{"id":"aqua_rat:126680bb290ba1d557f23e2df8d61b38","source_id":"aqua_rat","source_item_id":"126680bb290ba1d557f23e2df8d61b38","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 box contains a certain number of balls, marked successively from 1 to n. If there are 45 different ways that two balls can be selected from the box such that the ball with number 3 marked on it is not selected, then what is the value of n?","stimulus":"","stimulus_html":null,"stem_html":"<p>A box contains a certain number of balls, marked successively from 1 to n. If there are 45 different ways that two balls can be selected from the box such that the ball with number 3 marked on it is not selected, then what is the value of n?</p>","rationale_html":"<p>(n-1)C2=45</p><p>n-1=10</p><p>n=11</p><p>The answer is A.</p>","correct_answer":["A"],"equiv_key":"5b1aeca7874d52ee02fdf4d8","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>11</p>","ord":0},{"label":"B","content_html":"<p>10</p>","ord":1},{"label":"C","content_html":"<p>9</p>","ord":2},{"label":"D","content_html":"<p>8</p>","ord":3},{"label":"E","content_html":"<p>7</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":[]}