{"status": "success", "data": {"description_md": "At a competition with $N$ players, the number of players given elite status is equal to $2^{1+\\lfloor \\log_{2} (N-1) \\rfloor}-N$. Suppose that $19$ players are given elite status. What is the sum of the two smallest possible values of $N$?\n\n$\\textbf{(A)}\\ 38 \\qquad<br>\\textbf{(B)}\\ 90 \\qquad<br>\\textbf{(C)}\\ 154 \\qquad<br>\\textbf{(D)}\\ 406 \\qquad<br>\\textbf{(E)}\\ 1024$\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>At a competition with  <span class=\"katex--inline\">N</span>  players, the number of players given elite status is equal to  <span class=\"katex--inline\">2^{1+\\lfloor \\log_{2} (N-1) \\rfloor}-N</span> . Suppose that  <span class=\"katex--inline\">19</span>  players are given elite status. What is the sum of the two smallest possible values of  <span class=\"katex--inline\">N</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 38 \\qquad\\textbf{(B)}\\ 90 \\qquad\\textbf{(C)}\\ 154 \\qquad\\textbf{(D)}\\ 406 \\qquad\\textbf{(E)}\\ 1024</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": "2011 AMC 12A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc12A_p20", "prev": "/problem/11_amc12A_p18"}}