{"status": "success", "data": {"description_md": "Let $x$ be chosen at random from the interval $(0,1)$. What is the probability that\n\n$\\lfloor\\log_{10}4x\\rfloor - \\lfloor\\log_{10}x\\rfloor = 0$?<br>Here $\\lfloor x\\rfloor$ denotes the greatest integer that is less than or equal to $x$.\n\n$\\mathrm{(A)}\\ \\frac 18<br>\\qquad<br>\\mathrm{(B)}\\ \\frac 3{20}<br>\\qquad<br>\\mathrm{(C)}\\ \\frac 16<br>\\qquad<br>\\mathrm{(D)}\\ \\frac 15 <br>\\qquad<br>\\mathrm{(E)}\\ \\frac 14$\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>Let  <span class=\"katex--inline\">x</span>  be chosen at random from the interval  <span class=\"katex--inline\">(0,1)</span> . What is the probability that</p>&#10;<p> <span class=\"katex--inline\">\\lfloor\\log_{10}4x\\rfloor - \\lfloor\\log_{10}x\\rfloor = 0</span> ?<br/>Here  <span class=\"katex--inline\">\\lfloor x\\rfloor</span>  denotes the greatest integer that is less than or equal to  <span class=\"katex--inline\">x</span> .</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac 18\\qquad\\mathrm{(B)}\\ \\frac 3{20}\\qquad\\mathrm{(C)}\\ \\frac 16\\qquad\\mathrm{(D)}\\ \\frac 15 \\qquad\\mathrm{(E)}\\ \\frac 14</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": 3, "problem_name": "2006 AMC 12B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc12B_p21", "prev": "/problem/06_amc12B_p19"}}