{"status": "success", "data": {"description_md": "Positive integers $a,b,$ and $c$ are chosen so that $a<b<c$, and the system of equations $2x + y = 2003$ and $y = |x-a| + |x-b| + |x-c|$has exactly one solution. What is the minimum value of $c$?\n\n$\\mathrm{(A)}\\ 668\\qquad\\mathrm{(B)}\\ 669\\qquad\\mathrm{(C)}\\ 1002\\qquad\\mathrm{(D)}\\ 2003\\qquad\\mathrm{(E)}\\ 2004$\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>Positive integers <span class=\"katex--inline\">a,b,</span> and <span class=\"katex--inline\">c</span> are chosen so that <span class=\"katex--inline\">a&lt;b&lt;c</span>, and the system of equations <span class=\"katex--inline\">2x + y = 2003</span> and <span class=\"katex--inline\">y = |x-a| + |x-b| + |x-c|</span>has exactly one solution. What is the minimum value of <span class=\"katex--inline\">c</span>?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ 668\\qquad\\mathrm{(B)}\\ 669\\qquad\\mathrm{(C)}\\ 1002\\qquad\\mathrm{(D)}\\ 2003\\qquad\\mathrm{(E)}\\ 2004</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2003 AMC 12B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc12B_p25", "prev": "/problem/03_amc12B_p23"}}