{"status": "success", "data": {"description_md": "If the positive integer $c$ has positive integer divisors $a$ and $b$ with $c = ab$, then $a$ and $b$ are said to be *complementary* divisors of $c$. Suppose that $N$ is a positive integer that has one complementary pair of divisors that differ by $20$ and another pair of complementary divisors that differ by $23$. What is the sum of the digits of $N$?\n\n$\\textbf{(A) } 9 \\qquad \\textbf{(B) } 13\\qquad \\textbf{(C) } 15 \\qquad \\textbf{(D) } 17 \\qquad \\textbf{(E) } 19$", "description_html": "<p>If the positive integer <span class=\"katex--inline\">c</span> has positive integer divisors <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> with <span class=\"katex--inline\">c = ab</span>, then <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are said to be <em>complementary</em> divisors of <span class=\"katex--inline\">c</span>. Suppose that <span class=\"katex--inline\">N</span> is a positive integer that has one complementary pair of divisors that differ by <span class=\"katex--inline\">20</span> and another pair of complementary divisors that differ by <span class=\"katex--inline\">23</span>. What is the sum of the digits of <span class=\"katex--inline\">N</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A) } 9 \\qquad \\textbf{(B) } 13\\qquad \\textbf{(C) } 15 \\qquad \\textbf{(D) } 17 \\qquad \\textbf{(E) } 19</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2023 AMC 10A Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc10A_p24", "prev": "/problem/23_amc10A_p22"}}