AHSME 1969 Problem 24

When the natural numbers $P$ and $P'$, with $P>P'$, are divided by the natural number $D$, the remainders are $R$ and $R'$, respectively. When $PP'$ and $RR'$ are divided by $D$, the remainders are $r$ and $r'$, respectively. Then: $\text{(A) } r>r' \text{ always} \text{(B) } rr' \text{ sometimes and } rr' \text{ sometimes and } r=r' \text{ sometimes} \\ \text{(E) } r=r' \text{ always}$