{"id":"cb_question_bank:6c79e6ef-f147-40df-9047-2036943b35cd","source_id":"cb_question_bank","source_item_id":"6c79e6ef-f147-40df-9047-2036943b35cd","external_id":null,"ibn":"022215-DC","question_id":"49efde89","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The expression 2 x squared, plus a, x is equivalent to x times, open parenthesis, 2 x, plus 7, close parenthesis for some constant a . What is the value of a ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">The expression <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8260317c1b8c8f493074c510dc124253a24c857736540f0fd6abe96084377f23\" alt=\"2 x squared, plus a, x \"></span></span> is equivalent to <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e20b1e5b13d7490a69c938401d00234ad80a457489c59bdfd29d971be769a176\" alt=\"x times, open parenthesis, 2 x, plus 7, close parenthesis \"></span>&nbsp;</span>for some constant <span class=\"italic\">a</span>. What is the value of <span class=\"italic\">a</span> ?</p>\n","rationale_html":"<p>Choice D is correct. It’s given that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8260317c1b8c8f493074c510dc124253a24c857736540f0fd6abe96084377f23\" alt=\"2 x squared, plus a, x \"></span> is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e20b1e5b13d7490a69c938401d00234ad80a457489c59bdfd29d971be769a176\" alt=\"x times, open parenthesis, 2 x plus 7, close parenthesis\"></span> for some constant <span class=\"italic\">a</span>. Distributing the <span class=\"italic\">x</span> over each term in the parentheses gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0c4a34a7d8a3fda5348c55e797884cfd312ee7ae627ad80992a56b379f9b184f\" alt=\"2 x squared, plus 7 x\"></span>, which is in the same form as the first given expression, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8260317c1b8c8f493074c510dc124253a24c857736540f0fd6abe96084377f23\" alt=\"2 x squared, plus a, x\"></span>. The coefficient of the second term in <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0c4a34a7d8a3fda5348c55e797884cfd312ee7ae627ad80992a56b379f9b184f\" alt=\"2 x squared, plus 7 x\"></span> is 7. Therefore, the value of <span class=\"italic\">a</span> is 7.</p><p>Choice A is incorrect. If the value of <span class=\"italic\">a</span> were 2, then <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8260317c1b8c8f493074c510dc124253a24c857736540f0fd6abe96084377f23\" alt=\"2 x squared, plus a, x \"></span> would be equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/426ab351ee7d579be83dda81fbc2eb8e3beb726f605b5fbb07dbb41ed9a551e4\" alt=\"2 x squared, plus 2 x\"></span>, which isn’t equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e20b1e5b13d7490a69c938401d00234ad80a457489c59bdfd29d971be769a176\" alt=\"x times, open parenthesis, 2 x plus 7, close parenthesis\"></span>. Choice B is incorrect. If the value of <span class=\"italic\">a</span> were 3, then <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8260317c1b8c8f493074c510dc124253a24c857736540f0fd6abe96084377f23\" alt=\"2 x squared, plus a, x\"></span> would be equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b0e779bf9ba454b8ee86e8d14d3b928b7b5e59b9f88fd39e30a622211227503b\" alt=\"2 x squared, plus 3 x\"></span>, which isn’t equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e20b1e5b13d7490a69c938401d00234ad80a457489c59bdfd29d971be769a176\" alt=\"x times, open parenthesis, 2 x plus 7, close parenthesis\"></span>. Choice C is incorrect. If the value of <span class=\"italic\">a</span> were 4, then <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8260317c1b8c8f493074c510dc124253a24c857736540f0fd6abe96084377f23\" alt=\"2 x squared, plus a, x\"></span> would be equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dfda78e3bc11fbff2c1933bbb2c76635bc1bff989a7bcd0631685e80f7663522\" alt=\"2 x squared, plus 4 x\"></span>, which isn’t equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e20b1e5b13d7490a69c938401d00234ad80a457489c59bdfd29d971be769a176\" alt=\"x times, open parenthesis, 2 x plus 7, close parenthesis\"></span>.</p><p>&nbsp;</p><p></p>\n","correct_answer":["D"],"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 \">2</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">3</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">4</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">7</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}}