{"status": "success", "data": {"description_md": "For all positive integers $n$ less than $2002$, let \n\n$$\\begin{eqnarray*}
a_n =\\left\\{
\\begin{array}{lr}
11, & \\text{if\\ }n\\ \\text{is\\ divisible\\ by\\ }13\\ \\text{and\\ }14;\\\\
13, & \\text{if\\ }n\\ \\text{is\\ divisible\\ by\\ }14\\ \\text{and\\ }11;\\\\
14, & \\text{if\\ }n\\ \\text{is\\ divisible\\ by\\ }11\\ \\text{and\\ }13;\\\\
0, & \\text{otherwise}.
\\end{array}
\\right.
\\end{eqnarray*}$$
Calculate $\\sum_{n=1}^{2001} a_n$.\n\n$\\mathrm{(A)}\\ 448
\\qquad\\mathrm{(B)}\\ 486
\\qquad\\mathrm{(C)}\\ 1560
\\qquad\\mathrm{(D)}\\ 2001
\\qquad\\mathrm{(E)}\\ 2002$\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": "

For all positive integers n less than 2002 , let

\\begin{eqnarray*}a_n =\\left\\{\\begin{array}{lr}11, & \\text{if\\ }n\\ \\text{is\\ divisible\\ by\\ }13\\ \\text{and\\ }14;\\\\13, & \\text{if\\ }n\\ \\text{is\\ divisible\\ by\\ }14\\ \\text{and\\ }11;\\\\14, & \\text{if\\ }n\\ \\text{is\\ divisible\\ by\\ }11\\ \\text{and\\ }13;\\\\0, & \\text{otherwise}.\\end{array}\\right.\\end{eqnarray*}
Calculate \\sum_{n=1}^{2001} a_n .

\\mathrm{(A)}\\ 448\\qquad\\mathrm{(B)}\\ 486\\qquad\\mathrm{(C)}\\ 1560\\qquad\\mathrm{(D)}\\ 2001\\qquad\\mathrm{(E)}\\ 2002

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2002 AMC 12B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc12B_p22", "prev": "/problem/02_amc12B_p20"}}