{"id":"cb_question_bank:ab2f2da4-40e1-4317-b670-ca003ff21cfd","source_id":"cb_question_bank","source_item_id":"ab2f2da4-40e1-4317-b670-ca003ff21cfd","external_id":"b52952eb-21e9-41d5-ac01-117586367fc5","ibn":null,"question_id":"20845d36","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 70 percent sign less than the positive number b . The number c is 60 percent sign greater than a . The number c is how many times b ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The number <math alttext=\"a\"><mi>a</mi>\n</math> is <math alttext=\"70 percent sign\"><mrow><mn>70</mn></mrow><mo>%</mo></math> less than the positive number <math alttext=\"b\"><mi>b</mi>\n</math>. The number <math alttext=\"c\"><mi>c</mi>\n</math> is <math alttext=\"60 percent sign\"><mrow><mn>60</mn></mrow><mo>%</mo></math> greater than <math alttext=\"a\"><mi>a</mi>\n</math>. The number <math alttext=\"c\"><mi>c</mi>\n</math> is how many times <math alttext=\"b\"><mi>b</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\".48\"><mo>.48</mo></math>. It's given that the number <math alttext=\"a\"><mi>a</mi>\n</math> is <math alttext=\"70 percent sign\"><mn>70</mn><mo>%</mo></math> less than the positive number <math alttext=\"b\"><mi>b</mi>\n</math>. Therefore,&nbsp;<math alttext=\"a equals left parenthesis 1 minus StartFraction 70 Over 100 EndFraction right parenthesis b\"><mi>a</mi><mo>=</mo><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mn>70</mn><mn>100</mn></mfrac></mrow></mfenced><mi>b</mi></math>, which is equivalent to&nbsp;<math alttext=\"a equals left parenthesis 1 minus 0.70 right parenthesis b\"><mi>a</mi><mo>=</mo><mfenced><mrow><mn>1</mn><mo>-</mo><mn>0.70</mn></mrow></mfenced><mi>b</mi></math>, or&nbsp;<math alttext=\"a equals 0.30 b\"><mi>a</mi><mo>=</mo><mn>0.30</mn><mi>b</mi></math>. It's also given that the number <math alttext=\"c\"><mi>c</mi>\n</math> is&nbsp;<math alttext=\"60 percent sign\"><mn>60</mn><mo>%</mo></math> greater than <math alttext=\"a\"><mi>a</mi>\n</math>. Therefore, <math alttext=\"c equals left parenthesis 1 plus StartFraction 60 Over 100 EndFraction right parenthesis a\"><mi>c</mi><mo>=</mo><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mn>60</mn><mn>100</mn></mfrac></mrow></mfenced><mi>a</mi></math>, which is equivalent to&nbsp;<math alttext=\"c equals left parenthesis 1 plus 0.60 right parenthesis a\"><mi>c</mi><mo>=</mo><mfenced><mrow><mn>1</mn><mo>+</mo><mn>0.60</mn></mrow></mfenced><mi>a</mi></math>, or&nbsp;<math alttext=\"c equals 1.60 a\"><mi>c</mi><mo>=</mo><mn>1.60</mn><mi>a</mi></math>. Since <math alttext=\"a equals 0.30 b\"><mrow>\n\t<mi>a</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>0.30</mn>\n\t\t<mi>b</mi>\n\t</mrow>\n</mrow>\n</math>, substituting <math alttext=\"0.30 b\"><mrow>\n\t<mn>0.30</mn>\n\t<mi>b</mi>\n</mrow>\n</math> for <math alttext=\"a\"><mi>a</mi>\n</math> in the equation <math alttext=\"c equals 1.60 a\"><mrow>\n\t<mi>c</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>1.60</mn>\n\t\t<mi>a</mi>\n\t</mrow>\n</mrow>\n</math> yields <math alttext=\"c equals 1.60 left parenthesis 0.30 b right parenthesis\"><mi>c</mi><mo>=</mo><mn>1.60</mn><mfenced><mrow><mn>0.30</mn><mi>b</mi></mrow></mfenced></math>, or&nbsp;<math alttext=\"c equals 0.48 b\"><mi>c</mi><mo>=</mo><mn>0.48</mn><mi>b</mi></math>. Thus, <math alttext=\"c\"><mi>c</mi>\n</math> is <math alttext=\"0.48\"><mn>0.48</mn>\n</math> times <math alttext=\"b\"><mi>b</mi>\n</math>. Note that .48 and 12/25 are examples of ways to enter a correct answer.</p>","correct_answer":[".48","12/25"],"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}}