you pick one card from each set and find the sum. how many different sums are possible?

Explanation:

Step1: List all combinations

List all possible pairs of numbers (one from the first - set and one from the second - set) and their sums. The first set is {4, 5, 6, 7, 8} and the second set is {3, 4, 5, 6, 7}. 4 + 3=7, 4 + 4 = 8, 4+5 = 9, 4 + 6=10, 4 + 7 = 11, 5 + 3=8, 5 + 4 = 9, 5+5 = 10, 5 + 6=11, 5 + 7 = 12, 6 + 3=9, 6 + 4 = 10, 6+5 = 11, 6 + 6=12, 6 + 7 = 13, 7 + 3=10, 7 + 4 = 11, 7+5 = 12, 7 + 6=13, 7 + 7 = 14, 8 + 3=11, 8 + 4 = 12, 8+5 = 13, 8 + 6=14, 8 + 7 = 15.

Step2: Remove duplicates

The set of sums is {7, 8, 9, 10, 11, 12, 13, 14, 15}.

Answer:

9