{"id":"cb_question_bank:ec98d7b7-2c69-420c-b19d-cff5e3723601","source_id":"cb_question_bank","source_item_id":"ec98d7b7-2c69-420c-b19d-cff5e3723601","external_id":"dabe922d-3778-48a9-88e7-926763881b51","ibn":null,"question_id":"34f8cd89","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.B.","skill":"Percentages","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"37 percent sign of the items in a box are green. Of those, 37 percent sign are also rectangular. Of the green rectangular items, 42 percent sign are also metal. Which of the following is closest to the percentage of the items in the box that are not rectangular green metal items?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\"><math alttext=\"37 percent sign\"><mn>37</mn>\n<mo>%</mo></math> of the items in a box are green. Of those, <math alttext=\"37 percent sign\"><mn>37</mn>\n<mo>%</mo></math> are also rectangular. Of the green rectangular items, <math alttext=\"42 percent sign\"><mn>42</mn>\n<mo>%</mo></math> are also metal. Which of the following is closest to the percentage of the items in the box that are <span style=\"text-decoration: underline;\">not</span> rectangular green metal items?</p>","rationale_html":"<p style=\"text-align: left;\">Choice C is correct. It's given that&nbsp;<math alttext=\"37 percent sign\"><mn>37</mn><mo>%</mo></math> of the items in a box are green. Let <math alttext=\"x\"><mi>x</mi>\n</math> represent the total number of items in the box. It follows that <math alttext=\"StartFraction 37 Over 100 EndFraction x\"><mfrac><mn>37</mn><mn>100</mn></mfrac><mi>x</mi></math>, or&nbsp;<math alttext=\"0.37 x\"><mn>0.37</mn><mi>x</mi></math>, items in the box are green. It's also given that of those,&nbsp;<math alttext=\"37 percent sign\"><mn>37</mn><mo>%</mo></math> are also rectangular. Therefore,&nbsp;<math alttext=\"StartFraction 37 Over 100 EndFraction left parenthesis 0.37 x right parenthesis\"><mfrac><mn>37</mn><mn>100</mn></mfrac><mfenced><mrow><mn>0.37</mn><mi>x</mi></mrow></mfenced></math>, or&nbsp;<math alttext=\"0.1369 x\"><mn>0.1369</mn><mi>x</mi></math>, items in the box are green rectangular items. It's also given that of the green rectangular items, <math alttext=\"42 percent sign\"><mn>42</mn><mo>%</mo></math> are also metal. Therefore,&nbsp;<math alttext=\"StartFraction 42 Over 100 EndFraction left parenthesis 0.1369 x right parenthesis\"><mfrac><mn>42</mn><mn>100</mn></mfrac><mfenced><mrow><mn>0.1369</mn><mi>x</mi></mrow></mfenced></math>, or&nbsp;<math alttext=\"0.057498 x\"><mn>0.057498</mn><mi>x</mi></math>, items in the box are rectangular green metal items. The number of the items in the box that are not rectangular green metal items is the total number of items in the box minus the number of rectangular green metal items in the box. Therefore, the number of items in the box that are not rectangular green metal items is <math alttext=\"x minus 0.057498 x\"><mi>x</mi><mo>-</mo><mn>0.057498</mn><mi>x</mi></math>, or&nbsp;<math alttext=\"0.942502 x\"><mn>0.942502</mn><mi>x</mi></math>. The percentage of items in the box that are not rectangular green metal items is the percentage that <math alttext=\"0.942502 x\"><mn>0.942502</mn><mi>x</mi></math> is of <math alttext=\"x\"><mi>x</mi>\n</math>. If <math alttext=\"p percent sign\"><mi>p</mi><mo>%</mo></math> represents this percentage, the value of <math alttext=\"p\"><mi>p</mi>\n</math> is&nbsp;<math alttext=\"100 left parenthesis StartFraction 0.942502 x Over x EndFraction right parenthesis\"><mn>100</mn><mfenced><mfrac><mrow><mn>0.942502</mn><mi>x</mi></mrow><mi>x</mi></mfrac></mfenced></math>, or&nbsp;<math alttext=\"94.2502\"><mn>94.2502</mn></math>. Of the given choices,&nbsp;<math alttext=\"94.25 percent sign\"><mn>94.25</mn><mo>%</mo></math> is closest to the percentage of items in the box that are not rectangular green metal items.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.831000+00:00","source_updated_at":"2023-08-02T20:25:59.831000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"1.16 percent sign\"><mn>1.16</mn>\n<mo>%</mo></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"57.50 percent sign\"><mn>57.50</mn>\n<mo>%</mo></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"94.25 percent sign\"><mn>94.25</mn>\n<mo>%</mo></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"98.84 percent sign\"><mn>98.84</mn>\n<mo>%</mo></math></p>","ord":3}],"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}}