Question

how many two digit numbers are divisible by either 3 or 5

Answer 1

10, 12, 15, 18, 20, 21, 24, 25, 27, 30, 33, 35, 36, 39, 40, 42, 45, 48, 50, 51, 54, 55, 57, 60, 63, 65, 66, 69, 70, 72, 75, 78, 80, 81, 84, 85, 87, 90, 93, 95, 96, 99.

42 all together I think

Answer 2

Use the inclusion/exclusion principle:
Let
A = set of 2-digit numbers divisible by 3
B = set of 2-digit numbers divisible by 5
A\(\cap\)B = set of 2-digit numbers divisible by 15 (i.e. by 3 and by 5)
and apply the following rule:
\(|A\cup B|=|A|+|B|-|A\cap B|\)
where |A| = number of elements in set A = cardinality of A