{"id":"cb_question_bank:33f9cecc-f6c4-432b-9b5b-995c8c45aae1","source_id":"cb_question_bank","source_item_id":"33f9cecc-f6c4-432b-9b5b-995c8c45aae1","external_id":null,"ibn":"028934-DC","question_id":"d8789a4c","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 above, b and c are positive integers. If the expression is equivalent to x plus b and x is not equal to b , which of the following could be the value of c ?","stimulus":"the fraction with numerator x squared, minus c, and denominator x minus b, end fraction","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/49665efd4759bd857cca9184618ebf775269d96dd4e242821dfd28db37021930\" alt=\"the fraction with numerator x squared, minus c, and denominator x minus b, end fraction\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">In the expression above, <span class=\"italic\">b</span> and <span class=\"italic\">c</span> are positive integers. If the expression is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dffd6a76204a285a842b659626c32300ac0f74800826d6de538e6a7eac5d5409\" alt=\"x plus b \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a7e4bc7212a9c48c0918705af335a802469f8a649a47f964e86c49d19eaa5794\" alt=\"x is not equal to b\"></span>, which of the following could be the value of <span class=\"italic\">c </span>?</p>\n","rationale_html":"<p>Choice A is correct. If the given expression is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dffd6a76204a285a842b659626c32300ac0f74800826d6de538e6a7eac5d5409\" alt=\"x plus b\"></span>, then <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/43466c513dbac45092ee42f337c15ca55ca5c7479260e229d0161e0f85449ef7\" alt=\"the fraction with numerator x squared, minus c, and denominator x minus b, end fraction, equals, x plus b\"></span>, where <span class=\"italic\">x</span> isn’t equal to <span class=\"italic\">b</span>. Multiplying both sides of this equation by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/110423bdaececc133a54bc3c784145e803b0b30ecd34b8a337705bd6c073266a\" alt=\"x  minus b \"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c39b239a4ba4bbd03a7d6e3f549557e899f82c3e85870252f12e5124f5d64e84\" alt=\"x squared, minus c, equals, open parenthesis, x plus b, close parenthesis, times, open parenthesis, x minus b, close parenthesis\"></span>. Since the right-hand side of this equation is in factored form for the difference of squares, the value of <span class=\"italic\">c</span> must be a perfect square. Only choice A gives a perfect square for the value of <span class=\"italic\">c</span>.</p><p>Choices B, C, and D are incorrect. None of these values of <span class=\"italic\">c</span> produces a difference of squares. For example, when 6 is substituted for <span class=\"italic\">c</span> in the given expression, the result is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/368816df41a460e4f8059b68344e7fc875fd8af52de922cdf25e6bd4037c8d17\" alt=\"the fraction with numerator x squared, minus 6, and denominator x minus b, end fraction\"></span>. The expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2f8b7f750b534ffbbe4b6aec2dffb03eba95da47aa5eda1096f9b826592b8819\" alt=\"x squared, minus 6 \"></span> can’t be factored with integer values, and therefore <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/368816df41a460e4f8059b68344e7fc875fd8af52de922cdf25e6bd4037c8d17\" alt=\"the fraction with numerator x squared, minus 6, and denominator x minus b, end fraction \"></span> isn’t equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dffd6a76204a285a842b659626c32300ac0f74800826d6de538e6a7eac5d5409\" alt=\"x plus b\"></span>.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.623000+00:00","source_updated_at":"2023-08-02T20:25:59.623000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">4</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">6</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">8</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">10</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}}