{"id":"cb_question_bank:a73a938a-d5cc-4213-aabe-43e9f19bf06c","source_id":"cb_question_bank","source_item_id":"a73a938a-d5cc-4213-aabe-43e9f19bf06c","external_id":null,"ibn":"028792-DC","question_id":"881ef5f5","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":"M","score_band":5,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If a is the mean and b is the median of nine consecutive integers, what is the value of the absolute value of, a, minus b, end absolute value ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">If <span class=\"italic\">a</span> is the mean and <span class=\"italic\">b</span> is the median of nine consecutive integers, what is the value of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1372b46eb28fde14702230caa7655831169773af8eb50c104d6aad7b02103122\" alt=\"the absolute value of, a, minus b, end absolute value\"></span></span> ?</p>\n","rationale_html":"<p>The correct answer is 0. Any nine consecutive integers can be written as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fc558131a7b65768c611c3ac386b023b73100f603708ed0fff57ecd8a33c90ea\" alt=\"k\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5827cb5807634acaee8c2ca9240da1e28f0fd7a32458cc5f1adbb241b9d748d9\" alt=\"k plus 1\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/87ceef465802e44383adbff801edaa7135246f9506d8f5dce92e9b3732322155\" alt=\"k plus 2\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a54edd1cd4a977df5ada6093e8e1c35e3f53e190cf49dbfb7ab6c83092925711\" alt=\"k plus 3\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a8653f70b116a43a13ad497a3d6f082c70eeab005a75ef70177211e001a73b7d\" alt=\"k plus 4\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c430ddae779ea34109bb482be333baa05e5f3d29d3330ee3b9f12f690b6dad18\" alt=\"k plus 5\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/055fed80b0db764646dd87049b4dc5c69d09c42ff65154c3096383c869e48f25\" alt=\"k plus 6\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0c479dba3c6c4efd3b8699de4a216587b2520b1b5f459fcb52ad1c1518830aec\" alt=\"k plus 7\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/30cb1df771606fdc40c97ad36d16caccc54e8f786e49369de065e008bbd697d5\" alt=\"k plus 8\"></span>. The mean of the integers is their sum divided by 9: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/49f02c9d2daf99e0d1f6038dbb4dd939a8d2179732837b5ecb8ccba58922d455\" alt=\"the fraction with numerator open parenthesis, k plus, k plus 1, plus, k plus 2, plus, dot dot dot, plus, k plus 8, close parenthesis, and denominator 9, equals, the fraction with numerator, open parenthesis, 9 k plus 36, close parenthesis, and denominator 9\"></span>, which simplifies to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a8653f70b116a43a13ad497a3d6f082c70eeab005a75ef70177211e001a73b7d\" alt=\"k plus 4\"></span>. So <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/771bf32d4beeec15063e18f64aee1946cee10cbaa90ca7435834271f5d0fa1b5\" alt=\"a, equals, k plus 4\"></span>. Since there is an odd number of integers (nine), the median is the integer in the middle when all the integers are ordered from least to greatest: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a8653f70b116a43a13ad497a3d6f082c70eeab005a75ef70177211e001a73b7d\" alt=\"k plus 4\"></span>. So <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2d0060288d376e9c6b64b911c6d2e4f6db85394c674852487adf18d476c23ab3\" alt=\"b equals, k plus 4\"></span>. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b3ac4428ad3e987b4f8c5c76ef2387b9813ec821260ca0480f2e25917f6c562c\" alt=\"the absolute value of a, minus b, end absolute value, equals, the absolute value of, open parenthesis, k plus 4, close parenthesis, minus, open parenthesis, k plus 4, close parenthesis, end absolute value\"></span>, which is 0.</p>\n","correct_answer":["0"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.622000+00:00","source_updated_at":"2023-08-02T20:25:59.622000+00:00","options":[],"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}}