{"id":"cb_question_bank:517a3a89-e9b3-4c48-8290-9add386f1a18","source_id":"cb_question_bank","source_item_id":"517a3a89-e9b3-4c48-8290-9add386f1a18","external_id":null,"ibn":"08243-DC","question_id":"c81b6c57","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the expression , p is a constant. This expression is equivalent to the expression 6 x squared minus 155 x plus 24 . What is the value of p ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">In the expression&nbsp;<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/261d4c4ddae2c695b35c754aea9ec173eb9453286fd66bd513a3e2f0aad2db15\" alt=\"\"></span> , <span class=\"italic\">p</span> is a constant. This expression is equivalent to the expression <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/aa1533216c1fcf9862f4ec86bdeb27a4452448131c6d65c1e962edc1a4b70765\" alt=\"6 x squared minus 155 x plus 24\"></span></span>. What is the value of <span class=\"italic\">p</span>&nbsp;?</p>\n","rationale_html":"<p>Choice B is correct. Using the distributive property, the first given expression can be rewritten as&nbsp;6<span class=\"italic\">x</span><sup>2</sup> + 3<span class=\"italic\">px </span>+ 24 – 16<span class=\"italic\">px</span> – 64<span class=\"italic\">x</span> + 24, and then rewritten as 6<span class=\"italic\">x</span><sup>2</sup> + (3<span class=\"italic\">p</span> – 16<span class=\"italic\">p</span> – 64)<span class=\"italic\">x</span> + 24. Since the expression 6<span class=\"italic\">x</span><sup>2</sup> + (3<span class=\"italic\">p</span> – 16<span class=\"italic\">p</span> – 64)<span class=\"italic\">x</span> + 24 is equivalent to 6<span class=\"italic\">x</span><sup>2</sup> – 155<span class=\"italic\">x</span> + 24, the coefficients of the <span class=\"italic\">x </span>terms from each expression are equivalent to each other; thus 3<span class=\"italic\">p</span> – 16<span class=\"italic\">p</span> – 64 = –155. Combining like terms gives –13<span class=\"italic\">p</span>&nbsp; – 64 = –155. Adding 64 to both sides of the equation gives –13<span class=\"italic\">p</span> = –71. Dividing both sides of the equation by –13 yields <span class=\"italic\">p</span> = 7.</p><p>Choice A is incorrect. If <span class=\"italic\">p </span>= –3, then the first expression would be equivalent to 6x<sup>2</sup> – 25<span class=\"italic\">x</span> + 24. Choice C is incorrect. If <span class=\"italic\">p</span> = 13, then the first expression would be equivalent to 6<span class=\"italic\">x</span><sup>2</sup> – 233<span class=\"italic\">x </span>+ 24. Choice D is incorrect. If <span class=\"italic\">p </span>= 155, then the first expression would be equivalent to 6<span class=\"italic\">x</span><sup>2</sup> – 2,079<span class=\"italic\">x</span> + 24.</p><p></p>\n","correct_answer":["B"],"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/d885ed8835afb01e8427c15ce78f065d62da416c14a434b720ba4833dec5a7c5\" alt=\"negative 3\"></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/aa4f2bc9f9d9e942987ab37126748b20a9f78e4ca3c017d7462926f46ed61f09\" alt=\"7\"></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/a017ed9a1a9530f0ea8cbd3ac63d72fb98d374b9ca259a9de917ba7cb4c6e8af\" alt=\"13\"></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/952b3517bed4dce3be9b8a7142391dcb795128ec78be7d1d8ebe3ad5107e9807\" alt=\"155\"></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}}