{"status": "success", "data": {"description_md": "Values for $A,B,C,$ and $D$ are to be selected from $\\{1, 2, 3, 4, 5, 6\\}$ without replacement (i.e. no two letters have the same value). How many ways are there to make such choices so that the two curves $y=Ax^2+B$ and $y=Cx^2+D$ intersect? (The order in which the curves are listed does not matter; for example, the choices $A=3, B=2, C=4, D=1$ is considered the same as the choices $A=4, B=1, C=3, D=2.$)\n\n$\\textbf{(A) }30 \\qquad \\textbf{(B) }60 \\qquad \\textbf{(C) }90 \\qquad \\textbf{(D) }180 \\qquad \\textbf{(E) }360$", "description_html": "<p>Values for  <span class=\"katex--inline\">A,B,C,</span>  and  <span class=\"katex--inline\">D</span>  are to be selected from  <span class=\"katex--inline\">\\{1, 2, 3, 4, 5, 6\\}</span>  without replacement (i.e. no two letters have the same value). How many ways are there to make such choices so that the two curves  <span class=\"katex--inline\">y=Ax^2+B</span>  and  <span class=\"katex--inline\">y=Cx^2+D</span>  intersect? (The order in which the curves are listed does not matter; for example, the choices  <span class=\"katex--inline\">A=3, B=2, C=4, D=1</span>  is considered the same as the choices  <span class=\"katex--inline\">A=4, B=1, C=3, D=2.</span> )</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }30 \\qquad \\textbf{(B) }60 \\qquad \\textbf{(C) }90 \\qquad \\textbf{(D) }180 \\qquad \\textbf{(E) }360</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": "2021 AMC 10A Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc10A_p16", "prev": "/problem/21_amc10A_p14"}}