In this question you have to remember that R can overwrite the assignment of variables.
\nLine 1 assigns $x=\\var{x}$.
\nIn line 2 R reassigns $x$ as the solution to the equation using $x=\\var{x}$ from line 1. Thus $x=\\simplify[basic,!collectnumbers]{{a}*{x}+{b}}$, which gives $x=\\var{a*x+b}$.
", "rulesets": {}, "parts": [{"distractors": ["", "", "", ""], "prompt": "What is the value of $x$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": true, "scripts": {}, "choices": ["{a*x+b}
", "{x}
", "{x+1}
", "{a*x}
"], "displayType": "radiogroup", "maxMarks": "1", "marks": 0, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": "0"}], "statement": "> x = {x}
> x = {a}*x+{b}
> x ", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}, "x": {"definition": "random(2..20#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "x", "description": ""}, "b": {"definition": "random(2..16#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Question 2 Basic what is x", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "functions": {}, "ungrouped_variables": ["x", "y", "a", "b"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "a) Lines 1 and 2 assign the values of $x$ and $y$.
\nLine 3 reassigns a new value for $x$ by solving an equation involving the values in lines 1 and 2. This gives $x=\\simplify[basic,!collectnumbers]{{x}+{a}*{y}}$, therefore R has reassigned a new value for $x$. This is $x=\\var{{x}+{a}*{y}}$.
\nLine 4 shows a calculation involving $x$. This bit is designed to catch you out. We haven't reassigned $x$ as a new value here so this doesn't change our $x$ value.
\nTherefore the value of $x$ remains as $x=\\var{{x}+{a}*{y}}$.
\nb) Line 2 assigns the value of $y$.
", "rulesets": {}, "parts": [{"displayColumns": 0, "prompt": "What is the value of $x$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": true, "distractors": ["", "", "", ""], "choices": ["{x+a*y}
", "{x+a*y+b}
", "{x}
", "{x+b}
"], "displayType": "radiogroup", "maxMarks": "1", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"displayColumns": 0, "prompt": "What is the value of $y$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": false, "distractors": ["", "", "", ""], "choices": ["{y}
", "{x}
", "{x+y}
", "{y+2}
"], "displayType": "radiogroup", "maxMarks": "1", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}], "statement": "> x = {x}
> y = {y}
> x = x + {a}*y
> x + {b}
> x ", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"y": {"definition": "random(10..20#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "y", "description": ""}, "x": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "x", "description": ""}, "b": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b", "description": ""}, "a": {"definition": "random(2..15#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}}, "metadata": {"notes": "Advice section doesn't show up when you click reveal?
", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Question 3 basic what is x ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "functions": {}, "ungrouped_variables": ["a", "b"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "a) Line 1 assigns $x=\\var{a}$.
\nb) $z=x/y$.
", "rulesets": {}, "parts": [{"prompt": "What is the value of $x$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": true, "scripts": {}, "choices": ["{a}
", "{a+a}
", "{b+a}
", "{b}
"], "marks": 0, "displayType": "radiogroup", "maxMarks": "1", "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "What is the value of $z$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": false, "scripts": {}, "choices": ["{a/b}
", "{a+a/b}
", "{2/b}
", "{a}
"], "marks": 0, "displayType": "radiogroup", "maxMarks": "1", "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}], "statement": "> x = {a}
> y = {b}
> x + {a}
> x
> z = x/y ", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..20#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}, "b": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Question 4 basic what is x", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "functions": {}, "ungrouped_variables": ["x", "a", "b"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "a) Line 1 assigns $x$ and line 2 assigns $y$ using $x$, therefore $y=\\var{{a}*{x}}$.
Line 3 is a calculation that uses $y$ but never reassigns any of the variables.
Line 4 then overwrites $x$ using $y$. Therefore $x=\\var{{a}*{b}*{x}}$.
b) The value of $z$ is the same as the value of $x$.
", "rulesets": {}, "parts": [{"prompt": "What is the value of $x$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": false, "scripts": {}, "choices": ["{b*a*x}
", "{b + a*x + 2}
", "{x}
", "{b + 2}
"], "marks": 0, "displayType": "radiogroup", "maxMarks": "1", "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "What is the value of $z$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": false, "scripts": {}, "choices": ["{b*a*x}
", "{b+a}
", "{b}
", "{a*x}
"], "marks": 0, "displayType": "radiogroup", "maxMarks": "1", "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}], "statement": "> x = {x}
> y = {a}*x
> y + 2
> x = {b}*y
> z = {b}*y", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}, "x": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "x", "description": ""}, "b": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Question 5 what is x", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "functions": {}, "ungrouped_variables": ["y"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "a) Line 1 assigns $y=\\var{y}$.
\nLine 2 assigns $x=\\var{y+2}$.
\nLine 3 reassigns $x$ using $x=\\var{y+2}$. Therefore $x=\\var{y+y+2+2}$.
\nb) Line 5 sets $z = x + x$ but then line 6 reassigns $z$ using the previous $z$ value.
", "rulesets": {}, "parts": [{"prompt": "What is the value of $x$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": false, "scripts": {}, "choices": ["{y+2+y+2}
", "{y+2}
", "{y+y}
", "{2}
"], "marks": 0, "displayType": "radiogroup", "maxMarks": "1", "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "What is the value of $z$?
