Question

Tom and Jim are distant cousins who meet during their family Thanksgiving meal. Tom tells Jim that he has 3 kids, and the product of their ages is 72. He also tells him the sum of their ages. Jim says he still can’t correctly guess the ages of Tom's kids. Finally, Tom says, "My youngest child's name is Joy." Jim can then correctly guess. What are the ages?

Answer 1

6, 6, 2

Explanation:

Factor 72:

72 = 2³ × 3²

Look for groups of 3 numbers whose products are 72 and their sums:

2, 4, 9: sum 15

8, 9, 1: sum 18

8, 3, 3: sum 14

6, 6, 2: sum 14

6, 4, 3: sum 13

12, 6, 1: sum 19

12, 3, 2: sum 17

18, 4, 1: sum 23

18, 2, 2: sum 22

24, 3, 1: sum 28

36, 2, 1: sum 39

72, 1, 1: sum 74

Jim knows the sum, but he can't guess the ages. that means the sum must be 14 for which there are two sets of ages which have a product of 72:

8, 3, 3 and 6, 6, 2

Then when he says "my youngest", that means one age is less than the other two. The only choice is 6, 6, 2.