{"status": "success", "data": {"description_md": "Let $S$ be the set of lattice points in the coordinate plane, both of whose coordinates are integers between $1$ and $30,$ inclusive. Exactly $300$ points in $S$ lie on or below a line with equation $y=mx.$ The possible values of $m$ lie in an interval of length $\\frac ab,$ where $a$ and $b$ are relatively prime positive integers. What is $a+b?$\n\n$\\textbf{(A) }31 \\qquad \\textbf{(B) }47 \\qquad \\textbf{(C) }62\\qquad \\textbf{(D) }72 \\qquad \\textbf{(E) }85$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

Let S be the set of lattice points in the coordinate plane, both of whose coordinates are integers between 1 and 30, inclusive. Exactly 300 points in S lie on or below a line with equation y=mx. The possible values of m lie in an interval of length \\frac ab, where a and b are relatively prime positive integers. What is a+b?

\\textbf{(A) }31 \\qquad \\textbf{(B) }47 \\qquad \\textbf{(C) }62\\qquad \\textbf{(D) }72 \\qquad \\textbf{(E) }85

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2021 AMC 12B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/21_amc12B_p24"}}