{"id":"cb_question_bank:5f766bd8-cf3d-4776-8b31-a6161e8e2d16","source_id":"cb_question_bank","source_item_id":"5f766bd8-cf3d-4776-8b31-a6161e8e2d16","external_id":null,"ibn":"09378-DC","question_id":"df32b09c","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.E.","skill":"Linear inequalities in one or two variables","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Tom scored 85, 78, and 98 on his first three exams in history class. Solving which inequality gives the score, G , on Tom’s fourth exam that will result in a mean score on all four exams of at least 90 ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Tom scored 85, 78, and 98 on his first three exams in history class. Solving which inequality gives the score, <span class=\"italic\">G</span>, on Tom’s fourth exam that will result in a mean score on all four exams of at least 90 ?</p>\n","rationale_html":"<p>Choice C is correct. The mean of the four scores (<span class=\"italic\">G</span>,<span class=\"italic\">&nbsp;</span>85, 78, and 98) can be expressed as&nbsp; <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/49145dd899405c204ef9c6aa90b6f07dbd87b15a97558c1b8fd010656c271f25\" alt=\"the fraction with numerator G, plus 85, plus 78, plus 98, and denominator 4\"></span>. The inequality that expresses the condition that the mean score is at least 90 can therefore be written as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bce6205b52279afb7102ee68099bb58c872cefc4edf35819dde1e69b5b8d44f7\" alt=\"the fraction with numerator G, plus 85, plus 78, plus 98, and denominator 4, is greater than or equal to 90\"></span>.</p><p>Choice A is incorrect. The sum of the scores (<span class=\"italic\">G</span>,<span class=\"italic\">&nbsp;</span>85, 78, and 98)&nbsp;isn’t divided by 4 to express the mean. Choice B is incorrect and may be the result of&nbsp;an algebraic error when multiplying both sides of the inequality by 4.&nbsp;Choice D is incorrect because it doesn’t include <span class=\"italic\">G</span> in the mean with the other three scores.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.637000+00:00","source_updated_at":"2023-08-02T20:25:59.637000+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/7c9e8a33b0d45d6d1cd8e84c014a599a3317d6f306abed3c3895c48de70fd788\" alt=\"90 minus, open parenthesis, 85 plus 78 plus 98, close parenthesis, is less than or equal to 4 G\"></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/428f2c7887951c6b3ce2a9c79672b6ce27d6e859ce25d7ea67a96e9ee4365c51\" alt=\"4 G, plus 85, plus 78, plus 98, is greater than or equal to 360\"></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/0721a96cb34cda543a7b03945a9ac73f5af92649a26a0e93ad0ee2c5eab931c1\" alt=\"the fraction with numerator, open parenthesis, G plus 85 plus 78 plus 98, close parenthesis, and denominator 4, end fraction, is greater than or equal to 90\"></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/e07402bc98f3fb7ccbd4b2c089391345d27ec269d106e1120db35a67a92d4f9d\" alt=\"the fraction with numerator, open parenthesis, 85 plus 78 plus 98, close parenthesis, and denominator 4, end fraction, is greater than or equal to 90 minus 4 G\"></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}}