// Numbas version: exam_results_page_options
{"name": "Lois'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": [{"functions": {}, "ungrouped_variables": ["females", "describefemales", "femaleproject", "males", "depmaleproject", "project", "depfemaleproject", "maleproject"], "name": "Lois's copy of Numerical reasoning - percentages of subsets", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>To solve this problem we need to 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}.\\]</p>\n<p>In terms of decimals this is {{femaleproject}/100} $\\times$ {{females}/100} = {{femaleproject}*{females}/10000}.</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}.\\]</p>\n<p>In terms of decimals this is {{maleproject}/100} $\\times$ {{males}/100} = {{maleproject}*{males}/10000}.</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;You might find this Mathcentre leaflet on <a href=\"http://www.mathscentre.ac.uk/resources/uploaded/mc-ty-percent-2009-1.pdf\">percentages</a> useful.</p>", "rulesets": {}, "parts": [{"prompt": "<p>What percentage of the department is working on the project?</p>\n      <p>[[0]] %</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{project}", "minValue": "{project}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "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": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"females": {"definition": "//percentage of all employees who are female\n    random(20..80#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "females", "description": ""}, "describefemales": {"definition": "//Give the percentage of females in the statement, or give the males?\n    random(true,false)", "templateType": "anything", "group": "Ungrouped variables", "name": "describefemales", "description": ""}, "femaleproject": {"definition": "//percentage of females working on the project\n    random(10..90#10)", "templateType": "anything", "group": "Ungrouped variables", "name": "femaleproject", "description": ""}, "males": {"definition": "//percentage of all employees who are male\n    100-females", "templateType": "anything", "group": "Ungrouped variables", "name": "males", "description": ""}, "depmaleproject": {"definition": "//proportion of employees who are male and working on the project\n    maleproject*males/100", "templateType": "anything", "group": "Ungrouped variables", "name": "depmaleproject", "description": ""}, "project": {"definition": "//total percentage of the department working on the project\n    (females*femaleproject+males*maleproject)/100", "templateType": "anything", "group": "Ungrouped variables", "name": "project", "description": ""}, "depfemaleproject": {"definition": "//proportion of employees who are female and working on the project\n    femaleproject*females/100", "templateType": "anything", "group": "Ungrouped variables", "name": "depfemaleproject", "description": ""}, "maleproject": {"definition": "//percentage of males working on the project\n    random(10..90#10)", "templateType": "anything", "group": "Ungrouped variables", "name": "maleproject", "description": ""}}, "metadata": {"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>\n<p>Added to calculator test.</p>\n<p>Added advice on using decimals.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}