{"id":"cb_question_bank:98c6874a-c3f5-40c8-ab29-042dda20cf20","source_id":"cb_question_bank","source_item_id":"98c6874a-c3f5-40c8-ab29-042dda20cf20","external_id":null,"ibn":"08177-DC","question_id":"a1696f3e","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear 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 is defined as g of x equals, 5 x plus a , where a is a constant. If g of 4 equals 31 , what is the value of a ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">The function <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b45d2ffc02b9f064e2f8b1ac6f50263e8799bd2d93e4461f64de3b92a3cdc759\" alt=\"\"></span>&nbsp;</span>is defined as <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7f59f4d8499c61ef86f10b9f43409ff2e974606ea26c01187f64fb7dda3c514f\" alt=\"g of x equals, 5 x plus a\"></span></span>, where <span class=\"italic\">a</span> is a constant. If <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b57ea322fa9937b4189c13b723e3a52d49a54e304e319fed2b9a7314f4e346ec\" alt=\"g of 4 equals 31\"></span></span>, what is the value of <span class=\"italic\">a</span> ?</p>\n","rationale_html":"<p>Choice C is correct. Substituting 4 for <span class=\"italic\">x</span> in <span class=\"italic\">g</span>(<span class=\"italic\">x</span>) = 5<span class=\"italic\">x</span> + <span class=\"italic\">a</span> gives <span class=\"italic\">g</span>(4) = 5(4) + <span class=\"italic\">a</span>. Since <span class=\"italic\">g</span>(4) = 31, the equation <span class=\"italic\">g</span>(4) = 5(4) + <span class=\"italic\">a</span> simplifies to 31 = 20 + <span class=\"italic\">a</span>. It follows that <span class=\"italic\">a</span> = 11.</p><p>Choices A, B, and D are incorrect and may result from arithmetic errors.</p><p>&nbsp;</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.635000+00:00","source_updated_at":"2023-08-02T20:25:59.635000+00:00","options":[{"label":"A","content_html":"<p><span class=\"choice_cell align:right \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/40c51a3aa7d4a224364911ca6d2a0e4c256eee0d75895adf949e82a0ee8aca1c\" alt=\"\"></span></span> </span></p>\n","ord":0},{"label":"B","content_html":"<p><span class=\"choice_cell align:right \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/77a46fe87d545cb6a8dff06bf35879d5ddbb8d296daf6e9fd5e392532a202289\" alt=\"\"></span></span> </span></p>\n","ord":1},{"label":"C","content_html":"<p><span class=\"choice_cell align:right \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8fbd29c3a3486ba440ae6af3e4966f6aa2128fd812968b2fa10fc2a8eb2054fd\" alt=\"\"></span></span> </span></p>\n","ord":2},{"label":"D","content_html":"<p><span class=\"choice_cell align:right \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4539f19b558372055d00be9d7570d8e9d57b2b4fc9535ad6cb68c770f0f2f59e\" alt=\"negative 23\"></span></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}}