When two positive integers $p$ and $q$ are multiplied together, their product is 75 . The sum of all of the possible values of $p$ is
(A) 96
(B) 48
(C) 109
(D) 115
(E) 124
Since $75=3 \times 5 \times 5$, we can factor 75 in three different ways:

$$
75=1 \times 75=3 \times 25=5 \times 15
$$

If $p q=75$ with $p$ and $q$ integers, then the possible values of $p$ are thus $1,3,5,15,25,75$. The sum of these values is $1+3+5+15+25+75=124$.

ANSWER: (E)