{"id":"cb_question_bank:5959ae23-c767-4eb2-bd53-558bd40ca88e","source_id":"cb_question_bank","source_item_id":"5959ae23-c767-4eb2-bd53-558bd40ca88e","external_id":"c498bacc-713c-42ba-a2e4-bc873030515a","ibn":null,"question_id":"d3fe472f","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Triangle upper A upper B upper C is similar to triangle upper X upper Y upper Z , such that upper A , upper B , and upper C correspond to upper X , upper Y , and upper Z respectively. The length of each side of triangle upper X upper Y upper Z is 2 times the length of its corresponding side in triangle upper A upper B upper C . The measure of side upper A upper B is 16 . What is the measure of side upper X upper Y ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Triangle <math alttext=\"upper A upper B upper C\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n\t<mi>C</mi>\n</mrow>\n</math> is similar to triangle <math alttext=\"upper X upper Y upper Z\"><mrow>\n\t<mi>X</mi>\n\t<mi>Y</mi>\n\t<mi>Z</mi>\n</mrow>\n</math>, such that <math alttext=\"upper A\"><mi>A</mi>\n</math>, <math alttext=\"upper B\"><mi>B</mi>\n</math>, and <math alttext=\"upper C\"><mi>C</mi>\n</math> correspond to <math alttext=\"upper X\"><mi>X</mi>\n</math>, <math alttext=\"upper Y\"><mi>Y</mi>\n</math>, and <math alttext=\"upper Z\"><mi>Z</mi>\n</math> respectively. The length of each side of triangle <math alttext=\"upper X upper Y upper Z\"><mrow>\n\t<mi>X</mi>\n\t<mi>Y</mi>\n\t<mi>Z</mi>\n</mrow>\n</math> is <math alttext=\"2\"><mn>2</mn>\n</math> times the length of its corresponding side in triangle <math alttext=\"upper A upper B upper C\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n\t<mi>C</mi>\n</mrow>\n</math>. The measure of side <math alttext=\"upper A upper B\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n</mrow>\n</math> is <math alttext=\"16\"><mrow><mn>16</mn></mrow></math>. What is the measure of side <math alttext=\"upper X upper Y\"><mrow>\n\t<mi>X</mi>\n\t<mi>Y</mi>\n</mrow>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. It's given that triangle&nbsp;<math alttext=\"upper A upper B upper C\"><mi>A</mi><mi>B</mi><mi>C</mi></math> is similar to triangle <math alttext=\"upper X upper Y upper Z\"><mi>X</mi><mi>Y</mi><mi>Z</mi></math>, such that <math alttext=\"upper A\"><mi>A</mi>\n</math>, <math alttext=\"upper B\"><mi>B</mi>\n</math>, and <math alttext=\"upper C\"><mi>C</mi>\n</math> correspond to <math alttext=\"upper X\"><mi>X</mi>\n</math>, <math alttext=\"upper Y\"><mi>Y</mi>\n</math>, and <math alttext=\"upper Z\"><mi>Z</mi>\n</math>, respectively. Therefore, side <math alttext=\"upper A upper B\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n</mrow>\n</math> corresponds to side <math alttext=\"upper X upper Y\"><mrow>\n\t<mi>X</mi>\n\t<mi>Y</mi>\n</mrow>\n</math>. Since the length of each side of triangle <math alttext=\"upper X upper Y upper Z\"><mi>X</mi><mi>Y</mi><mi>Z</mi></math> is <math alttext=\"2\"><mn>2</mn>\n</math> times the length of its corresponding side in triangle <math alttext=\"upper A upper B upper C\"><mi>A</mi><mi>B</mi><mi>C</mi></math>, it follows that the measure of side <math alttext=\"upper X upper Y\"><mrow>\n\t<mi>X</mi>\n\t<mi>Y</mi>\n</mrow>\n</math> is <math alttext=\"2\"><mn>2</mn>\n</math> times the measure of side <math alttext=\"upper A upper B\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n</mrow>\n</math>. Thus, since the measure of side <math alttext=\"upper A upper B\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n</mrow>\n</math> is <math alttext=\"16\"><mn>16</mn>\n</math>, then the measure of side <math alttext=\"upper X upper Y\"><mrow>\n\t<mi>X</mi>\n\t<mi>Y</mi>\n</mrow>\n</math> is <math alttext=\"2 left parenthesis 16 right parenthesis\"><mn>2</mn><mfenced><mn>16</mn></mfenced></math>, or <math alttext=\"32\"><mn>32</mn>\n</math>.</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. This is the measure of side <math alttext=\"upper A upper B\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n</mrow>\n</math>, not side <math alttext=\"upper X upper Y\"><mrow>\n\t<mi>X</mi>\n\t<mi>Y</mi>\n</mrow>\n</math>.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.838000+00:00","source_updated_at":"2023-08-02T20:25:59.838000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"14\"><mn>14</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"16\"><mn>16</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"18\"><mn>18</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"32\"><mn>32</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}}