22. Harriet tells Topaz that she is thinking of three positive integers, not necessarily all different. She tells her that the product of her three integers is 36 . She also tells her the sum of her three integers. However, Topaz still cannot work out what the three integers are.
What is the sum of Harriet's three integers?
A 10
B 11
C 13
D 14
E 16
22. C The possible groups of three integers with product 36 are $(1,1,36),(1,2,18),(1,3,12)$, $(1,4,9),(1,6,6),(2,2,9),(2,3,6)$ and $(3,3,4)$ with sums $38,21,16,14,13,13,11$ and 10 respectively. The only value for the sum that occurs twice is 13 . Hence, since Topaz does not know what the three integers chosen are, the sum of Harriet's three integers is 13 .