{"status": "success", "data": {"description_md": "If $a$ is a nonzero integer and $b$ is a positive number such that $ab^2=\\log_{10}b$, what is the median of the set $\\{0,1,a,b,1/b\\}$?\n\n$\\mathrm {(A)} 0\\qquad \\mathrm {(B)} 1\\qquad \\mathrm {(C)} a\\qquad \\mathrm {(D)} b\\qquad \\mathrm {(E)} \\frac{1}{b}$\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>If  <span class=\"katex--inline\">a</span>  is a nonzero integer and  <span class=\"katex--inline\">b</span>  is a positive number such that  <span class=\"katex--inline\">ab^2=\\log_{10}b</span> , what is the median of the set  <span class=\"katex--inline\">\\{0,1,a,b,1/b\\}</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm {(A)} 0\\qquad \\mathrm {(B)} 1\\qquad \\mathrm {(C)} a\\qquad \\mathrm {(D)} b\\qquad \\mathrm {(E)} \\frac{1}{b}</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": "2007 AMC 12B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc12B_p18", "prev": "/problem/07_amc12B_p16"}}