{"status": "success", "data": {"description_md": "A point is chosen at random within the square in the coordinate plane whose vertices are $(0, 0), (2020, 0), (2020, 2020),$ and $(0, 2020)$. The probability that the point is within $d$ units of a lattice point is $\\tfrac{1}{2}$. (A point $(x, y)$ is a lattice point if $x$ and $y$ are both integers.) What is $d$ to the nearest tenth$?$\n\n$\\textbf{(A) } 0.3 \\qquad \\textbf{(B) } 0.4 \\qquad \\textbf{(C) } 0.5 \\qquad \\textbf{(D) } 0.6 \\qquad \\textbf{(E) } 0.7$\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": "<p>A point is chosen at random within the square in the coordinate plane whose vertices are  <span class=\"katex--inline\">(0, 0), (2020, 0), (2020, 2020),</span>  and  <span class=\"katex--inline\">(0, 2020)</span> . The probability that the point is within  <span class=\"katex--inline\">d</span>  units of a lattice point is  <span class=\"katex--inline\">\\tfrac{1}{2}</span> . (A point  <span class=\"katex--inline\">(x, y)</span>  is a lattice point if  <span class=\"katex--inline\">x</span>  and  <span class=\"katex--inline\">y</span>  are both integers.) What is  <span class=\"katex--inline\">d</span>  to the nearest tenth <span class=\"katex--inline\">?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 0.3 \\qquad \\textbf{(B) } 0.4 \\qquad \\textbf{(C) } 0.5 \\qquad \\textbf{(D) } 0.6 \\qquad \\textbf{(E) } 0.7</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2020 AMC 12A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12A_p17", "prev": "/problem/20_amc12A_p15"}}