{"id":"cb_question_bank:06df2a0d-5fdc-401d-98ca-5e242e0f5b9c","source_id":"cb_question_bank","source_item_id":"06df2a0d-5fdc-401d-98ca-5e242e0f5b9c","external_id":null,"ibn":"025768-DC","question_id":"7f81d0c3","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"What values satisfy the equation above?","stimulus":"x squared, minus x, minus 1, equals 0","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7ec539498c935f6d3bc325a99195c9ea85189d9c5a2cbf44dac74e321d12acef\" alt=\"x squared, minus x, minus 1, equals 0\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">What values satisfy the equation above?</p>\n","rationale_html":"<p>Choice C is correct. Using the quadratic formula to solve the given expression yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1a3a3a63baf95834549c0825e9b774295393c069fdb96d05202772b6a0b8c7b1\" alt=\"x equals, the fraction with numerator negative, open parenthesis, negative 1, close parenthesis, plus or minus, the square root of open parenthesis, negative 1, close parenthesis, squared, minus, 4 times 1 times negative 1, end root, and denominator, 2 times 1, end fraction, which equals, the fraction with numerator 1, plus or minus, the square root of 5, and denominator 2\"></span><i>.</i> Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/915a34bf8c42c727c272dbe86cfcc30de37c35fd35c2c3ef99db50fe5ec9b746\" alt=\"x equals, the fraction with numerator 1 plus the square root of 5, and denominator 2\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/526d7abf2656c4430632aec1b3817b43503f28545701d3cb3346874a245ac447\" alt=\"x equals, the fraction with numerator 1 minus the square root of 5, and denominator 2\"></span> satisfy the given equation.</p><p>Choices A and B are incorrect and may result from incorrectly factoring or incorrectly applying the quadratic formula. Choice D is incorrect and may result from a sign error.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.619000+00:00","source_updated_at":"2023-08-02T20:25:59.619000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6e4319fe2c5755fc5aa3f69e1a43b989d061cbb17c450f24b51a6616f131de4b\" alt=\"x equals 1\"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/401169281090f4f1d9aafeeb928524e672d737cdce814b4e9256c5e06a42d325\" alt=\"x equals 2\"></span></span></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9fb52cd7397b384c0f810d7fa349f12cb6466e05b35d3941ffefa98fcece0582\" alt=\"x equals negative one half\"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2f9280cb724f9bc73a6cefe3bd4f0836da50ef56ce5749d0fae4a7089dcd5cb2\" alt=\"x equals three halves\"></span></span></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/915a34bf8c42c727c272dbe86cfcc30de37c35fd35c2c3ef99db50fe5ec9b746\" alt=\"x equals, the fraction with numerator 1 plus the square root of 5, and denominator 2\"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/526d7abf2656c4430632aec1b3817b43503f28545701d3cb3346874a245ac447\" alt=\"x equals, the fraction with numerator 1 minus the square root of 5, and denominator 2\"></span></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e1a8837b34cf78d7f54f1e0c6a902fc8389f2412e5feacef29e35729e1bcc747\" alt=\"x equals, the fraction with numerator negative 1 plus the square root of 5, and denominator 2\"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/13b7c9e59d19b42679370390fcbdfe872723259b759bf2e1e1234991304467b5\" alt=\"x equals, the fraction with numerator negative 1 minus the square root of 5, and denominator 2\"></span></span></p>\n","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}}