{"id":"cb_question_bank:8754179d-a293-40cc-86e7-5e22d53a2fa3","source_id":"cb_question_bank","source_item_id":"8754179d-a293-40cc-86e7-5e22d53a2fa3","external_id":"c58c16c7-0525-4a20-b6ce-33c59a2d682f","ibn":null,"question_id":"ba61d95f","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.B.","skill":"Percentages","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The population of Greenville increased by 7 percent sign from 2015 to 2016 . If the 2016 population is k times the 2015 population, what is the value of k ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The population of Greenville increased by <math alttext=\"7 percent sign\"><mn>7</mn>\n<mo>%</mo></math> from&nbsp;<math alttext=\"2015\"><mn>2015</mn></math> to <math alttext=\"2016\"><mn>2016</mn></math>. If the&nbsp;<math alttext=\"2016\"><mn>2016</mn></math> population is <math alttext=\"k\"><mi>k</mi>\n</math> times the&nbsp;<math alttext=\"2015\"><mn>2015</mn></math> population, what is the value of <math alttext=\"k\"><mi>k</mi>\n</math>?</p>","rationale_html":"<p>Choice C is correct. Let <math alttext=\"x\"><mi>x</mi>\n</math> be the 2015 population of Greenville. It's given that the population increased by <math alttext=\"7 percent sign\"><mn>7</mn><mo>%</mo></math> from 2015 to 2016. The increase in population can be written as <math alttext=\"left parenthesis 0.07 right parenthesis x\"><mfenced><mn>0.07</mn></mfenced><mi>x</mi></math>. The 2016 population of Greenville is given as the sum of the 2015 population of Greenville and the increase in population from 2015 to 2016. This can be rewritten as <math alttext=\"x plus left parenthesis 0.07 right parenthesis x\"><mi>x</mi><mo>+</mo><mfenced><mn>0.07</mn></mfenced><mi>x</mi></math>, or <math alttext=\"1.07 x\"><mn>1.07</mn><mi>x</mi></math>. Therefore, the value of <math alttext=\"k\"><mi>k</mi>\n</math> is <math alttext=\"1.07\"><mn>1.07</mn>\n</math>.</p>\n<p>Choice A is incorrect. This is the percent, represented as a decimal, that the population increased from 2015 to 2016, not the value of <math alttext=\"k\"><mi>k</mi>\n</math>.</p>\n<p>Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice D is incorrect. This is the value of <math alttext=\"k\"><mi>k</mi>\n</math> if the population increased by <math alttext=\"70 percent sign\"><mn>70</mn><mo>%</mo></math>, not&nbsp;<math alttext=\"7 percent sign\"><mn>7</mn><mo>%</mo></math>, from 2015 to 2016.</p>","correct_answer":["C"],"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":[{"label":"A","content_html":"<p><math alttext=\"0.07\"><mn>0.07</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"0.7\"><mn>0.7</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"1.07\"><mn>1.07</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"1.7\"><mn>1.7</mn>\n</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}}