{"id":"aqua_rat:ac47f04643e657ffc2766f7bc36af70e","source_id":"aqua_rat","source_item_id":"ac47f04643e657ffc2766f7bc36af70e","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":"How many ways A boy can reach the top of stairs which contain 10 steps, when he can take either one or two steps every time?","stimulus":"","stimulus_html":null,"stem_html":"<p>How many ways A boy can reach the top of stairs which contain 10 steps, when he can take either one or two steps every time?</p>","rationale_html":"<p>case 1:1 1 1 1 1 1 1 1 1 1 &gt; 1!</p><p>case 2:1 1 1 1 1 1 1 1 2 &gt; 9!/8!</p><p>case 3:1 1 1 1 1 1 2 2 &gt; 8!/6!*2!</p><p>case 4:1 1 1 1 2 2 2 &gt; 7!/4!*3!</p><p>case 5:1 1 2 2 2 2 &gt; 6!/4!*2!</p><p>case 6:2 2 2 2 2 &gt; 1!</p><p>add answers of all cases =&gt; 1+9+28+35+15+1= 89</p><p>B</p>","correct_answer":["B"],"equiv_key":"5938151f3f347cae26f81860","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>88</p>","ord":0},{"label":"B","content_html":"<p>89</p>","ord":1},{"label":"C","content_html":"<p>90</p>","ord":2},{"label":"D","content_html":"<p>91</p>","ord":3},{"label":"E","content_html":"<p>92</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":[]}