{"status": "success", "data": {"description_md": "Points $A$ and $B$ lie on the graph of $y=\\log_{2}x$. The midpoint of $\\overline{AB}$ is $(6, 2)$. What is the positive difference between the $x$-coordinates of $A$ and $B$?\n\n$\\textbf{(A)}~2\\sqrt{11}\\qquad\\textbf{(B)}~4\\sqrt{3}\\qquad\\textbf{(C)}~8\\qquad\\textbf{(D)}~4\\sqrt{5}\\qquad\\textbf{(E)}~9$\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>Points  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span>  lie on the graph of  <span class=\"katex--inline\">y=\\log_{2}x</span> . The midpoint of  <span class=\"katex--inline\">\\overline{AB}</span>  is  <span class=\"katex--inline\">(6, 2)</span> . What is the positive difference between the  <span class=\"katex--inline\">x</span> -coordinates of  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}~2\\sqrt{11}\\qquad\\textbf{(B)}~4\\sqrt{3}\\qquad\\textbf{(C)}~8\\qquad\\textbf{(D)}~4\\sqrt{5}\\qquad\\textbf{(E)}~9</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": "2023 AMC 12A Problem 6", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc12A_p07", "prev": "/problem/23_amc12A_p05"}}