Question

How many three-digit counting numbers are exactly divisible by 6 but not also exactly divisible by 9?

Answer 1

There are a total of 900 /999-99/ 3-digit numbers. And they are 900 consecutive numbers, 1/6th of these should be divisible by 6, 900/6=150 numbers. So the answer to your question is answer is... 150! :3

Hope I helped.

Answer 2

There are ⌊ 999 6 ⌋ − ⌊ 99 6 ⌋ numbers between 100 and 999 (i.e. three digit numbers) which are divisible by six.