{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"afa76f70-6e29-5d3f-9faf-25c543d4751f","task_key":"geometry--test--afa76f70-6e29-5d3f-9faf-25c543d4751f","task_revision_id":"1","upstream_id":"","short_description":"A solid right prism $ABCDEF$ has a height of $16$ and equilateral triangles…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"A solid right prism $ABCDEF$ has a height of $16$ and equilateral triangles bases with side length $12,$ as shown. $ABCDEF$ is sliced with a straight cut through points $M,$ $N,$ $P,$ and $Q$ on edges $DE,$ $DF,$ $CB,$ and $CA,$ respectively. If $DM=4,$ $DN=2,$ and $CQ=8,$ determine the volume of the solid $QPCDMN.$ [asy]\\n\\npair A, B, C, D, E, F, M,N,P,Q;\\nA=(0,0);\\nB=(12,0);\\nC=(6,-6);\\nD=(6,-22);\\nE=(0,-16);\\nF=(12,-16);\\nM=(2D+E)/3;\\nN=(5D+F)/6;\\nP=(2C+B)/3;\\nQ=(2A+C)/3;\\n\\ndraw(A--B--C--A--E--D--F--B--C--D);\\ndraw(M--N--P--Q--M, dashed);\\nlabel(\\\"$A$\\\", A, NW);\\nlabel(\\\"$B$\\\", B, NE);\\nlabel(\\\"$C$\\\", C, dir(90));\\nlabel(\\\"$D$\\\", D, S);\\nlabel(\\\"$E$\\\", E, SW);\\nlabel(\\\"$F$\\\", F, SE);\\nlabel(\\\"$M$\\\", M, SW);\\nlabel(\\\"$N$\\\", N, SE);\\nlabel(\\\"$P$\\\", P, SE);\\nlabel(\\\"$Q$\\\", Q, W);\\nlabel(\\\"12\\\", (A+B)/2, dir(90));\\nlabel(\\\"16\\\", (B+F)/2, dir(0));\\n[/asy]\",\"type\":\"Geometry\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}