{"id":"aqua_rat:4c0c436ddb1f75f57ad3d8cdf1eb0acb","source_id":"aqua_rat","source_item_id":"4c0c436ddb1f75f57ad3d8cdf1eb0acb","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":"If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 3?","stimulus":"","stimulus_html":null,"stem_html":"<p>If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 3?</p>","rationale_html":"<p>16 = ky+3</p><p>since -- &gt; 0 &lt;=remainder &lt; divisor</p><p>therefore y&gt;1</p><p>ky=13 =&gt; y =13/k :- possible values of k for y to be +int y=1,13</p><p>hence, sum = 14</p>","correct_answer":["A"],"equiv_key":"dd877e6fe739f9dfcaa00fb4","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>14</p>","ord":0},{"label":"B","content_html":"<p>9</p>","ord":1},{"label":"C","content_html":"<p>16</p>","ord":2},{"label":"D","content_html":"<p>23</p>","ord":3},{"label":"E","content_html":"<p>24</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":[]}