{"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":"8c9c1983-f03e-5142-8362-46e30fd41ddd","task_key":"geometry--test--8c9c1983-f03e-5142-8362-46e30fd41ddd","task_revision_id":"1","upstream_id":"","short_description":"Let $ABCD$ be a parallelogram. We have that $M$ is the midpoint of $AB$ and $N$…","config":"geometry","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"Let $ABCD$ be a parallelogram. We have that $M$ is the midpoint of $AB$ and $N$ is the midpoint of $BC.$ The segments $DM$ and $DN$ intersect $AC$ at $P$ and $Q$, respectively. If $AC = 15,$ what is $QA$? [asy]\\npair A, B, C, D, pM, pN, O, P, Q;\\nA = (25, 0) * dir(-20);\\nB = (15, 0) * dir(60);\\nC = (25, 0) * dir(160);\\nD = (15, 0) * dir(-120);\\npM = 0.5 * A + 0.5 * B;\\npN = 0.5 * B + 0.5 * C;\\nO = 0.25 * A + 0.25 * B + 0.25 * C + 0.25 * D;\\nP = 0.33 * C + 0.67 * A;\\nQ = 0.67 * C + 0.33 * A;\\ndraw(A--B--C--D--cycle);\\ndraw(A--C);\\ndraw(pM--D);\\ndraw(pN--D);\\nlabel(\\\"$A$\\\", A, S);\\nlabel(\\\"$B$\\\", B, NE);\\nlabel(\\\"$C$\\\", C, NW);\\nlabel(\\\"$D$\\\", D, S);\\nlabel(\\\"$M$\\\", pM, NE);\\nlabel(\\\"$N$\\\", pN, NW);\\nlabel(\\\"$P$\\\", P, N);\\nlabel(\\\"$Q$\\\", Q, NE);\\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":[]}