If $x$ and $y$ are two-digit positive integers with $x y=555$, what is $x+y$ ?
(A) 52
(B) 116
(C) 66
(D) 555
(E) 45
First, we find the prime factors of 555.

Since 555 ends with a 5 , it is divisible by 5 , with $555=5 \times 111$.

Since the sum of the digits of 111 is 3 , then 111 is divisible by 3 , with $111=3 \times 37$.

Therefore, $555=3 \times 5 \times 37$, and each of 3,5 and 37 is a prime number.

The possible ways to write 555 as the product of two integers are $1 \times 555,3 \times 185,5 \times 111$, and $15 \times 37$. (In each of these products, two or more of the prime factors have been combined to give a composite divisor.)

The only pair where both members are two-digit positive integers is 37 and 15 , so $x+y$ is $37+15=52$.

ANSWER: (A)