{"id":"cb_question_bank:9b279feb-b310-4fb9-9eed-1718ab4a4ff9","source_id":"cb_question_bank","source_item_id":"9b279feb-b310-4fb9-9eed-1718ab4a4ff9","external_id":null,"ibn":"015183-DC","question_id":"c77ef2fb","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Blood volume, V sub B , in a human can be determined using the equation V sub B equals, the fraction with numerator V sub P, and denominator 1 minus H, end fraction , where V sub P is the plasma volume and H is the hematocrit (the fraction of blood volume that is red blood cells). Which of the following correctly expresses the hematocrit in terms of the blood volume and the plasma volume?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Blood volume,<span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f1b7ab9d381b3aa5b9fc741499681541a61d45af5a1b525537eb39fa8854373c\" alt=\"V sub B\"></span></span>, in a human can be determined using the equation <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8ac1c591832ad56070a55b5bd0212a7e3e3b0e8389edae6044f2b097af26ffcd\" alt=\"V sub B equals, the fraction with numerator V sub P, and denominator 1 minus H, end fraction\"></span></span>, where <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b77b174112743177101efa9a6b3f1888c744bb61fcb6a0d2ef894a5214bf692b\" alt=\"V sub P\"></span></span> is the plasma volume and <span class=\"italic\">H</span> is the hematocrit (the fraction of blood volume that is red blood cells). Which of the following correctly expresses the hematocrit in terms of the blood volume and the plasma volume?</p>\n","rationale_html":"<p>Choice A is correct. The hematocrit can be expressed in terms of the blood volume and the plasma volume by solving the given equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8ac1c591832ad56070a55b5bd0212a7e3e3b0e8389edae6044f2b097af26ffcd\" alt=\"V sub B equals, the fraction with numerator V sub P, and denominator 1 minus H, end fraction\"></span> for <span class=\"italic\">H. </span>Multiplying both sides of this equation by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/99ae7bad7cdc68c313cab0825a6a2c187e6f6340b605f954b043e36cacbe4c9e\" alt=\"open parenthesis, 1 minus H, close parenthesis \"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9e5d710989136e8496a276d6d1cb6287048bdb62a933f1c08ecd0936396dc53f\" alt=\"V sub B, times, open parenthesis, 1 minus H, close parenthesis, equals V sub P\"></span>. Dividing both sides by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f1b7ab9d381b3aa5b9fc741499681541a61d45af5a1b525537eb39fa8854373c\" alt=\"V sub B \"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3f00bdfde0af0a6909e8a8abfe3d11130bbe79a2490335ba399648c805985c69\" alt=\"1 minus H equals, the fraction V sub P, over V sub B\"></span>. Subtracting 1 from both sides yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6db21be9790df405f2aef9ec3f44b69bd5aae035f26f58982415cbf6a959caf0\" alt=\"negative H equals, negative 1 plus, the fraction V sub P over V sub B\"></span>. Dividing both sides by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c1e573ec087416273e06563cee97890abeeed317436562b06a92c8920d4c759d\" alt=\"negative 1\"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b4be7544b5aeacf4afcaff1deb1f49f13e70c205ab1abdb0546f8e872af6b9ac\" alt=\"H equals, 1 minus, the fraction V sub P over V sub B\"></span>.</p><p>Choices B, C, and D are incorrect and may result from errors made when manipulating the equation.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.614000+00:00","source_updated_at":"2023-08-02T20:25:59.614000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b4be7544b5aeacf4afcaff1deb1f49f13e70c205ab1abdb0546f8e872af6b9ac\" alt=\"H equals, 1 minus the fraction V sub P over V sub B\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ce56e6b4182287eaadc9cabf21d830d60e3ada82693754652bbd4c491fa83f71\" alt=\"H equals, the fraction V sub B over V sub P\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3d91e1b34e6261cd510592ab77634749dfe1b8efbaffb452fea3d0a3cce2e788\" alt=\"H equals, 1 plus the fraction V sub B over V sub P\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5a5c54acb9d9eb69ceb5d2c78dc87c1553c01c46ba646fe4aedeb5ced91d2f9c\" alt=\"H equals, V sub B, minus V sub P\"></span></span>\n          </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}}