{"status": "success", "data": {"description_md": "Let $a$, $b$, $c$, and $d$ be real numbers with $|a-b|=2$, $|b-c|=3$, and $|c-d|=4$. What is the sum of all possible values of $|a-d|$?\n\n$\\mathrm{(A)}\\ 9\n\\qquad\n\\mathrm{(B)}\\ 12\n\\qquad\n\\mathrm{(C)}\\ 15\n\\qquad\n\\mathrm{(D)}\\ 18\n\\qquad\n\\mathrm{(E)}\\ 24$", "description_html": "<p>Let  <span class=\"katex--inline\">a</span> ,  <span class=\"katex--inline\">b</span> ,  <span class=\"katex--inline\">c</span> , and  <span class=\"katex--inline\">d</span>  be real numbers with  <span class=\"katex--inline\">|a-b|=2</span> ,  <span class=\"katex--inline\">|b-c|=3</span> , and  <span class=\"katex--inline\">|c-d|=4</span> . What is the sum of all possible values of  <span class=\"katex--inline\">|a-d|</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 9\n\\qquad\n\\mathrm{(B)}\\ 12\n\\qquad\n\\mathrm{(C)}\\ 15\n\\qquad\n\\mathrm{(D)}\\ 18\n\\qquad\n\\mathrm{(E)}\\ 24</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": 3, "problem_name": "2009 AMC 10A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc10A_p17", "prev": "/problem/09_amc10A_p15"}}