{"id":"cb_practice_pdf:t9-math-m1-q16","source_id":"cb_practice_pdf","source_item_id":"t9-math-m1-q16","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":null,"form_id":"cb_practice_pdf:test-9","module_number":1,"position":16,"stem":"A wire with a length of 106 inches is cut into two parts. One part has a length of x inches, and the other part has a length of y inches. The value of x is 6 more than 4 times the value of y. What is the value of x?","stimulus":"","stimulus_html":null,"stem_html":"<p>A wire with a length of 106 inches is cut into two parts. One part has a length of x inches, and the other part has a length of y inches. The value of x is 6 more than 4 times the value of y. What is the value of x?</p>","rationale_html":"<p>106 Choice D is correct. It’s given that a wire with a length of inches is cut into two parts. It’s also given that one part has a length of x inches and the other part + 1=0 6 has a length of y inches. This can be represented by the equation x y . It’s also given that the value of x is 6 more than 4 times the value of y. This can be =4 +6 4 +6 represented by the equation x y . Substituting y for x in the equation + =106 4 +6+ =106 5 +6=106 x y yields y y , or y . Subtracting 6 from each side 5 =100 of this equation yields y . Dividing each side of this equation by 5 yields =20 20 =4 +6 =4 20 +6 y . Substituting for y in the equation x y yields x ^ h , or =86 x . Choice A is incorrect. This value represents less than half of the total length of 106 inches; however, x represents the length of the longer part of the wire, since it’s given that the value of x is 6 more than 4 times the value of y. Choice B is 106 incorrect. This value represents less than half of the total length of inches; however, x represents the length of the longer part of the wire, since it’s given that the value of x is 6 more than 4 times the value of y. Choice C is incorrect. This represents a part that is 6 more than the length of the other part, rather than 6 more than 4 times the length of the other part.</p>","correct_answer":["D"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>25</p>","ord":0},{"label":"B","content_html":"<p>28</p>","ord":1},{"label":"C","content_html":"<p>56</p>","ord":2},{"label":"D","content_html":"<p>86</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}}