{"id":"cb_question_bank:60024e72-b40e-4cee-aa74-a421a61a5e79","source_id":"cb_question_bank","source_item_id":"60024e72-b40e-4cee-aa74-a421a61a5e79","external_id":"837ca3a4-1a14-44b1-84b5-5f2a706e30f9","ibn":null,"question_id":"8637294f","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.A.","skill":"Ratios, rates, proportional relationships, and units","difficulty":"H","score_band":7,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If StartFraction 4 a Over b EndFraction equals 6.7 and StartFraction a Over b n EndFraction equals 26.8 , what is the value of n ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">If <math alttext=\"StartFraction 4 a Over b EndFraction equals 6.7\"><mrow>\n\t<mrow>\n\t\t<mfrac>\n\t\t\t<mrow>\n\t\t\t\t<mn>4</mn>\n\t\t\t\t<mi>a</mi>\n\t\t\t</mrow>\n\t\t\t<mi>b</mi>\n\t\t</mfrac>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>6.7</mn>\n</mrow>\n</math> and <math alttext=\"StartFraction a Over b n EndFraction equals 26.8\"><mrow>\n\t<mrow>\n\t\t<mfrac>\n\t\t\t<mi>a</mi>\n\t\t\t<mrow>\n\t\t\t\t<mi>b</mi>\n\t\t\t\t<mi>n</mi>\n\t\t\t</mrow>\n\t\t</mfrac>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>26.8</mn>\n</mrow>\n</math>, what is the value of <math alttext=\"n\"><mi>n</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\".0625\"><mo>.0625</mo></math>. It's given that <math alttext=\"StartFraction 4 a Over b EndFraction equals 6.7\"><mfrac><mrow><mn>4</mn><mi>a</mi></mrow><mi>b</mi></mfrac><mo>=</mo><mn>6.7</mn></math> and <math alttext=\"StartFraction a Over b n EndFraction equals 26.8\"><mfrac><mi>a</mi><mrow><mi>b</mi><mi>n</mi></mrow></mfrac><mo>=</mo><mn>26.8</mn></math>. The equation <math alttext=\"StartFraction 4 a Over b EndFraction equals 6.7\"><mfrac><mrow><mn>4</mn><mi>a</mi></mrow><mi>b</mi></mfrac><mo>=</mo><mn>6.7</mn></math> can be rewritten as <math alttext=\"left parenthesis 4 right parenthesis left parenthesis StartFraction a Over b EndFraction right parenthesis equals 6.7\"><mfenced><mn>4</mn></mfenced><mfenced><mfrac><mi>a</mi><mi>b</mi></mfrac></mfenced><mo>=</mo><mn>6.7</mn></math>. Dividing both sides of this equation by <math alttext=\"4\"><mn>4</mn>\n</math> yields <math alttext=\"StartFraction a Over b EndFraction equals 1.675\"><mfrac><mi>a</mi><mi>b</mi></mfrac><mo>=</mo><mn>1.675</mn></math>. The equation <math alttext=\"StartFraction a Over b n EndFraction equals 26.8\"><mfrac><mi>a</mi><mrow><mi>b</mi><mi>n</mi></mrow></mfrac><mo>=</mo><mn>26.8</mn></math> can be rewritten as&nbsp;<math alttext=\"left parenthesis StartFraction a Over b EndFraction right parenthesis left parenthesis StartFraction 1 Over n EndFraction right parenthesis equals 26.8\"><mfenced><mfrac><mi>a</mi><mi>b</mi></mfrac></mfenced><mfenced><mfrac><mn>1</mn><mi>n</mi></mfrac></mfenced><mo>=</mo><mn>26.8</mn></math>. Substituting&nbsp;<math alttext=\"1.675\"><mn>1.675</mn></math> for <math alttext=\"StartFraction a Over b EndFraction\"><mfrac><mi>a</mi><mi>b</mi></mfrac></math> in this equation yields <math alttext=\"left parenthesis 1.675 right parenthesis left parenthesis StartFraction 1 Over n EndFraction right parenthesis equals 26.8\"><mfenced><mn>1.675</mn></mfenced><mfenced><mfrac><mn>1</mn><mi>n</mi></mfrac></mfenced><mo>=</mo><mn>26.8</mn></math>, or <math alttext=\"StartFraction 1.675 Over n EndFraction equals 26.8\"><mfrac><mn>1.675</mn><mi>n</mi></mfrac><mo>=</mo><mn>26.8</mn></math>. Multiplying both sides of this equation by <math alttext=\"n\"><mi>n</mi>\n</math> yields <math alttext=\"1.675 equals 26.8 n\"><mn>1.675</mn><mo>=</mo><mn>26.8</mn><mi>n</mi></math>. Dividing both sides of this equation by&nbsp;<math alttext=\"26.8\"><mn>26.8</mn></math> yields <math alttext=\"n equals 0.0625\"><mi>n</mi><mo>=</mo><mn>0.0625</mn></math>. Therefore, the value of <math alttext=\"n\"><mi>n</mi>\n</math> is <math alttext=\"0.0625\"><mn>0.0625</mn></math>. Note that .0625, 0.062, 0.063, and 1/16 are examples of ways to enter a correct answer.</p>","correct_answer":[".0625","1/16"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.830000+00:00","source_updated_at":"2023-08-02T20:25:59.830000+00:00","options":[],"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}}