{"id":"cb_question_bank:54b02ac7-8144-4e19-9478-f2a0125b0578","source_id":"cb_question_bank","source_item_id":"54b02ac7-8144-4e19-9478-f2a0125b0578","external_id":"63296c8a-e373-4a99-89f1-f1ceaa55e479","ibn":null,"question_id":"6d04c89d","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The expression StartFraction 24 Over 6 x plus 42 EndFraction is equivalent to StartFraction 4 Over x plus b EndFraction , where b is a constant and x greater than 0 . What is the value of b ?","stimulus":"","stimulus_html":null,"stem_html":"<p>The expression <math alttext=\"StartFraction 24 Over 6 x plus 42 EndFraction\"><mfrac>\n\t\t<mn>24</mn>\n\t\t<mrow>\n\t\t\t<mrow>\n\t\t\t\t<mn>6</mn>\n\t\t\t\t<mi>x</mi>\n\t\t\t</mrow>\n\t\t\t<mo>+</mo>\n\t\t\t<mn>42</mn>\n\t\t</mrow>\n\t</mfrac>\n</math> is equivalent to <math alttext=\"StartFraction 4 Over x plus b EndFraction\"><mfrac>\n\t\t<mn>4</mn>\n\t\t<mrow>\n\t\t\t<mi>x</mi>\n\t\t\t<mo>+</mo>\n\t\t\t<mi>b</mi>\n\t\t</mrow>\n\t</mfrac>\n</math>, where <em>b</em> is a constant and <math alttext=\"x greater than 0\"><mrow><mi>x</mi><mo>&gt;</mo><mn>0</mn></mrow></math>. What is the value of <em>b</em>?</p>","rationale_html":"<p>Choice A is correct. Since the given expressions are equivalent and the numerator of the second expression is&nbsp;<math alttext=\"one sixth\"><mfrac><mn>1</mn><mn>6</mn></mfrac></math> of the numerator of the first expression, the denominator of the second expression must also be&nbsp;<math alttext=\"one sixth\"><mfrac><mn>1</mn><mn>6</mn></mfrac></math> of the denominator of the first expression. By the distributive property,&nbsp; <math alttext=\"one sixth left parenthesis 6 x plus 42 right parenthesis\"><mfrac><mn>1</mn><mn>6</mn></mfrac><mfenced><mrow><mn>6</mn><mi>x</mi><mo>+</mo><mn>42</mn></mrow></mfenced></math> is equivalent to <math alttext=\"one sixth left parenthesis 6 x right parenthesis plus one sixth left parenthesis 42 right parenthesis\"><mfrac><mn>1</mn><mn>6</mn></mfrac><mfenced><mrow><mn>6</mn><mi>x</mi></mrow></mfenced><mo>+</mo><mfrac><mn>1</mn><mn>6</mn></mfrac><mfenced><mn>42</mn></mfenced></math>, or <math alttext=\"x plus 7\"><mi>x</mi><mo>+</mo><mn>7</mn></math>. Therefore, the value of <math alttext=\"b\"><mi>b</mi>\n</math> is <math alttext=\"7\"><mn>7</mn>\n</math>.</p>\n<p>Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.821000+00:00","source_updated_at":"2023-08-02T20:25:59.821000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"7\"><mn>7</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"10\"><mn>10</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"24\"><mn>24</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"252\"><mn>252</mn>\n</math></p>","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}}