{"status": "success", "data": {"description_md": "What is the volume of the region in three-dimensional space defined by the inequalities $|x|+|y|+|z|\\le1$ and $|x|+|y|+|z-1|\\le1$?\n\n$\\textbf{(A)}\\ \\frac{1}{6}\\qquad\\textbf{(B)}\\ \\frac{1}{4}\\qquad\\textbf{(C)}\\ \\frac{1}{3}\\qquad\\textbf{(D)}\\ \\frac{1}{2}\\qquad\\textbf{(E)}\\ 1$\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>What is the volume of the region in three-dimensional space defined by the inequalities  <span class=\"katex--inline\">|x|+|y|+|z|\\le1</span>  and  <span class=\"katex--inline\">|x|+|y|+|z-1|\\le1</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{1}{6}\\qquad\\textbf{(B)}\\ \\frac{1}{4}\\qquad\\textbf{(C)}\\ \\frac{1}{3}\\qquad\\textbf{(D)}\\ \\frac{1}{2}\\qquad\\textbf{(E)}\\ 1</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": "2016 AMC 12B Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12B_p24", "prev": "/problem/16_amc12B_p22"}}