{"status": "success", "data": {"description_md": "Four cubes with edge lengths $1$, $2$, $3$, and $4$ are stacked as shown. What is the length of the portion of $\\overline{XY}$ contained in the cube with edge length $3$?\n\n<center>\n<img class=\"problem-image\" height=\"475\" src=\"https://latex.artofproblemsolving.com/e/4/1/e41120e351bda42fada2fe2803e19a131bc30b96.png\" width=\"308\"/>\n</center><br>\n\n$\\textbf{(A)}\\ \\dfrac{3\\sqrt{33}}5\\qquad\\textbf{(B)}\\ 2\\sqrt3\\qquad\\textbf{(C)}\\ \\dfrac{2\\sqrt{33}}3\\qquad\\textbf{(D)}\\ 4\\qquad\\textbf{(E)}\\ 3\\sqrt2$", "description_html": "<p>Four cubes with edge lengths <span class=\"katex--inline\">1</span>, <span class=\"katex--inline\">2</span>, <span class=\"katex--inline\">3</span>, and <span class=\"katex--inline\">4</span> are stacked as shown. What is the length of the portion of <span class=\"katex--inline\">\\overline{XY}</span> contained in the cube with edge length <span class=\"katex--inline\">3</span>?</p>&#10;<center>&#10;<img class=\"problem-image\" height=\"475\" src=\"https://latex.artofproblemsolving.com/e/4/1/e41120e351bda42fada2fe2803e19a131bc30b96.png\" width=\"308\"/>&#10;</center><br/>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ \\dfrac{3\\sqrt{33}}5\\qquad\\textbf{(B)}\\ 2\\sqrt3\\qquad\\textbf{(C)}\\ \\dfrac{2\\sqrt{33}}3\\qquad\\textbf{(D)}\\ 4\\qquad\\textbf{(E)}\\ 3\\sqrt2</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2014 AMC 10A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc10A_p20", "prev": "/problem/14_amc10A_p18"}}