{"id":"aqua_rat:3470a940a8da5ec31b1b69cb61ed9455","source_id":"aqua_rat","source_item_id":"3470a940a8da5ec31b1b69cb61ed9455","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 3rd and 15th elements of an arithmetic progression is equal to the sum of the 6th, 11th and 13th elements of the same progression. Then, which element of the series should necessarily be equal to zero ?","stimulus":"","stimulus_html":null,"stem_html":"<p>The sum of 3rd and 15th elements of an arithmetic progression is equal to the sum of the 6th, 11th and 13th elements of the same progression. Then, which element of the series should necessarily be equal to zero ?</p>","rationale_html":"<p>Let the 1st term be ‘a’ and common difference be ‘d’</p><p>then we have 3rd term = a + 2d</p><p>15th term = a + 14d</p><p>6th term = a + 5d</p><p>11th term = a + 10d</p><p>13th term = a + 12d</p><p>Since sum of 3rd and 15th term = sum of 6th, 11th and 13th term, therefore we have</p><p>=&gt; 2a + 16d = 3a + 27d</p><p>=&gt; a + 11d = 0 i.e the 12th term.</p><p>C</p>","correct_answer":["C"],"equiv_key":"0d21aae10d4122a9a58ed611","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>1st</p>","ord":0},{"label":"B","content_html":"<p>9th</p>","ord":1},{"label":"C","content_html":"<p>12th</p>","ord":2},{"label":"D","content_html":"<p>None of these</p>","ord":3},{"label":"E","content_html":"<p>Cannot be determined</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":[]}