{"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$\\textbf{(A)}\\ \\text{a single point} \\qquad\\textbf{(B)}\\ \\text{two intersecting lines}$\n$\\textbf{(C)}\\ \\text{three lines whose pairwise intersections are three distinct points}$\n$\\textbf{(D)}\\ \\text{a triangle} \\qquad\\textbf{(E)}\\ \\text{three rays with a common endpoint}$", "description_html": "

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?

\\textbf{(A)}\\ \\text{a single point} \\qquad\\textbf{(B)}\\ \\text{two intersecting lines}
\\textbf{(C)}\\ \\text{three lines whose pairwise intersections are three distinct points}
\\textbf{(D)}\\ \\text{a triangle} \\qquad\\textbf{(E)}\\ \\text{three rays with a common endpoint}

", "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"}}