{"status": "success", "data": {"description_md": "Let $S$ be a subset of $\\{1,2,3,\\ldots,30\\}$ with the property that no pair of distinct elements in $S$ has a sum divisible by $5$.  What is the largest possible size of $S$?\n\n$\\textbf{(A)}\\ 10\\qquad\\textbf{(B)}\\ 13\\qquad\\textbf{(C)}\\ 15\\qquad\\textbf{(D)}\\ 16\\qquad\\textbf{(E)}\\ 18$\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>Let  <span class=\"katex--inline\">S</span>  be a subset of  <span class=\"katex--inline\">\\{1,2,3,\\ldots,30\\}</span>  with the property that no pair of distinct elements in  <span class=\"katex--inline\">S</span>  has a sum divisible by  <span class=\"katex--inline\">5</span> .  What is the largest possible size of  <span class=\"katex--inline\">S</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 10\\qquad\\textbf{(B)}\\ 13\\qquad\\textbf{(C)}\\ 15\\qquad\\textbf{(D)}\\ 16\\qquad\\textbf{(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": 3, "problem_name": "2012 AMC 12A Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/12_amc12A_p18", "prev": "/problem/12_amc12A_p16"}}