{"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":"83620697-45dd-5f01-880f-2f1c8f464708","task_key":"geometry--test--83620697-45dd-5f01-880f-2f1c8f464708","task_revision_id":"1","upstream_id":"","short_description":"In the diagram, points $X$, $Y$ and $Z$ are on the sides of $\\triangle UVW$, as…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"In the diagram, points $X$, $Y$ and $Z$ are on the sides of $\\\\triangle UVW$, as shown.  Line segments $UY$, $VZ$ and $WX$ intersect at $P$.  Point $Y$ is on $VW$ such that $VY:YW=4:3$. If $\\\\triangle PYW$ has an area of 30 and $\\\\triangle PZW$ has an area of 35, determine the area of $\\\\triangle UXP$. [asy]\\nsize(6cm);\\npair v = (0, 0); pair w = (10, 0); pair u = (3.5, 7);\\npair y = 4 * w / 7;\\npair x = 56 * u / 140;\\npair p = IP(w--x, u--y);\\npair z = IP(v--(10 * p), u--w);\\ndraw(u--v--w--cycle);\\ndraw(u--y);draw(x--w);draw(z--v);\\n\\nlabel(\\\"$U$\\\", u, N);\\nlabel(\\\"$X$\\\", x, NW);\\nlabel(\\\"$P$\\\", p, NE + 0.2 * W);\\nlabel(\\\"$Z$\\\", z, NE);\\nlabel(\\\"$V$\\\", v, SW);\\nlabel(\\\"$Y$\\\", y, S);\\nlabel(\\\"$W$\\\", w, SE);/*\\nlabel(\\\"$a$\\\", centroid(p, v, y), fontsize(10));\\nlabel(\\\"$b$\\\", centroid(p, z, u), fontsize(10));\\nlabel(\\\"$c$\\\", centroid(p, u, x), fontsize(10));\\nlabel(\\\"$d$\\\", centroid(p, x, v), fontsize(10));\\nlabel(\\\"$30$\\\", centroid(p, y, w) + 0.2 * W, fontsize(10));\\nlabel(\\\"$35$\\\", centroid(p, z, w), fontsize(10));*/\\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":[]}