1982 AHSME Problems/Problem 15

Problem

Let $[z]$ denote the greatest integer not exceeding $z$ . Let $x$ and $y$ satisfy the simultaneous equations

$\begin{aligned} y & = 2 [x] + 3 \\ y & = 3 [x - 2] + 5. \end{aligned}$ If $x$ is not an integer, then $x+y$ is

$\text {(A) } \text{ an integer} \qquad \text {(B) } \text{ between 4 and 5} \qquad \text{(C) }\text{ between -4 and 4}\qquad\\ \text{(D) }\text{ between 15 and 16}\qquad \text{(E) } 16.5$

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1982 AHSME Problems/Problem 15

Problem