{"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":"9c6bae9e-2bff-5f9a-a80e-4fed6ed61df5","task_key":"precalculus--test--9c6bae9e-2bff-5f9a-a80e-4fed6ed61df5","task_revision_id":"1","upstream_id":"","short_description":"Let $a,$ $b,$ $c,$ $p,$ $q,$ and $r$ be real numbers such that","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Let $a,$ $b,$ $c,$ $p,$ $q,$ and $r$ be real numbers such that\\n\\\\[\\\\begin{vmatrix} p & b & c \\\\\\\\ a & q & c \\\\\\\\ a & b & r \\\\end{vmatrix} = 0.\\\\]Assuming that $a \\\\neq p,$ $b \\\\neq q,$ and $c \\\\neq r,$ find the value of $\\\\frac{p}{p - a} + \\\\frac{q}{q - b} + \\\\frac{r}{r - c}.$\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}