{"id":"cb_question_bank:fcd805ea-f381-4e59-a94b-13f3609c631b","source_id":"cb_question_bank","source_item_id":"fcd805ea-f381-4e59-a94b-13f3609c631b","external_id":null,"ibn":"021520-DC","question_id":"ee05c84e","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The function f is defined above. What is the value of f of 20 ?","stimulus":"f of x equals, open parenthesis, x plus 0 point 2 5 x, close parenthesis, times, open parenthesis, 50 minus x, close parenthesis","stimulus_html":"<div class=\"stimulus_reference \">\n\t<p class=\"standalone_statement style:1 \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1fd7bf6ee6f5ed39d276fc6290c8c0ca0fdb7268c9d1a80e089ddb8918ed3214\" alt=\"f of x equals, open parenthesis, x plus 0 point 2 5 x, close parenthesis, times, open parenthesis, 50 minus x, close parenthesis\"></span></span></p>\n</div>\n","stem_html":"<p class=\"stem_paragraph \">The function <span class=\"italic\">f</span> is defined above. What is the value of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cb3b21e2bd0f33421b00e72ab556a772c7dc67593e92d0e159b08553eecb4926\" alt=\"f of 20 \"></span></span> ?</p>\n","rationale_html":"<p>Choice C is correct. Adding the like terms <span class=\"italic\">x</span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9984da9381da140d46fa4c61a0f1a58e1406dd8fa5a05ab5341c1e43389ac51d\" alt=\"0 point 2 5 x \"></span> yields the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1955bcabd9c586c4cce7e7f9dc237401c2cfe81a37740a881ff948ded4130fb0\" alt=\"f of x equals, 1 point 2 5 x times, open parenthesis, 50 minus x, close parenthesis\"></span>. Substituting 20 for <span class=\"italic\">x</span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/33145c8b101f0a6905ce8eb8cefced6b184bef133eff0dfda23e9e7628eb8910\" alt=\"f of 20 equals, open parenthesis, 1 point 2 5 times 20, close parenthesis, times, open parenthesis, 50 minus 20, close parenthesis\"></span>. The product <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/50ea730aa37cbb74ba1d7db06c547995b77dc6504c82fdfff8f8e8c81c00adeb\" alt=\"1 point 2 5 times 20 \"></span> is equal to 25, and the difference <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9a8a754b51b5114d1789af6b66a1a11ab97096dfa97bbc21fb31614ef4e78b89\" alt=\"50 minus 20 \"></span> is equal to 30. Substituting these values in the given equation gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/96ea06ac8f3cd87f16c60cc02fb411059cb7c6f2ba482d5d2436c06473af5978\" alt=\"f of 20 equals, 25 times 30\"></span>, and multiplying 25 by 30 results in&nbsp;<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f98b33dbe84783044b5c81c1d186dbed6ee6ec159ba26ab0a35f568c1a732130\" alt=\"f of 20 equals 750\"></span>.</p><p>Choices A, B, and D are incorrect and may result from conceptual or computational errors when finding the value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/79e7118480f2b0b9e77fc58b9ccb05d91a46ee1f9495202fc74490947ecb162b\" alt=\"f of 20\"></span>.</p><p>&nbsp;</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.617000+00:00","source_updated_at":"2023-08-02T20:25:59.617000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">250</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">500</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">750</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">2,000</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}}