{"status": "success", "data": {"description_md": "At a gathering of $30$ people, there are $20$ people who all know each other and $10$ people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur?\n\n$\\textbf{(A)}\\ 240\\qquad\\textbf{(B)}\\ 245\\qquad\\textbf{(C)}\\ 290\\qquad\\textbf{(D)}\\ 480\\qquad\\textbf{(E)}\\ 490$\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>At a gathering of  <span class=\"katex--inline\">30</span>  people, there are  <span class=\"katex--inline\">20</span>  people who all know each other and  <span class=\"katex--inline\">10</span>  people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 240\\qquad\\textbf{(B)}\\ 245\\qquad\\textbf{(C)}\\ 290\\qquad\\textbf{(D)}\\ 480\\qquad\\textbf{(E)}\\ 490</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": 2, "problem_name": "2017 AMC 12A Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc12A_p06", "prev": "/problem/17_amc12A_p04"}}