// Numbas version: exam_results_page_options
{"name": "Numerical Reasoning - percentage enlargement", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["dir1", "dir2", "final", "prop1", "prop2", "prop2rel", "verbed1", "verbed2"], "name": "Numerical Reasoning - percentage enlargement", "tags": ["maths-aid", "numerical reasoning", "percentage", "Proportion", "proportion", "ratio"], "advice": "<p>The picture has been {verbed1} to {prop1}% or $\\simplify{{prop1}/100} \\left(=\\frac{\\var{prop1}}{100}\\right)$ of its original size.</p>\n    <p>So to find the size of the first copy we multiply the original size by $\\simplify{{prop1}/100}$.</p>\n    <p>If we then {verbed2} the new size by {prop2}%, the final copy would be {prop2rel}% of the size of the first copy, i.e. $\\simplify{{prop2rel}/100}$ of the size of the first copy.</p>\n    <p>To get the size of the final copy as a proportion of the size of the original copy, we multiply $\\simplify{{prop1}/100}$ by $\\simplify{{prop2rel}/100}$ to get</p>\n    <p>\\[\\simplify{{prop1}/100} \\times \\simplify{{prop2rel}/100} = \\simplify{{prop1*prop2rel}/10000}\\]</p>\n    <p>Now to express this as a percentage we multiply by 100 and we obtain:</p>\n    <p>\\[\\simplify{{prop1*prop2rel}/10000} \\times 100 = \\var{final}\\%.\\]</p>\n    <p>So the final copy is {final}% of the size of the original picture.</p>", "rulesets": {}, "parts": [{"prompt": "<p>What percentage of the size of the original picture was the final copy?</p>\n<p>[[0]] %</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "final", "minValue": "final", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>A picture on a page was {verbed1} on a copier to {prop1}% of its original size, and this copy was then {verbed2} by {prop2}%.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"dir2": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "dir2", "description": ""}, "dir1": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "dir1", "description": ""}, "prop2rel": {"definition": "100+dir2*prop2", "templateType": "anything", "group": "Ungrouped variables", "name": "prop2rel", "description": ""}, "prop1": {"definition": "100+dir1*random(10..40#10)", "templateType": "anything", "group": "Ungrouped variables", "name": "prop1", "description": ""}, "prop2": {"definition": "random(10..40#10)", "templateType": "randrange", "group": "Ungrouped variables", "name": "prop2", "description": ""}, "verbed2": {"definition": "if(dir2=1,'increased','reduced')", "templateType": "anything", "group": "Ungrouped variables", "name": "verbed2", "description": ""}, "verbed1": {"definition": "if(dir1=1,'increased','reduced')", "templateType": "anything", "group": "Ungrouped variables", "name": "verbed1", "description": ""}, "final": {"definition": "(prop1/100)*(100+dir2*prop2)", "templateType": "anything", "group": "Ungrouped variables", "name": "final", "description": ""}}, "metadata": {"notes": "", "description": "<p>Scale a page to some percentage of its original size, then increase/decrease by another percentage. Find the size of the final copy as a percentage of the original.</p>\n                    <p>Based on question 2 from section 3 of the Maths-Aid workbook on numerical reasoning.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "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/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}