{"id":"cb_question_bank:51e437c3-a650-412c-83e1-e5b6ff0bc77b","source_id":"cb_question_bank","source_item_id":"51e437c3-a650-412c-83e1-e5b6ff0bc77b","external_id":null,"ibn":"022197-DC","question_id":"740bf79f","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the figure above, what is the length of line segment NQ ?","stimulus":"The figure presents right triangle M N P. Side M P is horizontal, with vertex M to the left of vertex P. Vertex N lies above side M P, and angle N is a right angle. Point Q lies on horizontal side M P directly below vertex N. Vertical line segment N Q is drawn, forming right triangles M N Q and Q N P. Side M N is labeled 3 and side N P is labeled 4.","stimulus_html":"<div class=\"stimulus_reference \">\n\t<div class=\"standalone_image \"><img src=\"/api/assets/24486c3d51ad25a4397f742284ad6e1c0d05777a9714cd18af5ea5dd15c902df\" alt=\"The figure presents right triangle M N P. Side M P is horizontal, with vertex M to the left of vertex P. Vertex N lies above side M P, and angle N is a right angle. Point Q lies on horizontal side M P directly below vertex N. Vertical line segment N Q is drawn, forming right triangles M N Q and Q N P. Side M N is labeled 3 and side N P is labeled 4.\" width=\"135\" height=\"79\"></div>\n</div>\n","stem_html":"<p class=\"stem_paragraph \">In the figure above, what is the length of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7445f2fc00eda5cb0e22fcdc5f29943579ba62d59e6b83b69e9bfaf44eb95534\" alt=\"line segment NQ\"></span></span> ?</p>\n","rationale_html":"<p>Choice C is correct. First, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/98148b164570fca15eb07c4d18fe3b049a07f5d2b8a22d974e89bc73b0eee200\" alt=\"line segment M P\"></span> is the hypotenuse of right <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/435e0354fe62a8fad8ae12227a3fce7038fcab93d6bc5b0f25f731d9d28c0bc1\" alt=\"triangle M N P\"></span>, whose legs have lengths 3 and 4. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/da9e713a37f8c83b5df2c3bb9aac5e9d7edbde272390d318eede70ff82705616\" alt=\"open parenthesis, the length of line segment M P, close parenthesis, squared, equals, 3 squared plus 4 squared\"></span>, so <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/eebfdba91aba99669769281e3bd28f0bf2f235e63da2bdbf8d5dbd3ee49072c2\" alt=\"open parenthesis, the length of line segment M P, close parenthesis, squared, equals 25\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d50e8e9ed7905898d13ed273369c0e185dda505e95bd48efd1f1680ca169af9c\" alt=\"the length of line segment M P equals 5\"></span>. Second, because <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cacc1be836772fdedfefd866c4709b7a01293550f1c4474aaa3a0eede05b015e\" alt=\"angle M N P\"></span> corresponds to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d35f09848d432af7d8071fa63ed48d59887eb855d1f3c5e076d2369ce3eed4b4\" alt=\"angle N Q P\"></span> and because <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b410457190bd871f78236f131562cb94140e20eb85115ec49604dcc494c13814\" alt=\"angle M P N\"></span> corresponds to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b500d3df3ae3cd9e5d3fb75575be94d9245f76e56f7b9ff870d99e3d80600122\" alt=\"angle N P Q\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/435e0354fe62a8fad8ae12227a3fce7038fcab93d6bc5b0f25f731d9d28c0bc1\" alt=\"triangle M N P\"></span> is similar to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cbc107f811b0dc8a0297c857d0740b5ecd25ea0f8bf77d766d6e559868be6b0a\" alt=\"triangle N Q P\"></span>. The ratio of corresponding sides of similar triangles is constant, so <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4799f666b3b1a53ab8998e97d17a9ecebc63ef759d95f40736ac538dc5daff47\" alt=\"the length of line segment N Q over the length of line segment M N equals the length of line segment N P over the length of line segment M P\"></span>. Since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d50e8e9ed7905898d13ed273369c0e185dda505e95bd48efd1f1680ca169af9c\" alt=\"M P equals 5\"></span> and it’s given that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bbe2e893d23f41299a3d2866332d4c810a143f73b9772f90f67c3a1245c7dd1a\" alt=\"the length of line segment M N equals 3\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f61ba1b50b27e7bcaf348f2f7e82d92efbdce5100130a1e999632ee3223b55aa\" alt=\"the length of line segment N P equals 4\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e24696a2d787c777cb9f8229a73143d311410a675ba8dfbab2141ecf95e9c207\" alt=\"the length of line segment N Q, over 3, equals 4 over 5\"></span>. Solving for <span class=\"italic\">NQ</span> results in <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/91aa070747b5f2d89a651e075468111b026831b9c5cb33a29e9e188c24255155\" alt=\"the length of line segment N Q equals 12 over 5\"></span>, or 2.4.</p><p>Choices A, B, and D are incorrect and may result from setting up incorrect ratios.</p><p>&nbsp;</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.617000+00:00","source_updated_at":"2023-08-02T20:25:59.617000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">2.2</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">2.3</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">2.4</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">2.5</p>\n","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}}