{"id":"cb_practice_pdf:t11-math-m2-q23","source_id":"cb_practice_pdf","source_item_id":"t11-math-m2-q23","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-11","module_number":2,"position":23,"stem":"23 In the figure shown, WZ and XY intersect at = = point Q, YQ 21, WQ 70, WX 60, and XQ = 120. What is the length of (=)/YZ?","stimulus":"","stimulus_html":null,"stem_html":"<p>23 In the figure shown, WZ and XY intersect at = = point Q, YQ 21, WQ 70, WX 60, and XQ = 120. What is the length of (=)/YZ?</p>","rationale_html":"<p>Choice A is correct. It’s given that WZ and XY intersect at point Q. It follows that + + WQX and YQZ are vertical angles, which means they are congruent to each + + other. The figure shows that W and Y both have a measure of a°, so they are 3 3 congruent to each other. Therefore, QWX and QYZ are similar triangles, where WQ corresponds to YQ and WX corresponds to YZ. Since the lengths of YZ =WX corresponding sides in similar triangles are proportional, it follows that . YQ WQ =21 =70 =60 21 70 It’s given that YQ , WQ , and WX . Substituting for YQ, for WQ, 60 6 60 YZ =WX YZ= YZ= and for WX in the equation yields 21 70, or 21 7. Multiplying each YQ WQ 21 =18 18 side of this equation by yields YZ . Therefore, the length of YZ is . Choice B is incorrect. This is the length of QZ, not YZ. Choice C is incorrect. This is the length of XQ, not YZ. Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>18</p>","ord":0},{"label":"B","content_html":"<p>36</p>","ord":1},{"label":"C","content_html":"<p>120</p>","ord":2},{"label":"D","content_html":"<p>200</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}}