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1982 AHSME Problems/Problem 15

Revision as of 21:56, 16 June 2021 by Aopspandy (talk | contribs) (Created page with "==Problem== Let <math>[z]</math> denote the greatest integer not exceeding <math>z</math>. Let <math>x</math> and <math>y</math> satisfy the simultaneous equations \begin{ali...")
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Problem

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

\begin{align*} y&=2[x]+3 \\ y&=3[x-2]+5. \end{align*} 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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