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

Question

shootforthestars · Answer

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

mathmate · Answer

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