{"status": "success", "data": {"description_md": "In the five-sided star shown, the letters $A$, $B$, $C$, $D$, and $E$ are replaced by the numbers $3$, $5$, $6$, $7$, and $9$, although not necessarily in this order. The sums of the numbers at the ends of the line segments $AB$, $BC$, $CD$, $DE$, and $EA$ form an arithmetic sequence, although not necessarily in this order. What is the middle term of the sequence? \n\n\n$\\mathrm{(A) \\ } 9\\qquad \\mathrm{(B) \\ } 10\\qquad \\mathrm{(C) \\ } 11\\qquad \\mathrm{(D) \\ } 12\\qquad \\mathrm{(E) \\ } 13$", "description_html": "<p>In the five-sided star shown, the letters  <span class=\"katex--inline\">A</span> ,  <span class=\"katex--inline\">B</span> ,  <span class=\"katex--inline\">C</span> ,  <span class=\"katex--inline\">D</span> , and  <span class=\"katex--inline\">E</span>  are replaced by the numbers  <span class=\"katex--inline\">3</span> ,  <span class=\"katex--inline\">5</span> ,  <span class=\"katex--inline\">6</span> ,  <span class=\"katex--inline\">7</span> , and  <span class=\"katex--inline\">9</span> , although not necessarily in this order. The sums of the numbers at the ends of the line segments  <span class=\"katex--inline\">AB</span> ,  <span class=\"katex--inline\">BC</span> ,  <span class=\"katex--inline\">CD</span> ,  <span class=\"katex--inline\">DE</span> , and  <span class=\"katex--inline\">EA</span>  form an arithmetic sequence, although not necessarily in this order. What is the middle term of the sequence?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } 9\\qquad \\mathrm{(B) \\ } 10\\qquad \\mathrm{(C) \\ } 11\\qquad \\mathrm{(D) \\ } 12\\qquad \\mathrm{(E) \\ } 13</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": 3, "problem_name": "2005 AMC 10A Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc10A_p18", "prev": "/problem/05_amc10A_p16"}}