{"id":"cb_question_bank:84ec27da-3dc6-438f-96c5-4186421a7722","source_id":"cb_question_bank","source_item_id":"84ec27da-3dc6-438f-96c5-4186421a7722","external_id":"0de0c801-a394-401e-86d9-293cbb485a91","ibn":null,"question_id":"29ed5d39","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"p equals 20 plus StartFraction 16 Over n EndFraction The given equation relates the numbers p and n , where n is not equal to 0 and p greater than 20 . Which equation correctly expresses n in terms of p ?","stimulus":"","stimulus_html":null,"stem_html":"

\n\tp\n\t=\n\t\n\t\t20\n\t\t+\n\t\t\n\t\t\t\n\t\t\t\t16\n\t\t\t\tn\n\t\t\t\n\t\t\n\t\n\n

\n

The given equation relates the numbers p\n and n\n, where n\n is not equal to 0\n and p>20. Which equation correctly expresses n\n in terms of p\n?

","rationale_html":"

Choice D is correct. To express n\n in terms of p\n, the given equation must be solved for n\n. Subtracting 9\n from both sides of the given equation yields p-9=14n. Since n\n is not equal to 0\n, multiplying both sides of this equation by n\n yields p-9n=14. It's given that p>9, which means \n\tp\n\t-\n\t9\n\n is not equal to 0\n. Therefore, dividing both sides of p-9n=14 by p-9 yields p-9np-9=14p-9, or n=14p-9.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.824000+00:00","source_updated_at":"2023-08-02T20:25:59.824000+00:00","options":[{"label":"A","content_html":"

n=p-2016

","ord":0},{"label":"B","content_html":"

\n\tn\n\t=\n\t\n\t\t\n\t\t\t\n\t\t\t\tp\n\t\t\t\t16\n\t\t\t\n\t\t\n\t\t+\n\t\t20\n\t\n\n

","ord":1},{"label":"C","content_html":"

\n\tn\n\t=\n\t\n\t\t\n\t\t\t\n\t\t\t\tp\n\t\t\t\t16\n\t\t\t\n\t\t\n\t\t-\n\t\t20\n\t\n\n

","ord":2},{"label":"D","content_html":"

\n\tn\n\t=\n\t\n\t\t\n\t\t\t16\n\t\t\t\n\t\t\t\tp\n\t\t\t\t-\n\t\t\t\t20\n\t\t\t\n\t\t\n\t\n\n

","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}}