A1. The sum of two natural numbers is equal to three times their difference, and their product is equal to four times their sum. What is the sum of these two natural numbers?
(A) 9
(B) 10
(C) 12
(D) 15
(E) 18
A1. Let's denote the two natural numbers by $m$ and $n$. Then we have $m+n=3(m-n)$ and $m n=4(m+n)$. From the first equation, we get $4 n=2 m$ or $m=2 n$. When we substitute this into the second equation, we get $2 n^{2}=12 n$, from which it follows that $n=6$. Therefore, $m=12$ and $m+n=18$.