33-35 Let $[Z]$ denote the greatest integer not exceeding $Z$, and $x$ and $y$ satisfy the system of equations
$$
\left\{\begin{array}{l}
y=2[x]+3, \\
y=3[x-2]+5 .
\end{array}\right.
$$

If $x$ is not an integer, then $x+y$ is
(A) an integer.
(B) between 4 and 5.
(C) between -4 and 4.
(D) between 15 and 16.
(E) 16.5 .
(33rd American High School Mathematics Examination, 1982)
［Solution 1］Solving the system of equations, we have

that is
and
$$
\begin{aligned}
2[x]+3 & =3[x-2]+5, \\
2[x]+3 & =3([x]-2)+5, \\
{[x] } & =4 .
\end{aligned}
$$

Since $x$ is not an integer, we have $4<x<5$,
$$
\begin{array}{l} 
y=2[x]+3=11 . \\
\therefore \quad 15<x+y<16 .
\end{array}
$$

Therefore, the answer is $(D)$.
［Solution 2］In the Cartesian coordinate system, draw the graphs of $y=$ $2[x]+3$ and $y=3[x-2]+5$ (see the right figure). From the graphs, we can see that at $4<x<5$, the graphs of the two functions coincide.
Substituting into the given equations, we can find
$$
15<x+y<16 \text{. }
$$

Therefore, the answer is $(D)$.