{"id":"cb_practice_pdf:t8-math-m1-q24","source_id":"cb_practice_pdf","source_item_id":"t8-math-m1-q24","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-8","module_number":1,"position":24,"stem":"- - - -_(x−a)(x−29) - - ~ x−29 = Which of the following are solutions to the given a > 30 equation, where a is a constant and? I. a a+1 II. 29 III.","stimulus":"","stimulus_html":null,"stem_html":"<p>- - - -_(x−a)(x−29) - - ~ x−29 = Which of the following are solutions to the given a &gt; 30 equation, where a is a constant and? I. a a+1 II. 29 III.</p>","rationale_html":"<p>-29 Choice C is correct. Subtracting the expression ^x h from both sides of the 0= - -29 - -29 given equation yields ^x ah^x h ^x h, which can be rewritten as 0= - -29 + -1 -29 ^x ah^x h ^ h^x h. Since the two terms on the right-hand side -29 of this equation have a common factor of ^x h, it can be rewritten as 0= -29 - + -1 0= -29 - -1 - - ^x h^x a ^ hh, or ^x h^x a h. Since x a1 is equivalent - + 0= -29 - -1 to x ^a 1h, the equation ^x h^x a h can be rewritten as 0= -29 - +1 -29=0 ^x h^x ^a hh. By the zero product property, it follows that x or - +1 =0 29 -29=0 =29 x ^a h . Adding to both sides of the equation x yields x . + - +1 =0 = + Adding a 1 to both sides of the equation x ^a h yields x a1 . Therefore, 29 + + 29 the two solutions to the given equation are and a 1. Thus, only a 1 and , not a, are solutions to the given equation. 38 SAT PRACTICE TEST #8 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1 Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["C"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>I and II only</p>","ord":0},{"label":"B","content_html":"<p>I and III only</p>","ord":1},{"label":"C","content_html":"<p>II and III only</p>","ord":2},{"label":"D","content_html":"<p>I, II, and III</p>","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}