{"status": "success", "data": {"description_md": "Let $f_0(x)=x+|x-100|-|x+100|$, and for $n\\geq 1$, let $f_n(x)=|f_{n-1}(x)|-1$.  For how many values of $x$ is $f_{100}(x)=0$?\n\n$\\textbf{(A) }299\\qquad<br>\\textbf{(B) }300\\qquad<br>\\textbf{(C) }301\\qquad<br>\\textbf{(D) }302\\qquad<br>\\textbf{(E) }303\\qquad$\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\">f_0(x)=x+|x-100|-|x+100|</span> , and for  <span class=\"katex--inline\">n\\geq 1</span> , let  <span class=\"katex--inline\">f_n(x)=|f_{n-1}(x)|-1</span> .  For how many values of  <span class=\"katex--inline\">x</span>  is  <span class=\"katex--inline\">f_{100}(x)=0</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }299\\qquad\\textbf{(B) }300\\qquad\\textbf{(C) }301\\qquad\\textbf{(D) }302\\qquad\\textbf{(E) }303\\qquad</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": "2014 AMC 12A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc12A_p25", "prev": "/problem/14_amc12A_p23"}}