{"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":"0f51e674-0d77-55f0-9317-7b491bdd8cef","task_key":"precalculus--test--0f51e674-0d77-55f0-9317-7b491bdd8cef","task_revision_id":"1","upstream_id":"","short_description":"Let $$P(x)=24x^{24}+\\sum_{j=1}^{23}(24-j)\\left(x^{24-j}+x^{24+j}\\right).$$Let…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let $$P(x)=24x^{24}+\\\\sum_{j=1}^{23}(24-j)\\\\left(x^{24-j}+x^{24+j}\\\\right).$$Let $z_1, z_2, \\\\ldots, z_r$ be the distinct zeros of $P(x)$, and let $z_k^2=a_k+b_{k}i$ for $k=1, 2, \\\\ldots, r$, where $i=\\\\sqrt{-1}$, and $a_k$ and $b_k$ are real numbers. Find\\n\\\\[\\\\sum_{k=1}^{r}|b_k|.\\\\]\",\"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":[]}