{"id":"cb_question_bank:1687b1d5-49f4-41bd-907e-cc3d881103fb","source_id":"cb_question_bank","source_item_id":"1687b1d5-49f4-41bd-907e-cc3d881103fb","external_id":"295c177c-ee26-49e1-8364-8c9b6677b31a","ibn":null,"question_id":"3726e079","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":"M","score_band":5,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If StartFraction x Over y EndFraction equals 4 and StartFraction 24 x Over n y EndFraction equals 4 , what is the value of n ?","stimulus":"","stimulus_html":null,"stem_html":"<p>If <math alttext=\"StartFraction x Over y EndFraction equals 4\"><mrow>\n\t<mrow>\n\t\t<mfrac>\n\t\t\t<mi>x</mi>\n\t\t\t<mi>y</mi>\n\t\t</mfrac>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>4</mn>\n</mrow>\n</math> and <math alttext=\"StartFraction 24 x Over n y EndFraction equals 4\"><mrow>\n\t<mrow>\n\t\t<mfrac>\n\t\t\t<mrow>\n\t\t\t\t<mn>24</mn>\n\t\t\t\t<mi>x</mi>\n\t\t\t</mrow>\n\t\t\t<mrow>\n\t\t\t\t<mi>n</mi>\n\t\t\t\t<mi>y</mi>\n\t\t\t</mrow>\n\t\t</mfrac>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>4</mn>\n</mrow>\n</math>, what is the value of <math alttext=\"n\"><mi>n</mi>\n</math>?</p>","rationale_html":"<p>The correct answer is <math alttext=\"24\"><mn>24</mn>\n</math>. The equation <math alttext=\"StartFraction 24 x Over n y EndFraction equals 4\"><mfrac><mrow><mn>24</mn><mi>x</mi></mrow><mrow><mi>n</mi><mi>y</mi></mrow></mfrac><mo>=</mo><mn>4</mn></math>&nbsp;can be rewritten as <math alttext=\"left parenthesis StartFraction 24 Over n EndFraction right parenthesis left parenthesis StartFraction x Over y EndFraction right parenthesis equals 4\"><mfenced><mfrac><mn>24</mn><mi>n</mi></mfrac></mfenced><mfenced><mfrac><mi>x</mi><mi>y</mi></mfrac></mfenced><mo>=</mo><mn>4</mn></math>. It's given that <math alttext=\"StartFraction x Over y EndFraction equals 4\"><mrow>\n\t<mfrac>\n\t\t\t<mi>x</mi>\n\t\t\t<mi>y</mi>\n\t\t</mfrac>\n\t<mo>=</mo>\n\t<mn>4</mn>\n</mrow>\n</math>. Substituting <math alttext=\"4\"><mn>4</mn>\n</math> for <math alttext=\"StartFraction x Over y EndFraction\"><mfrac>\n\t\t<mi>x</mi>\n\t\t<mi>y</mi>\n\t</mfrac>\n</math> in the equation <math alttext=\"left parenthesis StartFraction 24 Over n EndFraction right parenthesis left parenthesis StartFraction x Over y EndFraction right parenthesis equals 4\"><mfenced><mfrac><mn>24</mn><mi>n</mi></mfrac></mfenced><mfenced><mfrac><mi>x</mi><mi>y</mi></mfrac></mfenced><mo>=</mo><mn>4</mn></math> yields <math alttext=\"left parenthesis StartFraction 24 Over n EndFraction right parenthesis left parenthesis 4 right parenthesis equals 4\"><mfenced><mfrac><mn>24</mn><mi>n</mi></mfrac></mfenced><mfenced><mn>4</mn></mfenced><mo>=</mo><mn>4</mn></math>. Multiplying both sides of this equation by <math alttext=\"n\"><mi>n</mi>\n</math> yields <math alttext=\"left parenthesis 24 right parenthesis left parenthesis 4 right parenthesis equals 4 n\"><mfenced><mn>24</mn></mfenced><mfenced><mn>4</mn></mfenced><mo>=</mo><mn>4</mn><mi>n</mi></math>. Dividing both sides of this equation by <math alttext=\"4\"><mn>4</mn>\n</math> yields <math alttext=\"24 equals n\"><mrow>\n\t<mn>24</mn>\n\t<mo>=</mo>\n\t<mi>n</mi>\n</mrow>\n</math>. Therefore, the value of <math alttext=\"n\"><mi>n</mi>\n</math> is <math alttext=\"24\"><mn>24</mn>\n</math>.</p>","correct_answer":["24"],"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}}