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Difference between revisions of "2011 AMC 10B Problems/Problem 24"

(Created page with "== Problem 24 == A lattice point in an <math>xy</math>-coordinate system in any point <math>(x, y)</math> where both <math>x</math> and <math>y</math> are integers. The graph of...")
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Revision as of 14:16, 6 June 2011

Problem 24

A lattice point in an $xy$-coordinate system in any point $(x, y)$ where both $x$ and $y$ are integers. The graph of $y = mx +2$ passes through no lattice point with $0 < x \le 100$ for all $m$ such that $1/2 < m < a$. What is the maximum possible value of $a$?

$\textbf{(A)}\ \frac{51}{101} \qquad\textbf{(B)}\ \frac{50}{99} \qquad\textbf{(C)}\ \frac{51}{100} \qquad\textbf{(D)}\ \frac{52}{101} \qquad\textbf{(E)}\ \frac{13}{25}$

Solution

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