If Corina had added the numbers $P$ and $Q$ correctly, the answer would have been 16 . By mistake, she subtracted $Q$ from $P$. Her answer was 4 . What is the value of $P$ ?
(A) 4
(B) 5
(C) 8
(D) 10
(E) 16
Solution 1

From the given information, $P+Q=16$ and $P-Q=4$.

Adding these two equations, we obtain $P+Q+P-Q=16+4$ or $2 P=20$ or $P=10$.

## Solution 2

The value of $P$ is increased by $Q$ to give 16 and decreased by $Q$ to give 4 .

Thus, the difference of 12 between these two answers is twice the value of $Q$, so $2 Q=12$ whence $Q=6$.

Since $P+Q=16$, we have $P+6=16$ or $P=10$.

ANswer: (D)