17. Niall's four children have different integer ages under 18. The product of their ages is 882 . What is the sum of their ages?
A 23
B 25
C 27
D 31
E 33
17. D The prime factor decomposition of 882 is $2 \times 3^{2} \times 7^{2}$. The ages must be under 18 , so cannot be $3 \times 7=21$ or $7 \times 7=49$. Hence, the only way to create two different numbers using 7 are: 7 and $2 \times 7=14$. This leaves only $3^{2}$ which can create the two ages 1 and 9 . The sum of the ages is then $1+9+7+14=31$.