// Numbas version: finer_feedback_settings
{"showQuestionGroupNames": false, "feedback": {"showanswerstate": false, "allowrevealanswer": false, "showtotalmark": false, "advicethreshold": 0.0, "showactualmark": false, "enterreviewmodeimmediately": false, "showexpectedanswerswhen": "never", "showpartfeedbackmessageswhen": "never", "showactualmarkwhen": "never", "showtotalmarkwhen": "never", "showanswerstatewhen": "never", "showadvicewhen": "never"}, "name": "Sharika's copy of Numerical reasoning - money", "duration": 0.0, "shufflequestions": true, "navigation": {"showfrontpage": true, "allowregen": false, "preventleave": true, "showresultspage": "never", "browse": true, "onleave": {"action": "none", "message": ""}, "reverse": true}, "question_groups": [{"pickingStrategy": "all-ordered", "name": "", "questions": [{"name": "Numerical reasoning - tax", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["income", "money", "numerical reasoning", "percentage", "Percentage", "tax"], "metadata": {"description": "<p>Given an annual salary, tax allowance, tax rate and pension deduction, work out a person's take-home pay per month.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>{names} has a salary of <strong>&pound;{commanumber(salary)}</strong> per year.</p>\n<p>{capitalise(he)} has a tax allowance of <strong>&pound;{commanumber(allowance)}</strong> and {he} pays income tax at <strong>{tax}%</strong> on the rest.</p>\n<p>{capitalise(he)} pays into a pension and for this {his} salary is deducted <strong>{pension}%</strong> after tax has been deducted.</p>", "advice": "<p>{names} is only taxed on the amount remaining after taking away the allowance, i.e. $&pound;\\var{commanumber(salary)} - &pound;\\var{commanumber(allowance)} = &pound;\\var{commanumber(salary-allowance)}.$</p>\n<p>Income tax is {tax}% on this $&pound;\\var{commanumber(salary-allowance)}$ and is $&pound;\\var{latex(commanumber(salary-allowance))} \\times \\frac{\\var{tax}}{100} &nbsp;= &pound;\\var{commanumber(taxedincome)}.$</p>\n<p>This leaves {names} with $&pound;\\var{commanumber(salary)} - &pound;\\var{commanumber(taxedincome)} = &pound;\\var{commanumber(aftertax)}.$</p>\n<p>{pension}% of this is for {his} pension contributions, i.e. $&pound;\\var{commanumber(aftertax)} \\times \\frac{\\var{pension}}{100} = &pound;\\var{commanumber(pensiondeduction)}.$</p>\n<p>The amount left is then $&pound;\\var{commanumber(aftertax)} - &pound;\\var{commanumber(pensiondeduction)} = &pound;\\var{commanumber(precround(netincome,2))}.$</p>\n<p>The take home pay per month is hence $\\frac{\\var{netincome}}{12} = &pound;\\var{commanumber(incomepermonth)}$, to the nearest penny.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"salary": {"name": "salary", "group": "Ungrouped variables", "definition": "random(18000..50000#1000)", "description": "", "templateType": "anything", "can_override": false}, "aftertax": {"name": "aftertax", "group": "Ungrouped variables", "definition": "salary-taxedincome", "description": "", "templateType": "anything", "can_override": false}, "incomepermonth": {"name": "incomepermonth", "group": "Ungrouped variables", "definition": "precround(netincome/12,2)", "description": "", "templateType": "anything", "can_override": false}, "his": {"name": "his", "group": "Ungrouped variables", "definition": "if(he='he','his','her')", "description": "", "templateType": "anything", "can_override": false}, "names": {"name": "names", "group": "Ungrouped variables", "definition": "if(he='he',random(['Bob','Bill','Ben','Barry']),random(['Bridget','Beth','Bea','Beatrice']))", "description": "", "templateType": "anything", "can_override": false}, "netincome": {"name": "netincome", "group": "Ungrouped variables", "definition": "(allowance+(salary-allowance)*(1-tax/100))*(1-pension/100)", "description": "", "templateType": "anything", "can_override": false}, "pensiondeduction": {"name": "pensiondeduction", "group": "Ungrouped variables", "definition": "aftertax*pension/100", "description": "", "templateType": "anything", "can_override": false}, "tax": {"name": "tax", "group": "Ungrouped