{"id":"cb_question_bank:52b4a07f-657d-4b2b-b9e8-cde51e3f2aad","source_id":"cb_question_bank","source_item_id":"52b4a07f-657d-4b2b-b9e8-cde51e3f2aad","external_id":"db08d5bc-9768-4b87-8642-1033890325ea","ibn":null,"question_id":"121dc44f","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 City A 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>The population of City A increased by <math alttext=\"7 percent sign\"><mrow><mn>7</mn></mrow><mo>%</mo></math> from <math alttext=\"2015\"><mn>2015</mn></math> to <math alttext=\"2016\"><mn>2016</mn></math>. If the <math alttext=\"2016\"><mn>2016</mn></math> population is <math alttext=\"k\"><mi>k</mi>\n</math> times the <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 style=\"text-align: left;\">Choice C is correct. It's given that the population of City A increased by <math alttext=\"7 percent sign\"><mn>7</mn><mo>%</mo></math> from <math alttext=\"20 15\"><mn>20</mn>\n<mn>15</mn>\n</math> to <math alttext=\"20 16\"><mn>20</mn>\n<mn>16</mn>\n</math>. Therefore, the population of City A in <math alttext=\"20 16\"><mn>20</mn>\n<mn>16</mn>\n</math> includes <math alttext=\"100 percent sign\"><mn>100</mn><mo>%</mo></math> of the population of City A in <math alttext=\"20 15\"><mn>20</mn>\n<mn>15</mn>\n</math> plus an additional <math alttext=\"7 percent sign\"><mn>7</mn><mo>%</mo></math> of the population of City A in <math alttext=\"20 15\"><mn>20</mn>\n<mn>15</mn>\n</math>. This means that the population of City A in <math alttext=\"20 16\"><mn>20</mn>\n<mn>16</mn>\n</math> is <math alttext=\"107 percent sign\"><mn>107</mn><mo>%</mo></math> of the population in <math alttext=\"20 15\"><mn>20</mn>\n<mn>15</mn>\n</math>. Thus, the population of City A in <math alttext=\"20 16\"><mn>20</mn>\n<mn>16</mn>\n</math> is <math alttext=\"StartFraction 107 Over 100 EndFraction\"><mfrac>\n\t<mn>107</mn>\n\t<mn>100</mn>\n</mfrac>\n</math>, or <math alttext=\"1.07\"><mn>1.07</mn>\n</math>, times the <math alttext=\"20 15\"><mn>20</mn>\n<mn>15</mn>\n</math> population. 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 style=\"text-align: left;\">Choice A is incorrect. This would be the value of <math alttext=\"k\"><mi>k</mi>\n</math> if the population in <math alttext=\"20 16\"><mn>20</mn>\n<mn>16</mn>\n</math> was <math alttext=\"7 percent sign\"><mn>7</mn><mo>%</mo></math> of the population in <math alttext=\"20 15\"><mn>20</mn>\n<mn>15</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This would be the value of <math alttext=\"k\"><mi>k</mi>\n</math> if the population in <math alttext=\"20 16\"><mn>20</mn>\n<mn>16</mn>\n</math> was <math alttext=\"70 percent sign\"><mn>70</mn><mo>%</mo></math> of the population in <math alttext=\"20 15\"><mn>20</mn>\n<mn>15</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This would be 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 <math alttext=\"7 percent sign\"><mn>7</mn><mo>%</mo></math>, from <math alttext=\"20 15\"><mn>20</mn>\n<mn>15</mn>\n</math> to <math alttext=\"20 16\"><mn>20</mn>\n<mn>16</mn>\n</math>.</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\"><mrow><mn>0.07</mn></mrow></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"0.7\"><mrow><mn>0.7</mn></mrow></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"1.07\"><mrow><mn>1.07</mn></mrow></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"1.7\"><mrow><mn>1.7</mn></mrow></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}}