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{"name": "James's copy of 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": [{"name": "James's copy of Numerical reasoning - percentages of subsets", "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": {}, "type": "question", "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>", "functions": {}, "variable_groups": [], "parts": [{"gaps": [{"maxvalue": "{project}", "showPrecisionHint": false, "marks": 1.0, "type": "numberentry", "minvalue": "{project}"}], "marks": 0.0, "type": "gapfill", "prompt": "<p>What percentage of the department is working on the project?</p>\n      <p>[[0]] %</p>"}], "progress": "ready", "variables": {"femaleproject": {"name": "femaleproject", "definition": "//percentage of females working on the project\n    random(10..90#10)"}, "depfemaleproject": {"name": "depfemaleproject", "definition": "//proportion of employees who are female and working on the project\n    femaleproject*females/100"}, "females": {"name": "females", "definition": "//percentage of all employees who are female\n    random(20..80#5)"}, "maleproject": {"name": "maleproject", "definition": "//percentage of males working on the project\n    random(10..90#10)"}, "males": {"name": "males", "definition": "//percentage of all employees who are male\n    100-females"}, "depmaleproject": {"name": "depmaleproject", "definition": "//proportion of employees who are male and working on the project\n    maleproject*males/100"}, "describefemales": {"name": "describefemales", "definition": "//Give the percentage of females in the statement, or give the males?\n    random(true,false)"}, "project": {"name": "project", "definition": "//total percentage of the department working on the project\n    (females*femaleproject+males*maleproject)/100"}}, "tags": ["numerical reasoning", "percentages", "ratio"], "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, "extensions": [], "question_groups": [{"name": "", "pickQuestions": 0, "pickingStrategy": "all-ordered", "questions": []}], "contributors": [{"name": "James McEvoy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/922/"}]}]}], "contributors": [{"name": "James McEvoy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/922/"}]}