Positive integers $s$ and $t$ have the property that $s(s-t)=29$. What is the value of $s+t$ ?
(A) 1
(B) 28
(C) 57
(D) 30
(E) 29

Part B: Each correct answer is worth 6.
We are given that $s$ and $t$ are positive integers and that $s(s-t)=29$.

Since $s$ and $t$ are positive, then $s-t$ is less than $s$.

Since $s$ is positive and 29 is positive and $s(s-t)=29$, then $s-t$ must also be positive.

Since 29 is a prime number, the only way that it can be written as a product of two positive integers is $29=29 \cdot 1$.

Since $s(s-t)=29$ and $s>s-t$, then we must have $s=29$ and $s-t=1$.

Since $s=29$ and $s-t=1$, we obtain $t=28$.

Therefore, $s+t=29+28=57$.

ANSWER: (C)