{"status": "success", "data": {"description_md": "Consider all 1000-element subsets of the set $\\{1,2,3,\\ldots,2015\\}$. From each such subset choose the least element. The arithmetic mean of all of these least elements is $\\tfrac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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>Consider all 1000-element subsets of the set <span class=\"katex--inline\">\\{1,2,3,\\ldots,2015\\}</span>. From each such subset choose the least element. The arithmetic mean of all of these least elements is <span class=\"katex--inline\">\\tfrac{p}{q}</span>, where <span class=\"katex--inline\">p</span> and <span class=\"katex--inline\">q</span> are relatively prime positive integers. Find <span class=\"katex--inline\">p+q</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": "2015 AIME I Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/15_aime_I_p13", "prev": "/problem/15_aime_I_p11"}}