divisible by 5: 40 numbers.

2. 02

   Divisible by both (that is, by 10): 20 numbers, counted twice above.

3. 03

   Divisible by 2 or $5 = 100 + 40 - 20 = 120$.

4. 04

   Divisible by neither = $200 - 120 = 80$.