{"id":"aqua_rat:80227a91260edf28f31d88b6a31d5c03","source_id":"aqua_rat","source_item_id":"80227a91260edf28f31d88b6a31d5c03","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":"The sum of the 5 consecutive two digit odd numbers when divided by 10 becomes a perfect square, which of the following can be one of these 5 numbers?","stimulus":"","stimulus_html":null,"stem_html":"<p>The sum of the 5 consecutive two digit odd numbers when divided by 10 becomes a perfect square, which of the following can be one of these 5 numbers?</p>","rationale_html":"<p>perfect square:- 1,4,9,16,25,36</p><p>sum=square*10=10,40,90,160,250,360</p><p>sum of 4 odd consecutive numbers is multiple of 4</p><p>so the only number left are 40,160,360</p><p>sum/4=40/4=10 is not possible</p><p>sum/4=360/4=90 is not possible</p><p>sum/4=160/4=40 is the only option available i.e 41</p><p>C</p>","correct_answer":["C"],"equiv_key":"7e237079a6b1e67daa9856c4","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>47</p>","ord":0},{"label":"B","content_html":"<p>91</p>","ord":1},{"label":"C","content_html":"<p>41</p>","ord":2},{"label":"D","content_html":"<p>67</p>","ord":3},{"label":"E","content_html":"<p>44</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":[]}