{"status": "success", "data": {"description_md": "Let $1$; $4$; $\\ldots$ and $9$; $16$; $\\ldots$ be two arithmetic progressions. The set $S$ is the union of the first $2004$ terms of each sequence. How many distinct numbers are in $S$?\n\n$\\mathrm{(A) \\ } 3722 \\qquad \\mathrm{(B) \\ } 3732 \\qquad \\mathrm{(C) \\ } 3914 \\qquad \\mathrm{(D) \\ } 3924 \\qquad \\mathrm{(E) \\ } 4007$", "description_html": "<p>Let  <span class=\"katex--inline\">1</span> ;  <span class=\"katex--inline\">4</span> ;  <span class=\"katex--inline\">\\ldots</span>  and  <span class=\"katex--inline\">9</span> ;  <span class=\"katex--inline\">16</span> ;  <span class=\"katex--inline\">\\ldots</span>  be two arithmetic progressions. The set  <span class=\"katex--inline\">S</span>  is the union of the first  <span class=\"katex--inline\">2004</span>  terms of each sequence. How many distinct numbers are in  <span class=\"katex--inline\">S</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } 3722 \\qquad \\mathrm{(B) \\ } 3732 \\qquad \\mathrm{(C) \\ } 3914 \\qquad \\mathrm{(D) \\ } 3924 \\qquad \\mathrm{(E) \\ } 4007</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": "2004 AMC 10B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10B_p22", "prev": "/problem/04_amc10B_p20"}}