If $10 x+y=75$ and $10 y+x=57$ for some positive integers $x$ and $y$, the value of $x+y$ is
(A) 12
(B) 5
(C) 7
(D) 77
(E) 132
Since $10 x+y=75$ and $10 y+x=57$, then

$$
(10 x+y)+(10 y+x)=75+57
$$

and so

$$
11 x+11 y=132
$$

Dividing by 11 , we get $x+y=12$.

(We could have noticed initially that $(x, y)=(7,5)$ is a pair that satisfies the two equations, thence concluding that $x+y=12$.)

ANSWER: (A)