{"id":"aqua_rat:90ebc3b7dfa00a1d86e961a1a05deb7d","source_id":"aqua_rat","source_item_id":"90ebc3b7dfa00a1d86e961a1a05deb7d","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":"Decipher the following multiplication table: M A D B E ------------- M A D R A E ------------- A M I D","stimulus":"","stimulus_html":null,"stem_html":"<p>Decipher the following multiplication table:</p><p>M A D</p><p>B E</p><p>-------------</p><p>M A D</p><p>R A E</p><p>-------------</p><p>A M I D</p>","rationale_html":"<p>It is clear that E = 1 as MAD×E=MAD</p><p>From the hundred&#x27;s line, M + A = 10 + M or 1 + M + A = 10 + M</p><p>As A = 10 not possible, A = 9</p><p>So I = 0.</p><p>and From the thousand&#x27;s line R + 1 = A. So R = 8.</p><p>M 9 D</p><p>B 1</p><p>-------------</p><p>M 9 D</p><p>8 9 1</p><p>-------------</p><p>9 M 0 D</p><p>-------------</p><p>As B×D = 1, B and D takes 3, 7 in some order.</p><p>If B = 7 and D = 3, then M93×7 = _51 is not satisfied. So B = 3 and D = 7.</p><p>2 9 7</p><p>3 1</p><p>-------------</p><p>2 9 7</p><p>8 9 1</p><p>-------------</p><p>9 2 0 7</p><p>-------------</p><p>D</p>","correct_answer":["D"],"equiv_key":"a0a9399ea8fd08e183de466d","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>9 2 0 0</p>","ord":0},{"label":"B","content_html":"<p>9 2 0 9</p>","ord":1},{"label":"C","content_html":"<p>9 2 0 1</p>","ord":2},{"label":"D","content_html":"<p>9 2 0 7</p>","ord":3},{"label":"E","content_html":"<p>9 2 2 2</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":[]}