{"id":"cb_question_bank:51ccf03e-f0b0-4dc0-8fa2-e811e6a0d271","source_id":"cb_question_bank","source_item_id":"51ccf03e-f0b0-4dc0-8fa2-e811e6a0d271","external_id":null,"ibn":"022254-DC","question_id":"651d83bb","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.C.","skill":"One-variable data: Distributions and measures of center and spread","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following MUST be true? Every member of team A completed the race in less time than any member of team B. The median time it took the members of team B to complete the race is greater than the median time it took the members of team A to complete the race. There is at least one member of team B who took more time to complete the race than some member of team A.","stimulus":"Two different teams consisting of 10 members each ran in a race. Each member’s completion time of the race was recorded. The mean of the completion times for each team was calculated and is shown below. Team A: 3.41 minutes Team B: 3.79 minutes","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"passage \">\n          <div class=\"prose style:1 \">\n            <p class=\"passage_para \">Two different teams consisting of 10 members each ran in a race. Each member’s completion time of the race was recorded. The mean of the completion times for each team was calculated and is shown below.</p>\n          </div>\n        </div>\n        <p class=\"standalone_statement style:1 \">Team A: 3.41 minutes<br><span class=\"formatted_line_break delivery_mode:PPT \"></span>Team B: 3.79 minutes</p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following MUST be true?</p><ol class=\"list_upper_roman\"><li class=\"list_paragraph \">Every member of team A completed the race in less time than any member of team B.</li>\n            <li class=\"list_paragraph \">The median time it took the members of team B to complete the race is greater than the median time it took the members of team A to complete the race.</li>\n            <li class=\"list_paragraph \">There is at least one member of team B who took more time to complete the race than some member of team A.</li>\n          </ol><p></p>\n","rationale_html":"<p>Choice A is correct. Since the average time for the 10 members of team A is 3.41 minutes, the sum of the 10 times for team A is equal to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ed22fdd2e9b5e5e08975f243c85e32e04f84b7b56fb430201081b49a353aa050\" alt=\"10 times 3 point 4 1, equals 34 point 1\"></span> minutes. Since the average time for the 10 members of team B is 3.79 minutes, the sum of the 10 times for team B is equal to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9e42ff58314a6e3f19f10e8c0bde52c03bca8ec28db30cb281a95acf3674c683\" alt=\"10 times 3 point 7 9, equals 37 point 9\"></span> minutes. Since the sum of the 10 times for team B is greater than the sum of the 10 times for team A, it must be true that at least one of the times for team B must be greater than one of the times for team A. Thus, statement III is true. However, it’s possible that at least some of the times for team A were greater than some of the times for team B. For example, all of team A’s times could be 3.41 minutes, and team B could have 1 time of 3.34 minutes and 9 times of 3.84 minutes. Thus, statement I need not be true. It’s also possible that the median of the times for team B is less than the median of the times for team A. For example, all of team A’s times could be 3.41 minutes, and team B could have 6 times of 3.37 minutes and 4 times of 4.42 minutes; then the median of team B’s times would be 3.37 minutes and the median of team A’s times would be 3.41 minutes. Thus, statement II need not be true.</p><p>Choices B, C, and D are incorrect because neither statement I nor statement II must be true.</p><p></p>\n","correct_answer":["A"],"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 \">III only</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">I and III only</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">II and III only</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">I, II, and III</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}}