Each number from 1 to 6 replaces one of the letters $P, Q, R, S, T$, and $U$. The sum of $P$ and $Q$ is 5 and the difference between $R$ and $S$ is 5 . If $T$ is greater than $U$, what number replaces the letter $T$ ?
(A) 4
(B) 6
(C) 2
(D) 3
(E) 5
The sum of $P$ and $Q$ is equal to 5 , and so $P$ and $Q$ are (in some order) either equal to 1 and 4 , or they are equal to 2 and 3.

The difference between $R$ and $S$ is equal to 5 , and so $R$ and $S$ must be (in some order) equal to 1 and 6 .

Since $R$ and $S$ are equal to 1 and 6 , then neither $P$ nor $Q$ can be 1 , which means that $P$ and $Q$ cannot be equal to 1 and 4 , and so they must be equal to 2 and 3 .

The only numbers from 1 to 6 not accounted for are 4 and 5 .

Since $T$ is greater than $U$, then the number that replaces $T$ is 5 .

ANSWER: (E)

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