{"id":"cb_question_bank:1b4a46e5-3584-4c30-994f-c0cb39a136e5","source_id":"cb_question_bank","source_item_id":"1b4a46e5-3584-4c30-994f-c0cb39a136e5","external_id":null,"ibn":"026304-DC","question_id":"8736334b","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":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Data set A and data set B each contain 5 numbers. If the mean of data set A is equal to the mean of data set B, what is the value of x ?","stimulus":"Data set A consists of the 5 numbers: 72, 73, 73, 76, and 76. Data set B consists of the 5 numbers: 61, 64, 74, 85, and x.","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f7f7baaf7b46bb608afbe7a66565bd61b24a8d2c6e9606aa2522e70031740716\" alt=\"Data set A consists of the 5 numbers: 72, 73, 73, 76, and 76. Data set B consists of the 5 numbers: 61, 64, 74, 85, and x.\"></span></p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Data set A and data set B each contain 5 numbers. If the mean of data set A is equal to the mean of data set B, what is the value of <span class=\"italic\">x </span>?</p>\n","rationale_html":"<p>Choice C is correct. The mean of a data set is found by dividing the sum of the values in the data set by the number of values in the data set. Therefore, the mean of data set A is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ef2ad68fb1d37db91c7ad086a10fb801a199e2f9904cb2e9b3dc0f26169c1d65\" alt=\"the fraction with numerator 72, plus 73, plus 73, plus 76, plus 76, and denominator 5\"></span>, which simplifies to 74. The mean of data set B is represented by the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1668b3ef276dec308f24a2c03b3f4cfc53fe6411842ad10ea242489c5b713b52\" alt=\"the fraction with numerator 61, plus 64, plus 74, plus 85, plus x, and denominator 5\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/276aa980a4ad13dfab7fd957389ca7e0a52eb274e18bcf8d96e81c21957087f3\" alt=\"the fraction with numerator 284 plus x, and denominator 5\"></span>. It’s given that the mean of data set A is equal to the mean of data set B. Therefore, the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0011323855b1fc0b5200fd8771cd64e408dcdc3bd8c33113df611499f040fc17\" alt=\"74 equals, the fraction with numerator 284 plus x, and denominator 5\"></span> can be used to solve for <span class=\"italic\">x</span>. Multiplying both sides of this equation by 5 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d62594de32eea9e5d2df5000e15b7e77d50eb79131cf5e9092a61cfcbd7cd48a\" alt=\"370 equals, 284 plus x\"></span>. Subtracting 284 from both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9e7893dd0a3189c38876fc8781ac6f6d43c8fdb7d616c8a4d18b51142b755158\" alt=\"86 equals x\"></span>.</p><p>Choices A, B, and D are incorrect and may result from calculation errors.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.620000+00:00","source_updated_at":"2023-08-02T20:25:59.620000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph block_choice\">77</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph block_choice\">85</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph block_choice\">86</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph block_choice\">95</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}}