{"id":"aqua_rat:5df26735166695ef304c7d55759b3b70","source_id":"aqua_rat","source_item_id":"5df26735166695ef304c7d55759b3b70","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":"Two balls A and B rotate along a circular track. Ball A makes 2 full rotations in 26 minutes. Ball B makes 5 full rotation in 35 minutes. If they start rotating now from the same point, when will they be at the same starting point again?","stimulus":"","stimulus_html":null,"stem_html":"<p>Two balls A and B rotate along a circular track. Ball A makes 2 full rotations in 26 minutes. Ball B makes 5 full rotation in 35 minutes. If they start rotating now from the same point, when will they be at the same starting point again?</p>","rationale_html":"<p>If ball A makes 2 rotations in 26 minutes, it makes 1 rotation in 13 minutes. If ball B makes 5 rotations in 35 minutes, it makes 1 rotation in 7 minutes.</p><p>The two balls start rotating now and makes several rotations before they are at the SAME starting points. Ball A would have done a WHOLE number X of rotations and ball B would have done a WHOLE number Y of rotations. Also they would have rotated during the same period of time T. Hence</p><p>T = 13 X = 7 Y</p><p>Hence 13 X = 7 Y</p><p>Solve the above for X</p><p>X = 7 Y / 13</p><p>We want the time when they are FIRST at the same starting point. Therefore X and Y are the smallest whole numbers of the equation X = 7 Y / 13. The smallest value of Y that gives X as a whole number is 13. Hence</p><p>X = 7 (13) / 13 = 7</p><p>Time T is given by</p><p>T = 13 X = 13 * 7 = 91 minutes = 1 hour and 31 minutes</p><p>correct answer A</p>","correct_answer":["A"],"equiv_key":"7fe6d13d879bce0d22708071","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>1 hour and 31 minutes</p>","ord":0},{"label":"B","content_html":"<p>2 hour and 31 minutes</p>","ord":1},{"label":"C","content_html":"<p>3 hour and 31 minutes</p>","ord":2},{"label":"D","content_html":"<p>4 hour and 31 minutes</p>","ord":3},{"label":"E","content_html":"<p>5 hour and 31 minutes</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":[]}