{"status": "success", "data": {"description_md": "Alice, Bob, and Charlie were on a hike and were wondering how far away the nearest town was. When Alice said, \"We are at least $6$ miles away,\" Bob replied, \"We are at most $5$ miles away.\" Charlie then remarked, \"Actually the nearest town is at most $4$ miles away.\" It turned out that none of the three statements were true. Let $d$ be the distance in miles to the nearest town. Which of the following intervals is the set of all possible values of $d$?\n\n$\\textbf{(A) }   (0,4)   \\qquad        \\textbf{(B) }   (4,5)   \\qquad    \\textbf{(C) }   (4,6)   \\qquad   \\textbf{(D) }  (5,6)  \\qquad  \\textbf{(E) }   (5,\\infty)$", "description_html": "<p>Alice, Bob, and Charlie were on a hike and were wondering how far away the nearest town was. When Alice said, &#8220;We are at least  <span class=\"katex--inline\">6</span>  miles away,&#8221; Bob replied, &#8220;We are at most  <span class=\"katex--inline\">5</span>  miles away.&#8221; Charlie then remarked, &#8220;Actually the nearest town is at most  <span class=\"katex--inline\">4</span>  miles away.&#8221; It turned out that none of the three statements were true. Let  <span class=\"katex--inline\">d</span>  be the distance in miles to the nearest town. Which of the following intervals is the set of all possible values of  <span class=\"katex--inline\">d</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }   (0,4)   \\qquad        \\textbf{(B) }   (4,5)   \\qquad    \\textbf{(C) }   (4,6)   \\qquad   \\textbf{(D) }  (5,6)  \\qquad  \\textbf{(E) }   (5,\\infty)</span> </p>\n<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": 1, "problem_name": "2018 AMC 10A Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc10A_p06", "prev": "/problem/18_amc10A_p04"}}