// Numbas version: exam_results_page_options
{"name": "Divisibility: 250", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "rulesets": {}, "variable_groups": [], "name": "Divisibility: 250", "ungrouped_variables": ["seed", "twentyfiver", "num", "thismany", "d0", "d1", "d2"], "statement": "<p>If you are unsure of how to do&nbsp;a question, click on&nbsp;<em>Show steps</em>&nbsp;to see the full working. Then, once you understand how to do the question, click on&nbsp;<em>Try another question like this one</em>&nbsp;to start again.</p>", "metadata": {"description": "<p>Is this number divisible by 250? Half the time the number is, half the time it isn't. Steps&nbsp;give the divisibility test.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "variables": {"d1": {"description": "", "definition": "mod(floor(num/10),10)", "group": "Ungrouped variables", "templateType": "anything", "name": "d1"}, "d0": {"description": "", "definition": "mod(num,10)", "group": "Ungrouped variables", "templateType": "anything", "name": "d0"}, "thismany": {"description": "", "definition": "num/250", "group": "Ungrouped variables", "templateType": "anything", "name": "thismany"}, "num": {"description": "", "definition": "if(seed=0, twentyfiver+random(1..249),twentyfiver)", "group": "Ungrouped variables", "templateType": "anything", "name": "num"}, "d2": {"description": "", "definition": "mod(floor(num/100),10)", "group": "Ungrouped variables", "templateType": "anything", "name": "d2"}, "twentyfiver": {"description": "", "definition": "random(750..10000#250)", "group": "Ungrouped variables", "templateType": "anything", "name": "twentyfiver"}, "seed": {"description": "", "definition": "random(0,1)", "group": "Ungrouped variables", "templateType": "anything", "name": "seed"}}, "parts": [{"stepsPenalty": "1", "marks": 0, "showCellAnswerState": true, "scripts": {}, "shuffleChoices": false, "minMarks": 0, "showCorrectAnswer": true, "distractors": ["", ""], "type": "1_n_2", "displayColumns": 0, "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "showFeedbackIcon": true, "steps": [{"showCorrectAnswer": true, "variableReplacements": [], "type": "information", "scripts": {}, "unitTests": [], "customMarkingAlgorithm": "", "prompt": "<p>A numbers is&nbsp;divisible by $250$ if and only if it ends&nbsp;with the digits&nbsp;$000, \\, 250,\\, 500$ or $750$.&nbsp;</p>\n<p><span data-jme-visible=\"seed=0\">Since $\\var{num}$ ends with the digits $\\var{d2}\\var{d1}\\var{d0}$ it is NOT divisible by $250$.</span></p>\n<p><span data-jme-visible=\"seed=1\">Since $\\var{num}$ ends with the digits $\\var{d2}\\var{d1}\\var{d0}$ it is divisible by $250$. </span></p>\n<p><span data-jme-visible=\"seed=1\">To work out how many $250$s&nbsp;are in a number we could just count up by $250$s or you could cross off the last zero (i.e. divide by $10$) and then divide&nbsp;by $25$, that is, double the number, double it again, and then cross off the last two zero digits (this works because&nbsp;multiplying by $4$ and then dividing by $100$ is equivalent to dividing by $25$). </span></p>\n<p><span data-jme-visible=\"seed=1\">For instance, crossing off the last digit of $\\var{num}$ gives $\\var{num/10}$. Then this doubles to give $\\var{2*num/10}$, doubling again gives $\\var{4*num/10}$ so&nbsp;we can cross of the last two zeros and conclude there are $\\var{thismany}$ two-hundred and fifties&nbsp;in $\\var{num}$. In other words, $\\frac{\\var{num}}{250}=\\var{thismany}$.</span>&nbsp;</p>\n<p></p>\n<p></p>", "marks": 0, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true}], "prompt": "<p>Is $\\var{num}$ divisible by $250$?</p>", "extendBaseMarkingAlgorithm": true, "matrix": ["seed", "1-seed"], "choices": ["Yes", "No"], "variableReplacements": [], "unitTests": [], "customMarkingAlgorithm": "", "maxMarks": 0}], "preamble": {"css": "", "js": ""}, "advice": "", "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}