How many of the numbers from 1 to 100 are divisible by neither 2 nor 5?

Multiples of 2: 50. Multiples of 5: 20. Multiples of both (i.e. of 10): 10. So the count divisible by 2 or 5 is 50 + 20 − 10 = 60, and the rest is 100 − 60 = 40. Forgetting to add back the 10 overlap gives the wrong answer 30.