variables", "definition": "random(15..30)", "description": "", "templateType": "anything", "can_override": false}, "pension": {"name": "pension", "group": "Ungrouped variables", "definition": "random(3..15)", "description": "", "templateType": "anything", "can_override": false}, "taxedincome": {"name": "taxedincome", "group": "Ungrouped variables", "definition": "(salary-allowance)*tax/100", "description": "", "templateType": "anything", "can_override": false}, "allowance": {"name": "allowance", "group": "Ungrouped variables", "definition": "random(1000..10000#1000)", "description": "", "templateType": "anything", "can_override": false}, "he": {"name": "he", "group": "Ungrouped variables", "definition": "random('he','she')", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["salary", "aftertax", "incomepermonth", "his", "names", "netincome", "pensiondeduction", "tax", "pension", "taxedincome", "he", "allowance"], "variable_groups": [], "functions": {"commanumber": {"parameters": [["n", "number"]], "type": "string", "language": "javascript", "definition": "var parts=n.toString().split(\".\");\n        if(parts[1] && parts[1].length<2) {\n      parts[1]+='0';\n        }\n        return parts[0].replace(/\\B(?=(\\d{3})+(?!\\d))/g, \",\") + (parts[1] ? \".\" + parts[1] : \"\");"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>How much does {he} get per month, assuming that these are the only deductions?</p>\n<p>&pound; [[0]] (to the nearest penny)</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "incomepermonth", "maxValue": "incomepermonth", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 2, "precisionPartialCredit": 100, "precisionMessage": "", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Numerical reasoning - price markup", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "functions": {}, "tags": ["maths-aid", "money", "numerical reasoning", "percentage", "price", "profit"], "advice": "<p>In order to realise a profit of {profit}%, the selling price of the item must be {100+profit}% of the cost of production.</p>\n  <p>This price is $\\frac{\\var{100+profit}}{100} \\times \\var{produce} = &pound;\\var{sell}.$</p>\n  <p>When rounding this to the nearest penny, a decision has to be made whether the price is &pound;{floor(sell*100)/100} or &pound;{ceil(sell*100)/100}. Usually,&nbsp;if the&nbsp;next digit after the one being rounded is&nbsp;{if(fract(sell*100)&lt;0.5,'less than 5 then we round down','greater than or equal to 5 then we round up')}, so we take the price to be <strong>&pound;{dpformat(sell,2)}</strong>.</p>", "rulesets": {}, "parts": [{"prompt": "<p>Give your answer to the nearest penny.</p>\n      <p>&pound; [[0]]</p>", "gaps": [{"precisiontype": "dp", "precisionmessage": "<p>You didn't give your answer to the nearest penny. Round your answer to two decimal places.</p>", "maxvalue": "precround(sell,2)+0.005", "minvalue": "precround(sell,2)-0.005", "precisionpartialcredit": 50.0, "precision": 2.0, "marks": 1.0, "type": "numberentry", "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}], "statement": "<p>An item costs <strong>&pound;{dpformat(produce,2)}&nbsp;</strong>to produce. How much should the manufacturer sell these items for if it wants to realise a profit of&nbsp;<strong>{profit}%</strong>&nbsp;on these items?</p>", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"profit": {"definition": "random(5..35#10)", "name": "profit"}, "sell": {"definition": "produce*(1+profit/100)", "name": "sell"}, "produce": {"definition": "random(2..10)+random(0.25,0.75,0.50)", "name": "produce"}}, "metadata": {"notes": "", "description": "<p>Given the cost to produce an item and a desired markup, calculate the appropriate sale price.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Numerical reasoning - average salary", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "functions": {"commanumber": {"definition": "var parts=n.toString().split(\".\");\n        if(parts[1] && parts[1].length<2) {\n      parts[1]+='0';\n        }\n        return parts[0].replace(/\\B(?=(\\d{3})+(?!\\d))/g, \",\") + (parts[1] ? \".\" + parts[1] : \"\");", "type": "string", "language": "javascript", "parameters": [["n", "number"]]}}, "tags": ["average", "maths-aid", "mean", "money", "numerical reasoning", "percentage", "weighted"], "advice": "<p>This is a weighted average.