{"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":"decf79fa-f016-5f0e-86b2-9a523b8b03dc","task_key":"geometry--test--decf79fa-f016-5f0e-86b2-9a523b8b03dc","task_revision_id":"1","upstream_id":"","short_description":"In rectangle $ABCD$, $AD=1$, $P$ is on $\\overline{AB}$, and $\\overline{DB}$ and…","config":"geometry","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"In rectangle $ABCD$, $AD=1$, $P$ is on $\\\\overline{AB}$, and $\\\\overline{DB}$ and $\\\\overline{DP}$ trisect $\\\\angle ADC$. Write the perimeter of $\\\\triangle BDP$ in simplest form as:  $w + \\\\frac{x \\\\cdot \\\\sqrt{y}}{z}$, where $w, x, y, z$ are nonnegative integers.  What is $w + x + y + z$?\\n\\n[asy]\\npair A,B,C,D,P;\\nA=(0,5);\\nB=(8,5);\\nC=(8,0);\\nD=(0,0);\\nP=(3,5);\\ndraw(A--B--C--D--cycle);\\ndraw(P--D--B);\\nlabel(\\\"$A$\\\",A,N);\\nlabel(\\\"$B$\\\",B,N);\\nlabel(\\\"$C$\\\",C,S);\\nlabel(\\\"$D$\\\",D,S);\\nlabel(\\\"$P$\\\",P,N);\\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":[]}