Difference between revisions of "1982 AHSME Problems/Problem 15"
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==Problem== | ==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 | + | 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{align*} y&=2[x]+3 \\ y&=3[x-2]+5. \end{align*} | + | <cmath>\begin{align*} y&=2[x]+3 \\ y&=3[x-2]+5. \end{align*}</cmath> |
| − | |||
| − | <math>\text {(A) } \text{ an integer} \qquad | + | If <math>x</math> is not an integer, then <math>x+y</math> is |
| + | |||
| + | <math>\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 </math> | ||
Revision as of 21:56, 16 June 2021
Problem
Let ![$[z]$](http://latex.artofproblemsolving.com/d/4/d/d4d87c4df7a861f6bc1a1be5600dcf4111c49841.png)
denote the greatest integer not exceeding 
. Let 
and 
satisfy the simultaneous equations
![\begin{align*} y&=2[x]+3 \\ y&=3[x-2]+5. \end{align*}](http://latex.artofproblemsolving.com/f/f/7/ff782175135bd971a28e6945e86c1f39acff0559.png)
If is not an integer, then 
is
