{"status": "success", "data": {"description_md": "Suppose that $S$ is a finite set of positive integers. If the greatest integer in $S$ is removed from $S$, then the average value (arithmetic mean) of the integers remaining is $32$. If the least integer in $S$ is also removed, then the average value of the integers remaining is $35$. If the greatest integer is then returned to the set, the average value of the integers rises to $40$. The greatest integer in the original set $S$ is $72$ greater than the least integer in $S$. What is the average value of all the integers in the set $S$?\n\n$\\textbf{(A) }36.2 \\qquad \\textbf{(B) }36.4 \\qquad \\textbf{(C) }36.6\\qquad \\textbf{(D) }36.8 \\qquad \\textbf{(E) }37$\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>Suppose that  <span class=\"katex--inline\">S</span>  is a finite set of positive integers. If the greatest integer in  <span class=\"katex--inline\">S</span>  is removed from  <span class=\"katex--inline\">S</span> , then the average value (arithmetic mean) of the integers remaining is  <span class=\"katex--inline\">32</span> . If the least integer in  <span class=\"katex--inline\">S</span>  is also removed, then the average value of the integers remaining is  <span class=\"katex--inline\">35</span> . If the greatest integer is then returned to the set, the average value of the integers rises to  <span class=\"katex--inline\">40</span> . The greatest integer in the original set  <span class=\"katex--inline\">S</span>  is  <span class=\"katex--inline\">72</span>  greater than the least integer in  <span class=\"katex--inline\">S</span> . What is the average value of all the integers in the set  <span class=\"katex--inline\">S</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }36.2 \\qquad \\textbf{(B) }36.4 \\qquad \\textbf{(C) }36.6\\qquad \\textbf{(D) }36.8 \\qquad \\textbf{(E) }37</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": "2021 AMC 12B Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc12B_p13", "prev": "/problem/21_amc12B_p11"}}