// Numbas version: exam_results_page_options
{"name": "Lois's copy of 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": "Lois's copy of Numerical Reasoning - percentage enlargement", "tags": [], "advice": "<p>The picture was&nbsp;first&nbsp;{verbed1} to {prop1}% of its original size. So we need to multiply its size by&nbsp;$ \\frac{\\var{prop1}}{100}=\\simplify{{prop1}/100}$ or {{prop1}/100}.&nbsp;</p>\n<p>The first copy is then {verbed2} by&nbsp;{prop2}% &nbsp;so we need to multiply by&nbsp;$\\frac{\\var{prop2rel}}{100}=\\simplify{{prop2rel}/100}$ &nbsp;or {{prop2rel}/100}.</p>\n<p>To find out how the size of the final copy compares to the original we need to multiply these two numbers together.</p>\n<p>Using fractions we have:</p>\n<p>\\[\\simplify{{prop1}/100} \\times \\simplify{{prop2rel}/100} = \\simplify{{prop1*prop2rel}/10000}\\]&nbsp;</p>\n<p>\\[\\simplify{{prop1*prop2rel}/10000} \\times 100 = \\var{final}. \\] So the final copy is {final}% of the size of the original picture.</p>\n<p>Using decimals we have:</p>\n<p>{{prop1}/100} $\\times$ {{prop2rel}/100} = {{prop1}*{prop2rel}/10000} = {final}%.</p>\n<p></p>\n<p>You can find more information about percentages on&nbsp;this <a href=\"http://www.mathscentre.ac.uk/resources/uploaded/mc-ty-percent-2009-1.pdf\">leaflet</a> from Mathcentre.</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", "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>A picture 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,'enlarged','reduced')", "templateType": "anything", "group": "Ungrouped variables", "name": "verbed2", "description": ""}, "verbed1": {"definition": "if(dir1=1,'enlarged','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": {"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>\n<p>(Added a decimal version to advice - and changed increased to enlarged)</p>\n<p>Used in non-calculator quiz.</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/"}]}