// Numbas version: exam_results_page_options
{"name": "Q4r Choose the multiples (13)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Q4r Choose the multiples (13)", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p></p>\n<p></p>", "advice": "<p>The <em>multiples</em> of a number are obtained by multiplying the number by $1, 2, 3, 4, 5$ and so on.</p>\n<p>For example, the multiples of $4$ are $4, 8, 12, 16, 20$ and so on.</p>\n<p>You are asked to determine which numbers are multiples of both $\\var{a} \\text{ and } \\var{b}$.</p>\n<p><span data-jme-visible=\"mod(b,a)=0\">In this case, {a} is a factor of {b} so we can simply check for multiples of {b}.&nbsp;</span><span data-jme-visible=\"mod(b,a)=0\">Divide each given number by {b} and if the remainder is zero, then the number is a multiple of both {a} and {b}.</span></p>\n<p><span data-jme-visible=\"mod(a,b)=0\">In this case,&nbsp;{b} is a factor of {a} so we can simply check for multiples of {a}.&nbsp;</span><span data-jme-visible=\"mod(a,b)=0\">Divide each given number by {a} and if the remainder is zero, then the number is a multiple of both {a} and {b}.</span></p>\n<p><span data-jme-visible=\"c=24\">In this case, we can simply check for multiples of 12 (the lowest common multiple of 6 and 4). If a number is a multiple of 12, it will also be a multiple of both 6 and 4.</span></p>\n<p><span data-jme-visible=\"mod(a,b)&lt;&gt;0 and mod(b,a)&lt;&gt;0 and c&lt;&gt;24\">If a number is a multiple of both {a} and {b}, it will be a multiple of $\\var{a} \\times \\var{b} = \\var{c}$.&nbsp;</span><span data-jme-visible=\"mod(a,b)&lt;&gt;0 and mod(b,a)&lt;&gt;0 and c&lt;&gt;24\">Divide each given number by {c} and if the remainder is zero, then the number is a multiple of both {a} and {b}.</span></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Part a", "definition": "random(2..7 except 5)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Part a", "definition": "random(4..6 except a)", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Part a", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Part a", "definition": "random(2..5 except m)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Part a", "definition": "a*b", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Part a", "definition": "random(24..80 except [c,c*2,c*3,c*4,c*5,c*6,c*7,c*8,c*9,c*10])", "description": "", "templateType": "anything", "can_override": false}, "l": {"name": "l", "group": "Part a", "definition": "random(2..6 except m except n)", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Part a", "definition": "a*b*l", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Part a", "definition": "random(x,h,h)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Part a", "variables": ["a", "b", "c", "m", "n", "l", "h", "x", "y"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "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>Do not use a calculator for this question.</p>\n<p>Select all of the numbers below which are multiples of both $\\var{a}$ and $\\var{b}$.</p>", "minMarks": 0, "maxMarks": "0", "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["$\\var{c*m}$", "$\\var{c*n}$", "$\\var{y}$", "$\\var{a+b}$"], "matrix": ["1", "1", "if(y=h,0,1)", 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}]}], "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}