{"id":"aqua_rat:bb25027e75ec582f6f3ec7b4d0aa49f6","source_id":"aqua_rat","source_item_id":"bb25027e75ec582f6f3ec7b4d0aa49f6","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 k consecutive integers is 51. If the least integer is -50, then k =","stimulus":"","stimulus_html":null,"stem_html":"<p>The sum of k consecutive integers is 51. If the least integer is -50, then k =</p>","rationale_html":"<p>The difference is consistent with each integers , therefore the series can be A.P.</p><p>Sum of A.P. = A + (N-1) D</p><p>A=First term</p><p>D=Difference between each integer</p><p>N=number of terms</p><p>Sum = A + (N - 1 ) D</p><p>51= -50 + N - 1</p><p>N = 102</p><p>Answer = E</p>","correct_answer":["E"],"equiv_key":"f60611e378ac38d703958839","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>40</p>","ord":0},{"label":"B","content_html":"<p>62</p>","ord":1},{"label":"C","content_html":"<p>82</p>","ord":2},{"label":"D","content_html":"<p>92</p>","ord":3},{"label":"E","content_html":"<p>102</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":[]}