Difference between revisions of "2021 AMC 12B Problems/Problem 25"

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Let <math>S</math> be the set of lattice points in the coordinate plane, both of whose coordinates are integers between <math>1</math> and <math>30</math>, inclusive. Exactly <math>300</math> points in <math>S</math> lie on or below a line with equation <math>y = mx</math>. The possible values of <math>m</math> lie in an interval of length <math>\frac{a}{b}</math>, where <math>a</math> and <math>b</math> are relatively prime positive integers. What is <math>a + b ?</math>
<math>\textbf{(A)} ~31 \qquad\textbf{(B)} ~47 \qquad\textbf{(C)} ~62 \qquad\textbf{(D)} ~72 \qquad\textbf{(E)} ~85</math>
==See Also==
{{AMC12 box|year=2021|ab=B|num-b=24|after=Last Problem}}
{{MAA Notice}}

Revision as of 23:13, 11 February 2021

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