{"status": "success", "data": {"description_md": "Let $a, b, c,$ and $d$ be positive integers such that $\\gcd(a, b)=24$, $\\gcd(b, c)=36$, $\\gcd(c, d)=54$, and $70<\\gcd(d, a)<100$. Which of the following must be a divisor of $a$?\n\n$\\textbf{(A)} \\text{ 5} \\qquad \\textbf{(B)} \\text{ 7} \\qquad \\textbf{(C)} \\text{ 11} \\qquad \\textbf{(D)} \\text{ 13} \\qquad \\textbf{(E)} \\text{ 17}$", "description_html": "<p>Let  <span class=\"katex--inline\">a, b, c,</span>  and  <span class=\"katex--inline\">d</span>  be positive integers such that  <span class=\"katex--inline\">\\gcd(a, b)=24</span> ,  <span class=\"katex--inline\">\\gcd(b, c)=36</span> ,  <span class=\"katex--inline\">\\gcd(c, d)=54</span> , and  <span class=\"katex--inline\">70&lt;\\gcd(d, a)&lt;100</span> . Which of the following must be a divisor of  <span class=\"katex--inline\">a</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)} \\text{ 5} \\qquad \\textbf{(B)} \\text{ 7} \\qquad \\textbf{(C)} \\text{ 11} \\qquad \\textbf{(D)} \\text{ 13} \\qquad \\textbf{(E)} \\text{ 17}</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": "2018 AMC 10A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc10A_p23", "prev": "/problem/18_amc10A_p21"}}