{"status": "success", "data": {"description_md": "Let $n$ be a $5$-digit number, and let $q$ and $r$ be the quotient and the remainder, respectively, when $n$ is divided by $100$. For how many values of $n$ is $q+r$ divisible by $11$? \n\n$\\mathrm{(A) \\ } 8180\\qquad \\mathrm{(B) \\ } 8181\\qquad \\mathrm{(C) \\ } 8182\\qquad \\mathrm{(D) \\ } 9000\\qquad \\mathrm{(E) \\ } 9090$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let  <span class=\"katex--inline\">n</span>  be a  <span class=\"katex--inline\">5</span> -digit number, and let  <span class=\"katex--inline\">q</span>  and  <span class=\"katex--inline\">r</span>  be the quotient and the remainder, respectively, when  <span class=\"katex--inline\">n</span>  is divided by  <span class=\"katex--inline\">100</span> . For how many values of  <span class=\"katex--inline\">n</span>  is  <span class=\"katex--inline\">q+r</span>  divisible by  <span class=\"katex--inline\">11</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } 8180\\qquad \\mathrm{(B) \\ } 8181\\qquad \\mathrm{(C) \\ } 8182\\qquad \\mathrm{(D) \\ } 9000\\qquad \\mathrm{(E) \\ } 9090</span> </p>&#10;<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": "2003 AMC 12A Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc12A_p19", "prev": "/problem/03_amc12A_p17"}}