{"status": "success", "data": {"description_md": "The remainder can be defined for all real numbers $x$ and $y$ with $y \\neq 0$ by $$\\text{rem} (x ,y)=x-y\\left \\lfloor \\frac{x}{y} \\right \\rfloor$$where $\\left \\lfloor \\tfrac{x}{y} \\right \\rfloor$ denotes the greatest integer less than or equal to $\\tfrac{x}{y}$. What is the value of $\\text{rem} (\\tfrac{3}{8}, -\\tfrac{2}{5} )$?\n\n$\\textbf{(A) } -\\frac{3}{8} \\qquad \\textbf{(B) } -\\frac{1}{40} \\qquad \\textbf{(C) } 0 \\qquad \\textbf{(D) } \\frac{3}{8} \\qquad \\textbf{(E) } \\frac{31}{40}$\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>The remainder can be defined for all real numbers  <span class=\"katex--inline\">x</span>  and  <span class=\"katex--inline\">y</span>  with  <span class=\"katex--inline\">y \\neq 0</span>  by  <span class=\"katex--display\">\\text{rem} (x ,y)=x-y\\left \\lfloor \\frac{x}{y} \\right \\rfloor</span> where  <span class=\"katex--inline\">\\left \\lfloor \\tfrac{x}{y} \\right \\rfloor</span>  denotes the greatest integer less than or equal to  <span class=\"katex--inline\">\\tfrac{x}{y}</span> . What is the value of  <span class=\"katex--inline\">\\text{rem} (\\tfrac{3}{8}, -\\tfrac{2}{5} )</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } -\\frac{3}{8} \\qquad \\textbf{(B) } -\\frac{1}{40} \\qquad \\textbf{(C) } 0 \\qquad \\textbf{(D) } \\frac{3}{8} \\qquad \\textbf{(E) } \\frac{31}{40}</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": 2, "problem_name": "2016 AMC 12A Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12A_p04", "prev": "/problem/16_amc12A_p02"}}