{"id":"aqua_rat:ba069f960a28404b961aa01f969112c1","source_id":"aqua_rat","source_item_id":"ba069f960a28404b961aa01f969112c1","external_id":null,"program":null,"section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":null,"scored":true,"layout_warning":null,"stem":"A password to a certain database consists of digits that cannot be repeated. If the password is known to consist of at least 8 digits and it takes 12 seconds to try one combination, what is the amount of time, in minutes, necessary to guarantee access to database?","stimulus":"","stimulus_html":null,"stem_html":"<p>A password to a certain database consists of digits that cannot be repeated. If the password is known to consist of at least 8 digits and it takes 12 seconds to try one combination, what is the amount of time, in minutes, necessary to guarantee access to database?</p>","rationale_html":"<p>Total # of passwords possible for 8 digits is P810=10!2</p><p>Total # of passwords possible for 9 digits is P910=10!</p><p>Total # of passwords possible for 10 digits is P1010=10!</p><p>Time needed to guarantee access to database is (10!2+10!+10!)∗15=10!2 minutes.</p><p>D.</p>","correct_answer":["D"],"equiv_key":"eadef89b8178f330c00822a8","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>8!/5</p>","ord":0},{"label":"B","content_html":"<p>8!/2</p>","ord":1},{"label":"C","content_html":"<p>8!</p>","ord":2},{"label":"D","content_html":"<p>10!/2</p>","ord":3},{"label":"E","content_html":"<p>5/2.10!</p>","ord":4}],"passage":null,"attribution":{"source_id":"aqua_rat","source_name":"AQuA-RAT algebra word problems with rationales","rights_holder":"Google DeepMind and the AQuA-RAT contributors","canonical_url":"https://github.com/google-deepmind/AQuA","retrieved_from":"https://raw.githubusercontent.com/google-deepmind/AQuA/master/","attribution":"Algebra word problems from the AQuA-RAT dataset (Ling et al., 2017), published by Google DeepMind under the Apache License 2.0.","disclaimer":"AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.","license":"Apache License 2.0. Crowdsourced by DeepMind and published for free use, including commercially.","redistributable":true,"item_count":508},"equivalents":[]}