# 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 22:56, 16 June 2021

## Problem

Let denote the greatest integer not exceeding . Let and satisfy the simultaneous equations

If is not an integer, then is