// Numbas version: exam_results_page_options
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"a1*(c2*b1-c1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "part a", "variables": ["a1", "k1", "b1", "k2", "c1", "c2", "k3", "kk", "kk1", "x1"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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>Is the following constraint satisfiable?</p>\n<p>$(\\simplify{{a1} X +&nbsp; Y = {k1}})$ $\\land$ $(\\simplify{{b1} Y + Z = {k2}})$ $\\land$ $(\\simplify{{c1} Y + {c2} Z} &gt; \\var{k3})$</p>\n<p><strong>Step 1: </strong>Isolate $Y$ in the first primitive:</p>\n<p>$Y=$ [[0]]</p>\n<p><strong>Step 2: </strong>Propagate:</p>\n<p>$(Y=$[[0]]$) \\land ($[[1]]$=&nbsp; \\var{k2}) \\land ($[[2]]$&gt; \\var{k3})$</p>\n<p><strong>Step 3: </strong>Isolate $Z$ in the second primitive:</p>\n<p>$Z=$[[3]]</p>\n<p><strong>Step 4: </strong>Propagate:</p>\n<p>$(Y=$[[0]]$) \\land (Z=$[[3]]$) \\land ($[[4]]$&gt; \\var{k3})$</p>\n<p><strong></strong></p>\n<p><strong>Step 5-</strong><strong>Conclusion:</strong> We find that given constraint is satisfied for any number&nbsp;</p>\n<p>$X$[[5]] [[6]]</p>\n<p>and $Y=$[[7]], $Z = $[[8]]</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": 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