{"id":"aqua_rat:82aa052fa639e62872507978306e756f","source_id":"aqua_rat","source_item_id":"82aa052fa639e62872507978306e756f","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 n is such that 36 ≤ n ≤ 72, then x = (n2 + 2√n(n + 4) + 16) / (n+ 4√n+ 4) satisfies","stimulus":"","stimulus_html":null,"stem_html":"<p>If n is such that 36 ≤ n ≤ 72, then x = (n2 + 2√n(n + 4) + 16) / (n+ 4√n+ 4) satisfies</p>","rationale_html":"<p>36 ≤ n ≤ 72</p><p>x = (n2 + 2√n(n + 4) + 16) / (n+ 4√n+ 4)</p><p>Put x = 36,</p><p>x = (362 + 2√36(36 + 4) + 16) / (36+ 4√36+ 4)</p><p>i.e which is least value for n = 28.</p><p>D</p>","correct_answer":["D"],"equiv_key":"684037a5e618a73d46d808a0","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>20 &lt; x &lt; 54</p>","ord":0},{"label":"B","content_html":"<p>23 &lt; x &lt; 58</p>","ord":1},{"label":"C","content_html":"<p>25 &lt; x &lt; 64</p>","ord":2},{"label":"D","content_html":"<p>28 &lt; x &lt; 60</p>","ord":3},{"label":"E","content_html":"<p>None of these</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":[]}