{"status": "success", "data": {"description_md": "Let $S$ be the set of the $2005$ smallest positive multiples of $4$, and let $T$ be the set of the $2005$ smallest positive multiples of $6$. How many elements are common to $S$ and $T$?\n\n$\\mathrm{(A) \\ } 166\\qquad \\mathrm{(B) \\ } 333\\qquad \\mathrm{(C) \\ } 500\\qquad \\mathrm{(D) \\ } 668\\qquad \\mathrm{(E) \\ } 1001$", "description_html": "<p>Let  <span class=\"katex--inline\">S</span>  be the set of the  <span class=\"katex--inline\">2005</span>  smallest positive multiples of  <span class=\"katex--inline\">4</span> , and let  <span class=\"katex--inline\">T</span>  be the set of the  <span class=\"katex--inline\">2005</span>  smallest positive multiples of  <span class=\"katex--inline\">6</span> . How many elements are common to  <span class=\"katex--inline\">S</span>  and  <span class=\"katex--inline\">T</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } 166\\qquad \\mathrm{(B) \\ } 333\\qquad \\mathrm{(C) \\ } 500\\qquad \\mathrm{(D) \\ } 668\\qquad \\mathrm{(E) \\ } 1001</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": "2005 AMC 10A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc10A_p23", "prev": "/problem/05_amc10A_p21"}}