// Numbas version: exam_results_page_options
{"name": "Number puzzle (8)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Number puzzle (8)", "tags": ["LANTITE"], "metadata": {"description": "<p>Written for the Western Sydney University MESH numeracy preparation workshop for the LANTITE test (Australia).&nbsp;Students must work backwards to work out what the original number was, or alternatively test out each supplied multiple choice option. There are 8 possible randomised numbers in this question.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Jill is thinking of a number. If this number is doubled, then reduced by one, then squared, the answer is&nbsp; $\\var{answer}$.</p>", "advice": "<p>This&nbsp; problem can be solved with algebra, or by carefully working backwards.</p>\n<p>However, this is an example of a problem where it might be quicker to test each answer, and see which one works. Did you use this strategy?</p>\n<p>For example, test the number&nbsp; $\\var{number-1}$&nbsp; to see if it is the solution.</p>\n<p>First we double the number:&nbsp; $2 \\times \\var{number-1} = \\var{2*(number-1)}$.</p>\n<p>Then we reduce it by one:&nbsp; $\\var{2*(number-1)} - 1 = \\var{2*(number-1)-1}$.</p>\n<p>Next we square this answer:&nbsp; $\\var{2*(number-1)-1}^2 = \\var{2*(number-1)-1} \\times \\var{2*(number-1)-1} = \\var{(2*(number-1)-1)*(2*(number-1)-1)}$.</p>\n<p>However, we were expecting&nbsp; $\\var{answer}$, so&nbsp; $\\var{number-1}$ (the number we just tested) is not the correct solution.</p>\n<p>If you continue in this way to test the other options, you will discover that the number&nbsp; $\\var{number}$&nbsp; works.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"number": {"name": "number", "group": "Ungrouped variables", "definition": "random(3..10)", "description": "<p>The answer to the puzzle. That is, the original number.</p>", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "(2*number-1)^2", "description": "<p>The number displayed in the question.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["number", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_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>Which number was Jill thinking of?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["$\\var{number}$", "$\\var{number-1}$", "$\\var{number+1}$", "$\\var{number*2}$"], "matrix": ["1", 0, 0, 0], "distractors": ["Well done - you are correct!", "Does this number give the right answer if it is doubled, reduced by one, then squared?", "Does this number give the right answer if it is doubled, reduced by one, then squared?", "Does this number give the right answer if it is doubled, reduced by one, then squared?"]}], "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/"}]}