{"status": "success", "data": {"description_md": "All three vertices of an equilateral triangle are on the parabola $y=x^2$, and one of its sides has a slope of $2$.  The $x$-coordinates of the three vertices have a sum of $m/n$, where $m$ and $n$ are relatively prime positive integers.  What is the value of $m+n$?\n\n$\\mathrm{(A)}\\ {{{14}}} \\qquad \\mathrm{(B)}\\ {{{15}}} \\qquad \\mathrm{(C)}\\ {{{16}}} \\qquad \\mathrm{(D)}\\ {{{17}}} \\qquad \\mathrm{(E)}\\ {{{18}}}$\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>All three vertices of an equilateral triangle are on the parabola  <span class=\"katex--inline\">y=x^2</span> , and one of its sides has a slope of  <span class=\"katex--inline\">2</span> .  The  <span class=\"katex--inline\">x</span> -coordinates of the three vertices have a sum of  <span class=\"katex--inline\">m/n</span> , where  <span class=\"katex--inline\">m</span>  and  <span class=\"katex--inline\">n</span>  are relatively prime positive integers.  What is the value of  <span class=\"katex--inline\">m+n</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ {{{14}}} \\qquad \\mathrm{(B)}\\ {{{15}}} \\qquad \\mathrm{(C)}\\ {{{16}}} \\qquad \\mathrm{(D)}\\ {{{17}}} \\qquad \\mathrm{(E)}\\ {{{18}}}</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": 5, "problem_name": "2005 AMC 12B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc12B_p25", "prev": "/problem/05_amc12B_p23"}}