{"id":"cb_practice_pdf:t8-math-m1-q18","source_id":"cb_practice_pdf","source_item_id":"t8-math-m1-q18","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-8","module_number":1,"position":18,"stem":"- - - - -_3n - - - - - Circle A has a radius of and circle B has a radius 129n of, where n is a positive constant. The area of circle B is how many times the area of circle A?","stimulus":"","stimulus_html":null,"stem_html":"<p>- - - - -_3n - - - - - Circle A has a radius of and circle B has a radius 129n of, where n is a positive constant. The area of circle B is how many times the area of circle A?</p>","rationale_html":"<p>=r 2 Choice D is correct. The area of a circle can be found by using the formula A r , where A is the area and r is the radius of the circle. It’s given that the radius of =r 2 circle A is 3n. Substituting this value for r into the formula A r gives =r 3 2 9r 2 129 A ^ nh , or n . It’s also given that the radius of circle B is n. Substituting =r 2 =r 129 2 16,641r 2 this value for r into the formula A r gives A ^ nh , or n . Dividing 16,641r 2 1,849 n the area of circle B by the area of circle A gives 9r 2 , which simplifies to . n 1,849 Therefore, the area of circle B is times the area of circle A. Choice A is incorrect. This is how many times greater the radius of circle B is than the radius of circle A. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect. This is the coefficient on the term that describes the radius of circle B.</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>43</p>","ord":0},{"label":"B","content_html":"<p>86</p>","ord":1},{"label":"C","content_html":"<p>129</p>","ord":2},{"label":"D","content_html":"<p>1,849</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}}