{"id":"cb_question_bank:bb8c34f4-a2e1-40a5-bbbd-9f916a94893c","source_id":"cb_question_bank","source_item_id":"bb8c34f4-a2e1-40a5-bbbd-9f916a94893c","external_id":"a441304f-3293-46ff-a2c2-cdbb915b8b11","ibn":null,"question_id":"2e92cc21","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.B.","skill":"Percentages","difficulty":"H","score_band":7,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The number a is 110 percent sign greater than the number b . The number b is 90 percent sign less than 47 . What is the value of a ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The number <math alttext=\"a\"><mi>a</mi>\n</math> is <math alttext=\"110 percent sign\"><mrow><mn>110</mn></mrow><mo>%</mo></math> greater than the number <math alttext=\"b\"><mi>b</mi>\n</math>. The number <math alttext=\"b\"><mi>b</mi>\n</math> is <math alttext=\"90 percent sign\"><mrow><mn>90</mn></mrow><mo>%</mo></math> less than <math alttext=\"47\"><mn>47</mn>\n</math>. What is the value of <math alttext=\"a\"><mi>a</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"9.87\"><mn>9.87</mn>\n</math>. It’s given that the number <math alttext=\"a\"><mi>a</mi>\n</math> is <math alttext=\"110 percent sign\"><mn>110</mn><mo>%</mo></math> greater than the number <math alttext=\"b\"><mi>b</mi>\n</math>. It follows that <math alttext=\"a equals left parenthesis 1 plus StartFraction 110 Over 100 EndFraction right parenthesis b\"><mi>a</mi><mo>=</mo><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mn>110</mn><mn>100</mn></mfrac></mrow></mfenced><mi>b</mi></math>, or <math alttext=\"a equals 2.1 b\"><mrow>\n\t<mi>a</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>2.1</mn>\n\t\t<mi>b</mi>\n\t</mrow>\n</mrow>\n</math>. It’s also given that the number <math alttext=\"b\"><mi>b</mi>\n</math> is <math alttext=\"90 percent sign\"><mn>90</mn><mo>%</mo></math> less than <math alttext=\"47\"><mn>47</mn>\n</math>. It follows that <math alttext=\"b equals left parenthesis 1 minus StartFraction 90 Over 100 EndFraction right parenthesis left parenthesis 47 right parenthesis\"><mi>b</mi><mo>=</mo><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mn>90</mn><mn>100</mn></mfrac></mrow></mfenced><mfenced><mn>47</mn></mfenced></math>, or <math alttext=\"b equals 0.1 left parenthesis 47 right parenthesis\"><mi>b</mi><mo>=</mo><mn>0.1</mn><mfenced><mn>47</mn></mfenced></math>, which yields <math alttext=\"b equals 4.7\"><mrow>\n\t<mi>b</mi>\n\t<mo>=</mo>\n\t<mn>4.7</mn>\n</mrow>\n</math>. Substituting <math alttext=\"4.7\"><mn>4.7</mn>\n</math> for <math alttext=\"b\"><mi>b</mi>\n</math> in the equation <math alttext=\"a equals 2.1 b\"><mrow>\n\t<mi>a</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>2.1</mn>\n\t\t<mi>b</mi>\n\t</mrow>\n</mrow>\n</math> yields <math alttext=\"a equals 2.1 left parenthesis 4.7 right parenthesis\"><mi>a</mi><mo>=</mo><mn>2.1</mn><mfenced><mn>4.7</mn></mfenced></math>, which is equivalent to <math alttext=\"a equals 9.87\"><mrow>\n\t<mi>a</mi>\n\t<mo>=</mo>\n\t<mn>9.87</mn>\n</mrow>\n</math>. Therefore, the value of <math alttext=\"a\"><mi>a</mi>\n</math> is <math alttext=\"9.87\"><mn>9.87</mn>\n</math>.</p>","correct_answer":["9.87","987/100"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.832000+00:00","source_updated_at":"2023-08-02T20:25:59.832000+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}}