{"id":"aqua_rat:a87b300ad50798ab6a5958bce13eefc3","source_id":"aqua_rat","source_item_id":"a87b300ad50798ab6a5958bce13eefc3","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":"A rectangular piece of 150 sq m has a length which is 1m more than the 4 times the breadth. What is the perimeter of the piece?","stimulus":"","stimulus_html":null,"stem_html":"<p>A rectangular piece of 150 sq m has a length which is 1m more than the 4 times the breadth. What is the perimeter of the piece?</p>","rationale_html":"<p>Let its breadth be = x m.</p><p>So length will be = (4x+1) m.</p><p>Now,</p><p>x * (4x+1) = 150</p><p>or, 4x^2+x-150 = 0</p><p>or, (4x+25)(x-6) = 0</p><p>Either 4x = -25 or x = 6</p><p>As breadth can not take negetive value so x = 6</p><p>So its length is 4*6+1 = 25</p><p>So perimeter will be 2*(25+6)=62 mLet its breadth be = x m.</p><p>So length will be = (4x+1) m.</p><p>Now,</p><p>x * (4x+1) = 150</p><p>or, 4x^2+x-150 = 0</p><p>or, (4x+25)(x-6) = 0</p><p>Either 4x = -25 or x = 6</p><p>As breadth can not take negetive value so x = 6</p><p>So its length is 4*6+1 = 25</p><p>So perimeter will be 2*(25+6)=62 m</p><p>C</p>","correct_answer":["C"],"equiv_key":"9a438e4948e46460b5abed63","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>60 m</p>","ord":0},{"label":"B","content_html":"<p>61 m</p>","ord":1},{"label":"C","content_html":"<p>62 m</p>","ord":2},{"label":"D","content_html":"<p>63 m</p>","ord":3},{"label":"E","content_html":"<p>64 m</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":[]}