{"status": "success", "data": {"description_md": "Let $n$ be the least positive integer greater than $1000$ for which$$\\gcd(63, n+120) =21\\quad \\text{and} \\quad \\gcd(n+63, 120)=60.$$What is the sum of the digits of $n$?\n\n$\\textbf{(A) } 12 \\qquad\\textbf{(B) } 15 \\qquad\\textbf{(C) } 18 \\qquad\\textbf{(D) } 21\\qquad\\textbf{(E) } 24$", "description_html": "<p>Let  <span class=\"katex--inline\">n</span>  be the least positive integer greater than  <span class=\"katex--inline\">1000</span>  for which <span class=\"katex--display\">\\gcd(63, n+120) =21\\quad \\text{and} \\quad \\gcd(n+63, 120)=60.</span> What is the sum of the digits of  <span class=\"katex--inline\">n</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 12 \\qquad\\textbf{(B) } 15 \\qquad\\textbf{(C) } 18 \\qquad\\textbf{(D) } 21\\qquad\\textbf{(E) } 24</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": "2020 AMC 10A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc10A_p25", "prev": "/problem/20_amc10A_p23"}}