{"id":"cb_question_bank:cbe6a927-5e13-486e-832f-0dc0d04b6dea","source_id":"cb_question_bank","source_item_id":"cbe6a927-5e13-486e-832f-0dc0d04b6dea","external_id":"62b8544c-e4cc-4953-8687-0729c0554f61","ibn":null,"question_id":"0aaef7aa","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The function p is defined by p left parenthesis n right parenthesis equals 7 n cubed . What is the value of n when p left parenthesis n right parenthesis is equal to 56 ?","stimulus":"","stimulus_html":null,"stem_html":"<p>The function <math alttext=\"p\"><mi>p</mi>\n</math> is defined by <math alttext=\"p left parenthesis n right parenthesis equals 7 n cubed\"><mi>p</mi><mfenced><mi>n</mi></mfenced><mo>=</mo><mrow><mn>7</mn></mrow><msup><mi>n</mi><mrow><mn>3</mn></mrow></msup></math>. What is the value of <math alttext=\"n\"><mi>n</mi>\n</math> when <math alttext=\"p left parenthesis n right parenthesis\"><mi>p</mi><mo>(</mo><mi>n</mi><mo>)</mo></math> is equal to <math alttext=\"56\"><mn>56</mn>\n</math>?</p>","rationale_html":"<p>Choice A is correct. It's given that <math alttext=\"p left parenthesis n right parenthesis equals 7 n cubed\"><mi>p</mi><mfenced><mi>n</mi></mfenced><mo>=</mo><mn>7</mn><msup><mi>n</mi><mn>3</mn></msup></math>. Substituting <math alttext=\"56\"><mn>56</mn>\n</math> for <math alttext=\"p left parenthesis n right parenthesis\"><mi>p</mi><mfenced><mi>n</mi></mfenced></math> in this equation yields <math alttext=\"56 equals 7 n cubed\"><mn>56</mn><mo>=</mo><mn>7</mn><msup><mi>n</mi><mn>3</mn></msup></math>. Dividing each side of this equation by <math alttext=\"7\"><mn>7</mn>\n</math> yields <math alttext=\"8 equals n cubed\"><mn>8</mn><mo>=</mo><msup><mi>n</mi><mn>3</mn></msup></math>. Taking the cube root of each side of this equation yields <math alttext=\"2 equals n\"><mn>2</mn><mo>=</mo><mi>n</mi></math>. Therefore, when <math alttext=\"p left parenthesis n right parenthesis\"><mi>p</mi><mfenced><mi>n</mi></mfenced></math> is equal to <math alttext=\"56\"><mn>56</mn>\n</math>, the value of <math alttext=\"n\"><mi>n</mi>\n</math> is <math alttext=\"2\"><mn>2</mn>\n</math>.</p>\n<p>Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.829000+00:00","source_updated_at":"2023-08-02T20:25:59.829000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"2\"><mn>2</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"eight thirds\"><mfrac>\n\t<mn>8</mn>\n\t<mn>3</mn>\n</mfrac>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"7\"><mn>7</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"8\"><mn>8</mn>\n</math></p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}