21. Several different positive integers are written on a blackboard. The product of the smallest two of them is 16. The product of the largest two of them is 225 . What is the sum of all the integers written on the blackboard?
A 38
B 42
C 44
D 58
E 243
21. C The only ways to express 16 as the product of two different positive integers are $1 \times 16$ and $2 \times 8$. The only ways to express 225 as the product of two different positive integers are $1 \times 225,3 \times 75,5 \times 45$ and $9 \times 25$. Therefore, since both integers in the first pair must be smaller than both integers in the second pair, the only possible combination is for the two smallest integers to be 2 and 8 and for the two largest integers to be 9 and 25 . There are no other integers written on the blackboard since they would need to be different from these four, be less than 9 and greater than 8 . Hence the sum of the integers written on the blackboard is $2+8+9+25=44$.