{"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":"18e68315-0399-5873-831b-1f8de4ef3621","task_key":"geometry--test--18e68315-0399-5873-831b-1f8de4ef3621","task_revision_id":"1","upstream_id":"","short_description":"In the diagram, $R$ is on $QS$ and $QR=8$. Also, $PR=12$, $\\angle…","config":"geometry","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"In the diagram, $R$ is on $QS$ and $QR=8$. Also, $PR=12$, $\\\\angle PRQ=120^\\\\circ$, and $\\\\angle RPS = 90^\\\\circ$. What is the area of $\\\\triangle QPS$? [asy]\\n//C19\\nsize(10cm); // ADJUST\\nimport olympiad;\\n\\n// Point coordinates\\npair r = (0, 0);\\npair q = (-8, 0);\\npair p = 12 * dir(60);\\npair s = (24, 0);\\n\\n// draw lines\\ndraw(p--s--r--p--q--r);\\n\\n// labels\\nlabel(\\\"$R$\\\", r, S);\\nlabel(\\\"$Q$\\\", q, SW);\\nlabel(\\\"$S$\\\", s, SE);\\nlabel(\\\"$P$\\\", p, N);\\nlabel(\\\"$12$\\\", r + (p - r) / 2, SE);\\nlabel(\\\"$8$\\\", r + (q - r) / 2, S);\\nlabel(\\\"$120^\\\\circ$\\\", r, NW + 0.2 * E);\\n\\nmarkscalefactor = 0.08;\\ndraw(rightanglemark(r, p, s));\\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":[]}