{"status": "success", "data": {"description_md": "Let $S$ be a set of points $(x,y)$ in the coordinate plane such that two of the three quantities $3,~x+2,$ and $y-4$ are equal and the third of the three quantities is no greater than this common value. Which of the following is a correct description for $S?$\n\n$\\textbf{(A)}\\ \\text{a single point} \\qquad\\textbf{(B)}\\ \\text{two intersecting lines} \\\\\\qquad\\textbf{(C)}\\ \\text{ three lines whose pairwise intersections are three distinct points} \\\\\\qquad\\textbf{(D)}\\ \\text{a triangle} \\qquad\\textbf{(E)}\\ \\text{three rays with a common endpoint}$", "description_html": "<p>Let  <span class=\"katex--inline\">S</span>  be a set of points  <span class=\"katex--inline\">(x,y)</span>  in the coordinate plane such that two of the three quantities  <span class=\"katex--inline\">3,~x+2,</span>  and  <span class=\"katex--inline\">y-4</span>  are equal and the third of the three quantities is no greater than this common value. Which of the following is a correct description for  <span class=\"katex--inline\">S?</span> </p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\text{a single point} \\qquad\\textbf{(B)}\\ \\text{two intersecting lines} \\\\\\qquad\\textbf{(C)}\\ \\text{ three lines whose pairwise intersections are three distinct points} \\\\\\qquad\\textbf{(D)}\\ \\text{a triangle} \\qquad\\textbf{(E)}\\ \\text{three rays with a common endpoint}</span> </p>\n<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": "2017 AMC 10A Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc10A_p13", "prev": "/problem/17_amc10A_p11"}}