{"id":"cb_question_bank:aea53a06-ddd1-4446-aba5-817c07214dbc","source_id":"cb_question_bank","source_item_id":"aea53a06-ddd1-4446-aba5-817c07214dbc","external_id":null,"ibn":"11250-DC","question_id":"87a3de81","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":"M","score_band":5,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If a is a solution of the equation above and a is greater than 0 , what is the value of a ?","stimulus":"x squared plus x, minus 12, equals 0","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/37dea9f591bdb309c99bfab75b9777a3559e9ad27619415e20cb3752ec506f12\" alt=\"x squared plus x, minus 12, equals 0\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">If <span class=\"italic\">a</span> is a solution of the equation above and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/33c34751dc58079dfcedcc52bf400c7ce4b20cd84522965f4c30a604a8fa62eb\" alt=\"a is greater than 0\"></span></span>, what is the value of <span class=\"italic\">a</span> ?</p>\n","rationale_html":"<p>The correct answer is 3. The solution to the given equation can be found by factoring the quadratic expression. The factors can be determined by finding two numbers with a sum of 1 and a product of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/adaa4559a5484d45e4ce9d629baf4e891fe63eb871ec062e9f04e820221ce8d4\" alt=\"negative 12\"></span>. The two numbers that meet these constraints are 4 and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b62558094601a23d6fe95ffbc037ca0c41dd10264b6e51f4163b9ed575c135a3\" alt=\"negative 3\"></span>. Therefore, the given equation can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4f268a4c68812f235de13edaa5a8324a06e32834061a097a896ab63a54eb7275\" alt=\"open parenthesis, x plus 4, close parenthesis, times, open parenthesis, x minus 3, close parenthesis, equals 0\"></span>. It follows that the solutions to the equation are <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b2271bf6a6395b1b35156f1d6b258d0ebf35d2f79134117675d045c2f48b0d63\" alt=\"x equals negative 4\"></span> or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ceba1165e53a8baa1cf03f75cde85da34750b8ab2728ef25385d77f80f8276c5\" alt=\"x equals 3\"></span>. Since it is given that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2e1b675bff50b2e5174ef90e2dbd3e6d03eab148944a57c76c89cb483a8fb2aa\" alt=\"a, is greater than 0\"></span>, <span class=\"italic\">a</span> must equal 3.</p>\n","correct_answer":["3"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.638000+00:00","source_updated_at":"2023-08-02T20:25:59.638000+00:00","options":[],"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}}