16. The product of two positive integers is equal to twice their sum. This product is also equal to six times the difference between the two integers. What is the sum of these two integers?
A 6
B 7
C 8
D 9
E 10
16. D Let the two positive integers be $m$ and $n$. Then $m n=2(m+n)=6(m-n)$. So $2 m+2 n=6 m-6 n$, that is $8 n=4 m$. Therefore $m=2 n$. Substituting for $m$ gives: $(2 n) n=2(2 n+n)$. So $2 n^{2}=6 n$, that is $2 n(n-3)=0$. Therefore $n=0$ or 3 . However, $n$ is positive so the only solution is $n=3$. Therefore $m=2 \times 3=6$ and $m+n=6+3=9$.