</p>\n    <p>The average value is given by multiplying each salary value by the frequency with which it occurs amongst the staff (in fraction form), and adding the resulting numbers together.</p>\n    <p>For example, the salary &pound;{commanumber(salary[0])} has a frequency of {per[0]}% which is $\\frac{\\var{per[0]}}{100} = \\var{per[0]/100}$. When we multiply these together we get \\[ &pound;\\var{latex(commanumber(salary[0]))} \\times \\frac{\\var{per[0]}}{100} = \\var{salary[0]*per[0]/100}. \\]</p>\n    <p>For this question we have 4 salary values and the weighted average is \\[\\begin{align} &amp; \\frac{\\var{per[0]}}{100} \\times \\var{latex(commanumber(salary[0]))} + \\frac{\\var{per[1]}}{100} \\times \\var{latex(commanumber(salary[1]))} + \\frac{\\var{per[2]}}{100} \\times \\var{latex(commanumber(salary[2]))} + \\frac{\\var{per[3]}}{100} \\times \\var{latex(commanumber(salary[3]))} \\\\ &amp;= &pound;\\var{latex(commanumber(salary[0]*per[0]/100))} +&nbsp;&pound;\\var{latex(commanumber(salary[1]*per[1]/100))} + &pound;\\var{latex(commanumber(salary[2]*per[2]/100))} + &pound;\\var{latex(commanumber(salary[3]*per[3]/100))} \\\\ &amp;= &pound;\\var{latex(commanumber(average))} \\end{align} \\]</p>", "rulesets": {}, "parts": [{"prompt": "<p>What is the average salary?</p>\n        <p>&pound; [[0]]</p>", "gaps": [{"minvalue": "average", "type": "numberentry", "maxvalue": "average", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}], "statement": "<p>In a department {per[0]}% of the staff have a salary of &pound;{commanumber(salary[0])}, {per[1]}% a salary of &pound;{commanumber(salary[1])}, {per[2]}% a salary of &pound;{commanumber(salary[2])}, and {per[3]}% a salary of &pound;{commanumber(salary[3])}.</p>", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"salary": {"definition": "shuffle([salary0,salary1,salary2,salary3])", "name": "salary"}, "salary1": {"definition": "random(15000..50000#5000 except salary0)", "name": "salary1"}, "salary0": {"definition": "random(15000..50000#5000)", "name": "salary0"}, "salary3": {"definition": "random(15000..50000#5000 except [salary0,salary1,salary2])", "name": "salary3"}, "salary2": {"definition": "random(15000..50000#5000 except [salary0,salary1])", "name": "salary2"}, "average": {"definition": "(per[0]*salary[0]+per[1]*salary[1]+per[2]*salary[2]+per[3]*salary[3])/100", "name": "average"}, "per": {"definition": "shuffle([per0,per1,per2,per3])", "name": "per"}, "per3": {"definition": "100-per0-per1-per2", "name": "per3"}, "per2": {"definition": "random(10..min(50,90-per0-per1)#10)", "name": "per2"}, "per1": {"definition": "random(10..min(50,80-per0)#10)", "name": "per1"}, "per0": {"definition": "random(10..50#10)", "name": "per0"}}, "metadata": {"notes": "", "description": "<p>Compute the weighted average salary in a department, given four salary levels and the percentages of staff earning them.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Numerical reasoning - lottery syndicate", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["lottery", "maths-aid", "money", "numerical reasoning", "ratio", "shares"], "metadata": {"description": "<p>Given the stakes of three people in a lottery syndicate, and the amount the syndicate won, work out each person's share of the winnings.</p>\n                    <p>Based on question 4 from section 3.2 of the Maths-Aid workbook on numerical reasoning.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>{names[0]}, {names[1]} and {names[2]} agree to buy {numbernames[total]} pounds' worth of lottery tickets, with {names[0]} contributing &pound;{share[0]}, {names[1]} contributing &pound;{share[1]} and {names[2]} contributing &pound;{share[2]}.</p>\n<p>They agree that if they win anything with any of these tickets that it should be shared out in the same ratio as their contributions.</p>", "advice": "<p>Their agreement means that the winnings should go to {names[0]}, {names[1]} and {names[2]} in the ratio $\\var{share[0]}:\\var{share[1]}:\\var{share[2]}$. Think of these as being shares in the winnings.