{"id":"cb_question_bank:29704632-c2c2-4050-931d-e4d9d6376e7e","source_id":"cb_question_bank","source_item_id":"29704632-c2c2-4050-931d-e4d9d6376e7e","external_id":null,"ibn":"016807-DC","question_id":"6ce95fc8","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":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following is a solution to the equation above?","stimulus":"2 x squared, minus 2, equals 2 x plus 3","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/3aa802042ec497ebeb8261a39f626de4b2b0d22f76661b25ad02b5da0d2fa707\" alt=\"2 x squared, minus 2, equals 2 x plus 3\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following is a solution to the equation above?</p>\n","rationale_html":"<p>Choice D is correct. A quadratic equation in the form <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2c869bdc70b1a9ecef53fb3c6051020877ac5c401e6cc5aaf10e36e3b7478c63\" alt=\"a, x squared, plus b x, plus c, equals 0\"></span>, where <span class=\"italic\">a</span>, <span class=\"italic\">b</span>, and <span class=\"italic\">c</span> are constants, can be solved using the quadratic formula: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2688dfc6adcebb064be581b68d3b5ce487f95792ae10472a925b67bbc0ed70c3\" alt=\"x equals, the fraction with numerator negative b plus or minus the square root of b squared, minus 4 a c, end root, and denominator 2 a, end fraction\"></span>. Subtracting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cd1a3946fa4d4f06ade7c9576d97cdd703eab67478ca27b912646511f21fdffc\" alt=\"2 x plus 3 \"></span> from both sides of the given equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3770b3dce94db2207ecbacfc471c67ecc165e5c447d619704f37a245c5e6baad\" alt=\"2 x squared, minus 2 x, minus 5, equals 0\"></span>. Applying the quadratic formula, where <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b8939f0089034fb0b27a6a9b987733739fbdb2c6f74447b4a31584d266b4c797\" alt=\"a, equals 2\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e29ee25a7682223772f17be6a97deca08e685762ed5525bda1c80ed739e29e35\" alt=\"b equals negative 2\"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/827355c1d759b812cc47fdf077d682d911009f3df4d212e91a678768a9059da3\" alt=\"c equals negative 5\"></span>, yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f5169c98897ef1e4624e55182959a9a843d4641b6b714c232ad48580970473d4\" alt=\"x equals the fraction with numerator negative, open parenthesis, negative 2, close parenthesis, plus or minus the square root of, open parenthesis, negative 2, close parenthesis, squared, minus 4 times 2, times negative 5, end root, and denominator 2 times 2, end fraction\"></span>. This can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0d063c6c87077c8ae943d5aca1e74f949a7c616f4166a7b65336eec8aa797105\" alt=\"x equals, the fraction with numerator 2 plus or minus the square root of 44, end root, and denominator 4 \"></span>. Since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e53fcdbc97646a5b87dbd89ee6b3b8319ed8f801fc2eeabc1f8bec22faeb660d\" alt=\"the square root of 44 equals, the square root of 2 squared, times 11, end root\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d82bd940baad53e65293a1d2c31964ee630e44313b32758ef960dab9dc38975f\" alt=\"2 times the square root of 11\"></span>, the equation can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e5b2335c7197c56775d4f11126fb2b0b1b436c41e53706bc336b225f33d8d394\" alt=\"x equals, the fraction with numerator 2 plus or minus 2 times the square root of 11, end root, and denominator 4\"></span>. Dividing 2 from both the numerator and denominator yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/18a4f9300f3e874327673a70458dbf6775452a97b771cbdcbbe9744cbaa79204\" alt=\"the fraction with numerator 1 plus the square root of 11, end root, and denominator 2\"></span> or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/38b216e4c37f9989524ebe2a053a245ccd51d9b5ff1aa5b32f87b4a6b0fdf80d\" alt=\"the fraction with numerator 1 minus the square root of 11, end root, and denominator 2\"></span>. Of these two solutions, only <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/18a4f9300f3e874327673a70458dbf6775452a97b771cbdcbbe9744cbaa79204\" alt=\"the fraction with numerator 1 plus the square root of 11, end root, and denominator 2\"></span> is present among the choices. Thus, the correct choice is D.</p><p>Choice A is incorrect and may result from a computational or conceptual error. Choice B is incorrect and may result from using <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/337937b26ff6a8d726f9d6c7cdd2944e940d51009d899a27dd98971158f1a207\" alt=\"x equals, the fraction with numerator negative b plus or minus the square root of b squared, minus 4 a c, end root, and denominator a, end fraction \"></span> instead of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2688dfc6adcebb064be581b68d3b5ce487f95792ae10472a925b67bbc0ed70c3\" alt=\"x equals, the fraction with numerator negative b, plus or minus the square root of b squared, minus 4 a c, end root, and denominator 2 a, end fraction \"></span> as the quadratic formula. Choice C is incorrect and may result from rewriting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/07087c7d440fb09c5c534080de17b3e38e56ff9d96b030c2203254f3c969a053\" alt=\"the square root of 44 \"></span> as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/32cc7dc7f1bdbc93cb404f85480987e968f58960b0105759779b0fec220eb1a0\" alt=\"4 times the square root of 11\"></span> instead of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d82bd940baad53e65293a1d2c31964ee630e44313b32758ef960dab9dc38975f\" alt=\"2 times the square root of 11\"></span>.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.615000+00:00","source_updated_at":"2023-08-02T20:25:59.615000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d870b3a6c89096490c39cc291dea5fd94193a953487d36d45d7f8548ac0b8f4e\" alt=\"2\"></span></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2930c2d5c0c518fac1af85d3b14c328210807dc37d7a3cd2752399bc23ad92af\" alt=\"1 minus the square root of 11\"></span></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1917f3cb599723d46df27ad2faf743c99a13de82c25922ef8ab272dc76234a41\" alt=\"one half plus the square root of 11\"></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/18a4f9300f3e874327673a70458dbf6775452a97b771cbdcbbe9744cbaa79204\" alt=\"the fraction with numerator 1 plus the square root of 11, and denominator 2\"></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}}