12. In this subtraction, $P, Q, R, S, T$ represent single digits. What is the value of $P+Q+R+S+T$ ?
\begin{tabular}{rrrrr} 7 & $Q$ & 2 & $S$ & $T$ \\ $-P$ & 3 & $R$ & 9 & 6 \\ \hline 2 & 2 & 2 & 2 & 2 \end{tabular}
A 30
B 29
C 28
D 27
E 26
SOLUTION
B Given any three numbers $x, y$ and $z$,
$$
x-y=z \quad \text { if, and only if, } \quad x=y+z .
$$

It follows that the subtraction sum in the question is equivalent to the addition sum shown on the right. We now work out the values of $P$, $Q, R, S$ and $T$ by working from right to left.
$$
\begin{array}{r}
P 3 R 96 \\
+22222 \\
\hline 7 Q 2 S T
\end{array}
$$

From the units column we see that $T=6+2=8$. Next, we look at the tens column. Since $9+2=11$, we have $S=1$ (and 1 is carried to the hundreds column). Therefore, from the hundreds column we see that, because $R+2+1$ cannot be 2 , we have $R+2+1=12$. Therefore $R=9$ (and 1 is carried to the thousands column). It follows from the thousands column that $Q=3+2+1=6$. Finally, from the ten-thousands column, we see that $P+2=7$ and so $P=5$.

Therefore
$$
P+Q+R+S+T=5+6+9+1+8=29 \text {. }
$$