Set X consists of the positive multiples of 5, and set Y

There is no real shortcut to this problem; we simply have to count the results.
Set X: [5, 10, 15, 20, 25...]
Set Y: [3, 5, 7, 11, 13, 17, 19]

Since Set Y is finite, start with the elements of Set Y. Start with 3, and list all of the product of 3 * the elements of Set X.
3 * 5 = 15
3 * 10 = 30
3 * 15 = 45
3 * 20 = 60
3 * 25 = 75
3 * 30 = 90
Anything greater than 30 would yield a product greater than 100, so those are the only results for 3. Now try 5:

5 * 5 = 25
5 * 10 = 50
5 * 15 = 75 --> this is a repeat - doesn't count
5 * 20 = 100 --> we're only looking for less than 100, so this doesn't count.

7 * 5 = 35
7 * 10 = 70

11 * 5 = 55
13 * 5 = 65
17 * 5 = 85
19 * 5 = 95

There are 14 distinct elements that are products of a member of Set X and a member of Set Y.

The answer is B.