// Numbas version: finer_feedback_settings
{"name": "Divisibility: 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "rulesets": {}, "extensions": [], "ungrouped_variables": ["seed", "fourer", "num", "thismany", "d1", "d0", "h", "q"], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "<p>Is this number divisible by 2? Half the time the number is, half the time it isn't. Steps&nbsp;give the divisibility test.</p>"}, "variable_groups": [], "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>", "preamble": {"js": "", "css": ""}, "name": "Divisibility: 4", "variables": {"d1": {"name": "d1", "definition": "mod(floor(num/10),10)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "q": {"name": "q", "definition": "h/2", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "h": {"name": "h", "definition": "(d1*10+d0)/2", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "seed": {"name": "seed", "definition": "random(0,1)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "fourer": {"name": "fourer", "definition": "random(300..2000#4)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "d0": {"name": "d0", "definition": "mod(num,10)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "num": {"name": "num", "definition": "if(seed=0, fourer+random(1..3),fourer)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "thismany": {"name": "thismany", "definition": "num/4", "group": "Ungrouped variables", "description": "", "templateType": "anything"}}, "advice": "", "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "parts": [{"distractors": ["", ""], "matrix": ["seed", "1-seed"], "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "maxMarks": 0, "showCellAnswerState": true, "customMarkingAlgorithm": "", "type": "1_n_2", "steps": [{"extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "type": "information", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "prompt": "<p>A number is&nbsp;divisible by $4$ if and only if the last two digits form a number that is divisible by $4$.&nbsp;</p>\n<p>Of course, this means you need to either know all the multiples of $4$ up to $100$ (unlikely) or be willing to divide the two digit number by $4$ (which is as easy as halving then halving again!) and see if you get a whole number!</p>\n<p>Also useful is realising a number must be divisible by $2$ to have any chance of being divisible by $4$.</p>\n<p><span data-jme-visible=\"seed=0\">$\\var{num}$ ends with the digits $\\var{d1}\\var{d0}$, which is NOT divisible by $4$ and so $\\var{num}$ is NOT divisible by $4$.</span></p>\n<p><span data-jme-visible=\"mod(num,2)=1\">How do we know $\\var{d1}\\var{d0}$ isn't divisible by $4$? Well,&nbsp;to be divisible by $4$ a number has to be divisible by $2$ (which means it has to end in a $0,\\,2,\\,4,\\,6$ or $8$) but&nbsp;$\\var{d1}\\var{d0}$ ends in a $\\var{d0}$ so it isn't even divisible by $2$ let alone&nbsp;$4$.</span></p>\n<p><span data-jme-visible=\"seed=0 and mod(num,2)=0\">How do we know $\\var{d1}\\var{d0}$ isn't divisible by $4$? Well, if we halve $\\var{d1}\\var{d0}$ we get $\\var{h}$.&nbsp;But if we try to halve $\\var{h}$ we will not get a whole number and so $\\var{d1}\\var{d0}$ is not divisible by $4$.</span></p>\n<p><span data-jme-visible=\"seed=1\">$\\var{num}$ ends with the digits $\\var{d1}\\var{d0}$ which is divisible by $4$ and so $\\var{num}$ is divisible by $4$.</span></p>\n<p><span data-jme-visible=\"seed=1\">How do we know $\\var{d1}\\var{d0}$ is divisible by $4$? Well, if we halve $\\var{d1}\\var{d0}$ we get $\\var{h}$ and if we halve $\\var{h}$ we get $\\var{q}$ which is a whole number and so&nbsp;$\\var{d1}\\var{d0}$ is divisible by $4$.&nbsp;</span></p>\n<p></p>\n<p></p>", "scripts": {}, "unitTests": [], "marks": 0, "showCorrectAnswer": true, "variableReplacements": []}], "showFeedbackIcon": true, "choices": ["Yes", "No"], "minMarks": 0, "showCorrectAnswer": true, "displayColumns": 0, "displayType": "radiogroup", "prompt": "<p>Is $\\var{num}$ divisible by $4$?</p>", "shuffleChoices": false, "stepsPenalty": "1", "marks": 0, "variableReplacementStrategy": "originalfirst", "unitTests": []}], "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/"}]}