{"id":"cb_question_bank:271cb234-a6b4-4e9e-8424-67f532b012e3","source_id":"cb_question_bank","source_item_id":"271cb234-a6b4-4e9e-8424-67f532b012e3","external_id":"1f3a2144-9cce-41ef-bcb2-8dfc5cc97d8b","ibn":null,"question_id":"190be2fc","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":7,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Data set A consists of 10 positive integers less than 60 . The list shown gives 9 of the integers from data set A. 43 , 45 , 44 , 43 , 38 , 39 , 40 , 46 , 40 The mean of these 9 integers is 42 . If the mean of data set A is an integer that is greater than 42 , what is the value of the largest integer from data set A?","stimulus":"","stimulus_html":null,"stem_html":"<p>Data set A consists of <math alttext=\"10\"><mn>10</mn>\n</math> positive integers less than <math alttext=\"60\"><mn>60</mn>\n</math>. The list shown gives <math alttext=\"9\"><mn>9</mn>\n</math> of the integers from data set A.</p>\n<p style=\"text-align: center;\"><math alttext=\"43\"><mn>43</mn>\n</math>, <math alttext=\"45\"><mn>45</mn>\n</math>, <math alttext=\"44\"><mn>44</mn>\n</math>, <math alttext=\"43\"><mn>43</mn>\n</math>, <math alttext=\"38\"><mn>38</mn>\n</math>, <math alttext=\"39\"><mn>39</mn>\n</math>, <math alttext=\"40\"><mn>40</mn>\n</math>, <math alttext=\"46\"><mn>46</mn>\n</math>, <math alttext=\"40\"><mn>40</mn>\n</math></p>\n<p>The mean of these <math alttext=\"9\"><mn>9</mn>\n</math> integers is <math alttext=\"42\"><mn>42</mn>\n</math>. If the mean of data set A is an integer that is greater than <math alttext=\"42\"><mn>42</mn>\n</math>, what is the value of the largest integer from data set A?</p>","rationale_html":"<p>The correct answer is <math alttext=\"52\"><mn>52</mn>\n</math>. The mean of a data set is calculated by dividing the sum of the data values by the number of values. It’s given that data set A consists of <math alttext=\"10\"><mn>10</mn>\n</math> values, <math alttext=\"9\"><mn>9</mn>\n</math> of which are shown. Let <math alttext=\"x\"><mi>x</mi>\n</math> represent the <math alttext=\"10 th\"><mn>10</mn><mtext>th</mtext></math> data value in data set A, which isn’t shown. The mean of data set A can be found using the expression <math alttext=\"StartFraction 43 plus 45 plus 44 plus 43 plus 38 plus 39 plus 40 plus 46 plus 40 plus x Over 10 EndFraction\"><mfrac><mrow><mn>43</mn><mo>+</mo><mn>45</mn><mo>+</mo><mn>44</mn><mo>+</mo><mn>43</mn><mo>+</mo><mn>38</mn><mo>+</mo><mn>39</mn><mo>+</mo><mn>40</mn><mo>+</mo><mn>46</mn><mo>+</mo><mn>40</mn><mo>+</mo><mi>x</mi></mrow><mn>10</mn></mfrac></math>, or <math alttext=\"StartFraction 378 plus x Over 10 EndFraction\"><mfrac><mrow><mn>378</mn><mo>+</mo><mi>x</mi></mrow><mn>10</mn></mfrac></math>. It’s given that the mean of the <math alttext=\"9\"><mn>9</mn>\n</math> values shown is <math alttext=\"42\"><mn>42</mn>\n</math> and that the mean of all <math alttext=\"10\"><mn>10</mn>\n</math> numbers is greater than <math alttext=\"42\"><mn>42</mn>\n</math>. Consequently, the <math alttext=\"10 th\"><mn>10</mn><mtext>th</mtext></math> data value, <math alttext=\"x\"><mi>x</mi>\n</math>, is larger than <math alttext=\"42\"><mn>42</mn>\n</math>. It’s also given that the data values in data set A are positive integers less than <math alttext=\"60\"><mn>60</mn>\n</math>. Thus, <math alttext=\"42 less than x less than 60\"><mn>42</mn><mo>&lt;</mo><mi>x</mi><mo>&lt;</mo><mn>60</mn></math>. Finally, it’s given that the mean of data set A is an integer. This means that the sum of the <math alttext=\"10\"><mn>10</mn>\n</math> data values, <math alttext=\"378 plus x\"><mn>378</mn><mo>+</mo><mi>x</mi></math>, is divisible by <math alttext=\"10\"><mn>10</mn>\n</math>. Thus, <math alttext=\"378 plus x\"><mn>378</mn><mo>+</mo><mi>x</mi></math> must have a ones digit of <math alttext=\"0\"><mn>0</mn>\n</math>. It follows that <math alttext=\"x\"><mi>x</mi>\n</math> must have a ones digit of <math alttext=\"2\"><mn>2</mn>\n</math>. Since <math alttext=\"42 less than x less than 60\"><mn>42</mn><mo>&lt;</mo><mi>x</mi><mo>&lt;</mo><mn>60</mn></math>&nbsp;and <math alttext=\"x\"><mi>x</mi>\n</math> has a ones digit of <math alttext=\"2\"><mn>2</mn>\n</math>, the only possible value of <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"52\"><mn>52</mn>\n</math>. Since <math alttext=\"52\"><mn>52</mn>\n</math> is larger than any of the integers shown, the largest integer from data set A is <math alttext=\"52\"><mn>52</mn>\n</math>.</p>","correct_answer":["52"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.833000+00:00","source_updated_at":"2023-08-02T20:25:59.833000+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}}