{"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":"c534e197-394a-5e09-bee6-02362bb3dca5","task_key":"intermediate~5falgebra--test--c534e197-394a-5e09-bee6-02362bb3dca5","task_revision_id":"1","upstream_id":"","short_description":"The sequence 1, 2, 4, 5, 10, 11, 22, 23, 46, 47, $\\dots$ is formed as follows:","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"The sequence 1, 2, 4, 5, 10, 11, 22, 23, 46, 47, $\\\\dots$ is formed as follows:\\n\\n$\\\\bullet$ Start with the number 1.\\n\\n$\\\\bullet$ Add one to get 2.\\n\\n$\\\\bullet$ Double that to get 4.\\n\\n$\\\\bullet$ Add one to get 5.\\n\\n$\\\\bullet$ Double that to get 10, and so on.\\n\\nWe repeat the steps of \\\"add one\\\" and \\\"double that\\\", alternating between them.\\n\\nThe 100th term will be of the form $3 \\\\cdot 2^k - 1.$  Compute $k.$\",\"type\":\"Intermediate Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}