{"status": "success", "data": {"description_md": "For some positive integers $p$, there is a quadrilateral $ABCD$ with positive integer side lengths, perimeter $p$, right angles at $B$ and $C$, $AB=2$, and $CD=AD$. How many different values of $p<2015$ are possible?\n\n$\\textbf{(A)}\\ 30 \\qquad\\textbf{(B)}\\ 31 \\qquad\\textbf{(C)}\\ 61 \\qquad\\textbf{(D)}\\ 62 \\qquad\\textbf{(E)}\\ 63$\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>For some positive integers  <span class=\"katex--inline\">p</span> , there is a quadrilateral  <span class=\"katex--inline\">ABCD</span>  with positive integer side lengths, perimeter  <span class=\"katex--inline\">p</span> , right angles at  <span class=\"katex--inline\">B</span>  and  <span class=\"katex--inline\">C</span> ,  <span class=\"katex--inline\">AB=2</span> , and  <span class=\"katex--inline\">CD=AD</span> . How many different values of  <span class=\"katex--inline\">p&lt;2015</span>  are possible?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 30 \\qquad\\textbf{(B)}\\ 31 \\qquad\\textbf{(C)}\\ 61 \\qquad\\textbf{(D)}\\ 62 \\qquad\\textbf{(E)}\\ 63</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": "2015 AMC 12A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/15_amc12A_p20", "prev": "/problem/15_amc12A_p18"}}