Answer: 27
Work Shown
A = positive multiples of 3 less than 100
A = {3, 6, 9, ..., 99}
There are 33 items in set A because 3*33 = 99.
B = positive multiples of 15 less than 100
B = {15,30,45,60,75,90}
There are 6 items in set B since 15*6 = 90.
Notice that any item inside set B is also in set A. This means B is a subset of A.
C = positive multiples of 3, but not multiples of 5
n(C) = number of values in set C
n(C) = n(A) - n(B)
n(C) = 33 - 6
n(C) = 27 is the final answer.
Here are the 27 values that are positive multiples of 3, but not multiples of 5. I've generated the list using a spreadsheet.
3, 6, 9, 12, 18, 21, 24, 27, 33,
36, 39, 42, 48, 51, 54, 57, 63, 66,
69, 72, 78, 81, 84, 87, 93, 96, 99