{"id":"cb_question_bank:f4bd2c4e-357c-42cb-80f2-351c3e4a6a16","source_id":"cb_question_bank","source_item_id":"f4bd2c4e-357c-42cb-80f2-351c3e4a6a16","external_id":"9ff69db4-88d5-4c3b-ad95-8bd4d0c3f462","ibn":null,"question_id":"763e6769","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.A.","skill":"Ratios, rates, proportional relationships, and units","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The ratio x to y is equivalent to the ratio 12 to t . When x equals 156 , what is the value of y in terms of t ?","stimulus":"","stimulus_html":null,"stem_html":"<p>The ratio <math alttext=\"x\"><mi>x</mi>\n</math> to <math alttext=\"y\"><mi>y</mi>\n</math> is equivalent to the ratio <math alttext=\"12\"><mn>12</mn>\n</math> to <math alttext=\"t\"><mi>t</mi>\n</math>. When <math alttext=\"x equals 156\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>156</mn>\n</mrow>\n</math>, what is the value of <math alttext=\"y\"><mi>y</mi>\n</math> in terms of <math alttext=\"t\"><mi>t</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. It's given that the ratio <math alttext=\"x\"><mi>x</mi>\n</math> to <math alttext=\"y\"><mi>y</mi>\n</math> is equivalent to the ratio <math alttext=\"12\"><mn>12</mn>\n</math> to <math alttext=\"t\"><mi>t</mi>\n</math>. This can be represented by <math alttext=\"StartFraction x Over y EndFraction equals StartFraction 12 Over t EndFraction\"><mfrac><mi>x</mi><mi>y</mi></mfrac><mo>=</mo><mfrac><mn>12</mn><mi>t</mi></mfrac></math>. Substituting <math alttext=\"156\"><mn>156</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in this equation yields <math alttext=\"StartFraction 156 Over y EndFraction equals StartFraction 12 Over t EndFraction\"><mfrac><mn>156</mn><mi>y</mi></mfrac><mo>=</mo><mfrac><mn>12</mn><mi>t</mi></mfrac></math>. This can be rewritten as <math alttext=\"12 y equals 156 t\"><mn>12</mn><mi>y</mi><mo>=</mo><mn>156</mn><mi>t</mi></math>. Dividing both sides of this equation by <math alttext=\"12\"><mn>12</mn>\n</math> yields <math alttext=\"y equals 13 t\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>13</mn>\n\t\t<mi>t</mi>\n\t</mrow>\n</mrow>\n</math>. Therefore, when <math alttext=\"x equals 156\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>156</mn>\n</mrow>\n</math>, the value of <math alttext=\"y\"><mi>y</mi>\n</math> in terms of <math alttext=\"t\"><mi>t</mi>\n</math> is <math alttext=\"13 t\"><mrow>\n\t<mn>13</mn>\n\t<mi>t</mi>\n</mrow>\n</math>.</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 C 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":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.830000+00:00","source_updated_at":"2023-08-02T20:25:59.830000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"13 t\"><mrow>\n\t<mn>13</mn>\n\t<mi>t</mi>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"12 t\"><mrow>\n\t<mn>12</mn>\n\t<mi>t</mi>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"144 t\"><mrow>\n\t<mn>144</mn>\n\t<mi>t</mi>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"168 t\"><mrow>\n\t<mn>168</mn>\n\t<mi>t</mi>\n</mrow>\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}}