{"status": "success", "data": {"description_md": "Let $f(x)=\\sum_{k=2}^{10}(\\lfloor kx \\rfloor -k \\lfloor x \\rfloor)$, where $\\lfloor r \\rfloor$ denotes the greatest integer less than or equal to $r$. How many distinct values does $f(x)$ assume for $x \\ge 0$?\n\n$\\textbf{(A)}\\ 32\\qquad\\textbf{(B)}\\ 36\\qquad\\textbf{(C)}\\ 45\\qquad\\textbf{(D)}\\ 46\\qquad\\textbf{(E)}\\ \\text{infinitely many}$", "description_html": "<p>Let  <span class=\"katex--inline\">f(x)=\\sum_{k=2}^{10}(\\lfloor kx \\rfloor -k \\lfloor x \\rfloor)</span> , where  <span class=\"katex--inline\">\\lfloor r \\rfloor</span>  denotes the greatest integer less than or equal to  <span class=\"katex--inline\">r</span> . How many distinct values does  <span class=\"katex--inline\">f(x)</span>  assume for  <span class=\"katex--inline\">x \\ge 0</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 32\\qquad\\textbf{(B)}\\ 36\\qquad\\textbf{(C)}\\ 45\\qquad\\textbf{(D)}\\ 46\\qquad\\textbf{(E)}\\ \\text{infinitely many}</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": "2016 AMC 10B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/16_amc10B_p24"}}