The product of two positive integers $p$ and $q$ is 100 . What is the largest possible value of $p+q$ ?
(A) 52
(B) 101
(C) 20
(D) 29
(E) 25
The product of two positive integers $p$ and $q$ is 100 . What is the largest possible value of $p+q$ ?
(A) 52
(B) 101
(C) 20
(D) 29
(E) 25

## Solution

The pairs of positive integers whose product is 100 are: 1 and 100, 2 and 50, 4 and 25, 5 and 20, 10 and 10. The pair with the largest sum is 1 and 100. The sum is 101 .

ANSWER: (B)