// Numbas version: exam_results_page_options
{"name": "Numerical reasoning - percentages of subsets", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Numerical reasoning - percentages of subsets", "tags": ["numerical reasoning", "percentages", "ratio"], "advice": "<p>Calculate separately the percentage of employees who are female and working on the project, and the percentage who are male and working on the project, and add them together.</p>\n  <h4>1. Females</h4>\n  <p>{females}% of the department is female and {femaleproject}% of females are working on the project, hence the proportion of workers who are female and working on the project is {femaleproject}% of {females}% of the workers.</p>\n  <p>In terms of fractions this is \\[ \\frac{\\var{femaleproject}}{100} \\times \\frac{\\var{females}}{100} = \\frac{\\var{femaleproject*females}}{10000} = \\frac{\\var{depfemaleproject}}{100}\\] of the workers, ie {depfemaleproject}%.</p>\n  <p>So <strong>{depfemaleproject}%</strong> of the departmental staff are working on the project and female.</p>\n  <h4>2. Males</h4>\n  <p>&nbsp;</p>\n  <p>{males}% of the department is male and {maleproject}% of males are working on the project, hence the proportion of workers who are male and working on the project is {maleproject}% of {males}% of the workers.</p>\n  <p>In terms of fractions this is \\[ \\frac{\\var{maleproject}}{100} \\times \\frac{\\var{males}}{100} = \\frac{\\var{maleproject*males}}{10000} = \\frac{\\var{depmaleproject}}{100}\\] of the workers, ie {depmaleproject}%.</p>\n  <p>So <strong>{depmaleproject}%</strong> of the departmental staff are working on the project and male.</p>\n  <p>So the total percentage of departmental staff working on the project is $\\var{depfemaleproject}\\% + \\var{depmaleproject}\\% = \\var{project}\\%$.</p>\n  <p>&nbsp;</p>", "rulesets": {}, "parts": [{"prompt": "<p>What percentage of the department is working on the project?</p>\n      <p>[[0]] %</p>", "gaps": [{"minvalue": "{project}", "type": "numberentry", "maxvalue": "{project}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}], "extensions": [], "statement": "<p>In a certain department, {femaleproject}% of the females and {maleproject}% of the males are working on a project. {if(describefemales,females,males)}% of the department is {if(describefemales,'female','male')}.</p>", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"females": {"definition": "//percentage of all employees who are female\n    random(20..80#5)", "name": "females"}, "describefemales": {"definition": "//Give the percentage of females in the statement, or give the males?\n    random(true,false)", "name": "describefemales"}, "femaleproject": {"definition": "//percentage of females working on the project\n    random(10..90#10)", "name": "femaleproject"}, "males": {"definition": "//percentage of all employees who are male\n    100-females", "name": "males"}, "depmaleproject": {"definition": "//proportion of employees who are male and working on the project\n    maleproject*males/100", "name": "depmaleproject"}, "project": {"definition": "//total percentage of the department working on the project\n    (females*femaleproject+males*maleproject)/100", "name": "project"}, "depfemaleproject": {"definition": "//proportion of employees who are female and working on the project\n    femaleproject*females/100", "name": "depfemaleproject"}, "maleproject": {"definition": "//percentage of males working on the project\n    random(10..90#10)", "name": "maleproject"}}, "metadata": {"notes": "", "description": "<p>Given percentages of males and females working on a project, and the percentage of the total staff who are male (or female), find the percentage of all staff working on the project.</p>\n                    <p>Based on question 3 from section 3 of the maths-aid workbook on numerical reasoning.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "John Ian Keng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5078/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "John Ian Keng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5078/"}]}