{"status": "success", "data": {"description_md": "The set of real numbers $x$ for which \n\n$$\\dfrac{1}{x-2009}+\\dfrac{1}{x-2010}+\\dfrac{1}{x-2011}\\ge1$$<br>is the union of intervals of the form $a<x\\le b$. What is the sum of the lengths of these intervals?\n\n$\\textbf{(A)}\\ \\dfrac{1003}{335} \\qquad \\textbf{(B)}\\ \\dfrac{1004}{335} \\qquad \\textbf{(C)}\\ 3 \\qquad \\textbf{(D)}\\ \\dfrac{403}{134} \\qquad \\textbf{(E)}\\ \\dfrac{202}{67}$\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 set of real numbers  <span class=\"katex--inline\">x</span>  for which</p>&#10;<p> <span class=\"katex--display\">\\dfrac{1}{x-2009}+\\dfrac{1}{x-2010}+\\dfrac{1}{x-2011}\\ge1</span> <br/>is the union of intervals of the form  <span class=\"katex--inline\">a&lt;x\\le b</span> . What is the sum of the lengths of these intervals?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\dfrac{1003}{335} \\qquad \\textbf{(B)}\\ \\dfrac{1004}{335} \\qquad \\textbf{(C)}\\ 3 \\qquad \\textbf{(D)}\\ \\dfrac{403}{134} \\qquad \\textbf{(E)}\\ \\dfrac{202}{67}</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": 5, "problem_name": "2010 AMC 12B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12B_p25", "prev": "/problem/10_amc12B_p23"}}