{"id":"cb_question_bank:c6b1a70a-30b6-4b0f-99f4-f520fbf4aeee","source_id":"cb_question_bank","source_item_id":"c6b1a70a-30b6-4b0f-99f4-f520fbf4aeee","external_id":"29c0769a-6466-4e2e-8793-1978ec02749c","ibn":null,"question_id":"8c5dbd3e","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 w is 110 percent sign greater than the number z . The number z is 55 percent sign less than 50 . What is the value of w ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The number <math alttext=\"w\"><mi>w</mi>\n</math> is <math alttext=\"110 percent sign\"><mn>110</mn><mo>%</mo></math> greater than the number <math alttext=\"z\"><mi>z</mi>\n</math>. The number <math alttext=\"z\"><mi>z</mi>\n</math> is <math alttext=\"55 percent sign\"><mn>55</mn><mo>%</mo></math> less than <math alttext=\"50\"><mn>50</mn>\n</math>. What is the value of <math alttext=\"w\"><mi>w</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"47.25\"><mn>47.25</mn>\n</math>. It’s given that the number <math alttext=\"w\"><mi>w</mi>\n</math> is <math alttext=\"110 percent sign\"><mn>110</mn><mo>%</mo></math> greater than the number <math alttext=\"z\"><mi>z</mi>\n</math>. It follows that <math alttext=\"w equals left parenthesis 1 plus StartFraction 110 Over 100 EndFraction right parenthesis z\"><mi>w</mi><mo>=</mo><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mn>110</mn><mn>100</mn></mfrac></mrow></mfenced><mi>z</mi></math>, or <math alttext=\"w equals 2.1 z\"><mi>w</mi><mo>=</mo><mn>2.1</mn><mi>z</mi></math>. It’s also given that the number <math alttext=\"z\"><mi>z</mi>\n</math> is <math alttext=\"55 percent sign\"><mn>55</mn><mo>%</mo></math> less than <math alttext=\"50\"><mn>50</mn>\n</math>. It follows that <math alttext=\"z equals left parenthesis 1 minus StartFraction 55 Over 100 EndFraction right parenthesis left parenthesis 50 right parenthesis\"><mi>z</mi><mo>=</mo><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mn>55</mn><mn>100</mn></mfrac></mrow></mfenced><mfenced><mn>50</mn></mfenced></math>, or <math alttext=\"z equals 0.45 left parenthesis 50 right parenthesis\"><mi>z</mi><mo>=</mo><mn>0.45</mn><mfenced><mn>50</mn></mfenced></math>, which yields <math alttext=\"z equals 22.5\"><mi>z</mi><mo>=</mo><mn>22.5</mn></math>. Substituting <math alttext=\"22.5\"><mn>22.5</mn></math> for <math alttext=\"z\"><mi>z</mi>\n</math> in the equation <math alttext=\"w equals 2.1 z\"><mi>w</mi><mo>=</mo><mn>2.1</mn><mi>z</mi></math> yields <math alttext=\"w equals 2.1 left parenthesis 22.5 right parenthesis\"><mi>w</mi><mo>=</mo><mn>2.1</mn><mfenced><mn>22.5</mn></mfenced></math>, which is equivalent to <math alttext=\"w equals 47.25\"><mrow>\n\t<mi>w</mi>\n\t<mo>=</mo>\n\t<mn>47.25</mn>\n</mrow>\n</math>. Therefore, the value of <math alttext=\"w\"><mi>w</mi>\n</math> is <math alttext=\"47.25\"><mn>47.25</mn>\n</math>. Note that 47.25 and 189/4 are examples of ways to enter a correct answer.</p>","correct_answer":["189/4","47.25"],"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}}