AMC 8 1993 Problem 23

Five runners, $P$, $Q$, $R$, $S$, $T$, have a race, and $P$ beats $Q$, $P$ beats $R$, $Q$ beats $S$, and $T$ finishes after $P$ and before $Q$. Who could NOT have finished third in the race? $\text{(A)}\ P\text{ and }Q \text{(B)}\ P\text{ and }R \text{(C)}\ P\text{ and }S \text{(D)}\ P\text{ and }T \text{(E)}\ P,S\text{ and }T$