{"status": "success", "data": {"description_md": "A rectangular box measures $a \\times b \\times c$, where $a$, $b$, and $c$ are integers and $1\\leq a \\leq b \\leq c$. The volume and the surface area of the box are numerically equal. How many ordered triples $(a,b,c)$ are possible?\n\n$\\textbf{(A)}\\; 4 \\qquad\\textbf{(B)}\\; 10 \\qquad\\textbf{(C)}\\; 12 \\qquad\\textbf{(D)}\\; 21 \\qquad\\textbf{(E)}\\; 26$\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>A rectangular box measures  <span class=\"katex--inline\">a \\times b \\times c</span> , where  <span class=\"katex--inline\">a</span> ,  <span class=\"katex--inline\">b</span> , and  <span class=\"katex--inline\">c</span>  are integers and  <span class=\"katex--inline\">1\\leq a \\leq b \\leq c</span> . The volume and the surface area of the box are numerically equal. How many ordered triples  <span class=\"katex--inline\">(a,b,c)</span>  are possible?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\; 4 \\qquad\\textbf{(B)}\\; 10 \\qquad\\textbf{(C)}\\; 12 \\qquad\\textbf{(D)}\\; 21 \\qquad\\textbf{(E)}\\; 26</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": "2015 AMC 12B Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/15_amc12B_p24", "prev": "/problem/15_amc12B_p22"}}