</p>\n<p>There are $\\var{share[0]}+\\var{share[1]}+\\var{share[2]} = \\var{total}$ shares in all for the &pound;{win}.</p>\n<p>Hence each share is worth $&pound;\\var{win} \\div \\var{total} = &pound;\\var{part}$.</p>\n<p>So {names[0]} gets {share[0]} {pluralise(share[0],'share','shares')} = $\\var{share[0]} \\times &pound;\\var{part} = &pound;\\var{winnings[0]}$, {names[1]} {share[1]} {pluralise(share[1],'share','shares')} = $\\var{share[1]} \\times &pound;\\var{part} = &pound;\\var{winnings[1]}$ and {names[2]} {share[2]} {pluralise(share[2],'share','shares')} = $\\var{share[2]} \\times &pound;\\var{part} = &pound;\\var{winnings[2]}$.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"numbernames": {"name": "numbernames", "group": "Ungrouped variables", "definition": "['zero','one','two','three','four','five','six','seven','eight','nine','ten','eleven','twelve','thirteen','fourteen','fifteen','sixteen','seventeen','eighteen','nineteen']", "description": "", "templateType": "anything", "can_override": false}, "winnings": {"name": "winnings", "group": "Ungrouped variables", "definition": "map(x*part,x,share)", "description": "", "templateType": "anything", "can_override": false}, "names": {"name": "names", "group": "Ungrouped variables", "definition": "shuffle(['Bob','Terry','Cilla','Jim','Margaret','Cyril','Ethel','Horace','Beryl'])[0..3]", "description": "", "templateType": "anything", "can_override": false}, "share": {"name": "share", "group": "Ungrouped variables", "definition": "shuffle([share0,share1,share2])", "description": "", "templateType": "anything", "can_override": false}, "share1": {"name": "share1", "group": "Ungrouped variables", "definition": "random(1..min(floor(total/2),total-1-share0))", "description": "", "templateType": "anything", "can_override": false}, "share0": {"name": "share0", "group": "Ungrouped variables", "definition": "random(1..floor(total/2))", "description": "", "templateType": "anything", "can_override": false}, "share2": {"name": "share2", "group": "Ungrouped variables", "definition": "total-share0-share1", "description": "", "templateType": "anything", "can_override": false}, "part": {"name": "part", "group": "Ungrouped variables", "definition": "win/total", "description": "", "templateType": "anything", "can_override": false}, "win": {"name": "win", "group": "Ungrouped variables", "definition": "random(2..10)*total*5", "description": "", "templateType": "anything", "can_override": false}, "total": {"name": "total", "group": "Ungrouped variables", "definition": "random(6..15)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["numbernames", "winnings", "names", "share", "share0", "share1", "share2", "part", "win", "total"], "variable_groups": [], "functions": {"pluralise": {"parameters": [["n", "number"], ["single", "string"], ["plural", "string"]], "type": "string", "language": "javascript", "definition": "return Numbas.util.pluralise(n,single,plural);"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>They win &pound;{win}. How much does each get?</p>\n<table>\n<tbody>\n<tr>\n<td>{names[0]}</td>\n<td>&pound; [[0]]</td>\n</tr>\n<tr>\n<td>{names[1]}</td>\n<td>&pound; [[1]]</td>\n</tr>\n<tr>\n<td>{names[2]}</td>\n<td>&pound; [[2]]</td>\n</tr>\n</tbody>\n</table>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "winnings[0]", "maxValue": "winnings[0]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "winnings[1]", "maxValue": "winnings[1]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "winnings[2]", "maxValue": "winnings[2]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}], "pickQuestions": 0}], "timing": {"timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "percentpass": 0.0, "allQuestions": true, "pickQuestions": 0, "questions": [], "metadata": {"description": "<p>Questions about percentage and ratio, applied to finance.</p>\n                <p>Based on section 3.2 of the Maths-Aid workbook on numerical reasoning.</p>", "licence": "Creative Commons Attribution 4.0 International", "notes": ""}, "type": "exam", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Sharika Mesba", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3475/"}], "extensions": [], "custom_part_types": [], "resources": []}