{"id":"aqua_rat:31a9d05da7ffeddc4a28a5f294b365fb","source_id":"aqua_rat","source_item_id":"31a9d05da7ffeddc4a28a5f294b365fb","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":"M = abc is a three digit number and N = cba, if M > N and M - N + 396c = 990. Then how many values of M are more than 300.","stimulus":"","stimulus_html":null,"stem_html":"<p>M = abc is a three digit number and N = cba, if M &gt; N and M - N + 396c = 990. Then how many values of M are more than 300.</p>","rationale_html":"<p>From the given data,</p><p>abc – cba + 396c = 990</p><p>100a + 10b + c – (100c + 10b + a) + 396c = 990</p><p>99a – 99c + 396c = 990</p><p>Observe that each term is divisible by 99. So on dividing the above expression by 99, we get</p><p>a – c + 4c = 10</p><p>a + 3c = 10</p><p>For c = 1, a = 7</p><p>c = 2, a = 4</p><p>c = 3, a = 1</p><p>&#x27;b&#x27; can take any value from 0 to 9</p><p>We have to find the value of M more than 300. So minimum value of &#x27;a&#x27; should be 4.</p><p>So total possibilities are 402, 412, ...., 492 = 10 values</p><p>701, 711, ....., 791 = 10 values</p><p>So total values = 20.</p><p>Correct option: A</p>","correct_answer":["A"],"equiv_key":"df6b1815bfc5f9abebe6e999","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>20</p>","ord":0},{"label":"B","content_html":"<p>30</p>","ord":1},{"label":"C","content_html":"<p>40</p>","ord":2},{"label":"D","content_html":"<p>200</p>","ord":3},{"label":"E","content_html":"<p>None</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":[]}