{"status": "success", "data": {"description_md": "Brian writes down four integers $w > x > y > z$ whose sum is $44$. The pairwise positive differences of these numbers are $1, 3, 4, 5, 6,$ and $9$. What is the sum of the possible values for $w$?\n\n$\\textbf{(A)}\\ 16 \\qquad\\textbf{(B)}\\ 31 \\qquad\\textbf{(C)}\\ 48 \\qquad\\textbf{(D)}\\ 62 \\qquad\\textbf{(E)}\\ 93$", "description_html": "<p>Brian writes down four integers  <span class=\"katex--inline\">w &gt; x &gt; y &gt; z</span>  whose sum is  <span class=\"katex--inline\">44</span> . The pairwise positive differences of these numbers are  <span class=\"katex--inline\">1, 3, 4, 5, 6,</span>  and  <span class=\"katex--inline\">9</span> . What is the sum of the possible values for  <span class=\"katex--inline\">w</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 16 \\qquad\\textbf{(B)}\\ 31 \\qquad\\textbf{(C)}\\ 48 \\qquad\\textbf{(D)}\\ 62 \\qquad\\textbf{(E)}\\ 93</span> </p>\n<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": 4, "problem_name": "2011 AMC 10B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc10B_p22", "prev": "/problem/11_amc10B_p20"}}