", "matrix": ["0", 0, 0, "1"], "shuffleChoices": false, "scripts": {}, "choices": ["{16*y+32}
", "{4*y+8}
", "{3*y+6}
", "{8*y+16}
"], "marks": 0, "displayType": "radiogroup", "maxMarks": "1", "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}], "statement": "> y = {y}
> x = y + 2
> x = x + x
> x
> z = x + x
> z = z + z", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"y": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "y", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Amy's copy of Question 1 Basic what is x", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "functions": {}, "ungrouped_variables": ["x", "b", "a"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "In this question you have to remember that R can overwrite the assignment of variables.
\nLine 1 assigns $x=\\var{x}$.
\nIn line 2 R reassigns $x$ as the solution to the equation using $x=\\var{x}$ from line 1. Thus $x=\\simplify[basic,!collectnumbers]{{a}/{x}-{b}}$, which gives $x=\\var{a/x-b}$.
", "rulesets": {}, "parts": [{"prompt": "What is the value of $x$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": true, "scripts": {}, "choices": ["{{a/x}-b}
", "{x}
", "{x-b}
", "{a/x}
"], "marks": 0, "displayType": "radiogroup", "maxMarks": "1", "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": "0"}], "statement": "> x = {x}
> x = ({a}/x)-{b}
> x ", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}, "x": {"definition": "random(2..20#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "x", "description": ""}, "b": {"definition": "random(2..16#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Amy's copy of Question 2 Basic what is x", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "functions": {}, "ungrouped_variables": ["x", "y", "a", "b"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "a) Lines 1 and 2 assign the values of $x$ and $y$.
\nLine 3 reassigns a new value for $x$ by solving an equation involving the values in lines 1 and 2. This gives $x=\\simplify[basic,!collectnumbers]{{x}-{a}/{y}}$, therefore R has reassigned a new value for $x$. This is $x=\\var{{x}-{a}/{y}}$.
\nLine 4 shows a calculation involving $x$. This bit is designed to catch you out. We haven't reassigned $x$ as a new value here so this doesn't change our $x$ value.
\nTherefore the value of $x$ remains as $x=\\var{{x}-{a}/{y}}$.
\nb) Line 2 assigns the value of $y$.
", "rulesets": {}, "parts": [{"prompt": "What is the value of $x$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": true, "scripts": {}, "choices": ["{x-(a/y)}
", "{x-(a/y)-b}
", "{x}
", "{x-b}
"], "marks": 0, "displayType": "radiogroup", "maxMarks": "1", "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "What is the value of $y$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": false, "scripts": {}, "choices": ["{y}
", "{x}
", "{x+y}
", "{y+2}
"], "marks": 0, "displayType": "radiogroup", "maxMarks": "1", "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}], "statement": "> x = {x}
> y = {y}
> x = x - ({a}/y)
> x - {b}
> x ", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"y": {"definition": "random(10..20#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "y", "description": ""}, "x": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "x", "description": ""}, "b": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b", "description": ""}, "a": {"definition": "random(2..15#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}}, "metadata": {"notes": "Advice section doesn't show up when you click reveal?
", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Amy's copy of Question 3 basic what is x ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "functions": {}, "ungrouped_variables": ["a", "b"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "a) Line 1 assigns $x=\\var{a}$. The third line just involves a calculation using $x$ but no reassignment.
\nb) $z=x - y$.
", "rulesets": {}, "parts": [{"prompt": "What is the value of $x$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": false, "scripts": {}, "choices": ["{a}
", "{a*b - a}
", "{b - a}
", "{b}
"], "marks": 0, "displayType": "radiogroup", "maxMarks": "1", "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "What is the value of $z$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": true, "scripts": {}, "choices": ["{a - b}
", "{a}
", "{2/b}
", "{a*b - a - b}
"], "marks": 0, "displayType": "radiogroup", "maxMarks": "1", "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}], "statement": "> x = {a}
> y = {b}
> (x*{b}) - {a}
> x
> z = x - y ", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..20#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}, "b": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Amy's copy of Question 4 basic what is x", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "functions": {}, "ungrouped_variables": ["x", "a", "b"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "a) Line 1 assigns $x$ and line 2 assigns $y$ using $x$, therefore $y=\\var{{a}+{x}}$.
Line 3 is a calculation that uses $y$ but never reassigns any of the variables.
Line 4 then overwrites $x$ using $y$. Therefore $x=\\var{{a}+{b}+{x}}$.
b) The value of $z$ is the same as the value of $x$.
", "rulesets": {}, "parts": [{"prompt": "What is the value of $x$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": true, "scripts": {}, "choices": ["{b+a+x}
", "{b + a + x + 2}
", "{x}
", "{b + 2}
"], "marks": 0, "displayType": "radiogroup", "maxMarks": "1", "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "What is the value of $z$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": true, "scripts": {}, "choices": ["{b+a+x}
", "{b+a}
", "{b}
", "{a*x}
"], "marks": 0, "displayType": "radiogroup", "maxMarks": "1", "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}], "statement": "> x = {x}
> y = {a} + x
> y + 2
> x = {b} + y
> z = {b} + y", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}, "x": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "x", "description": ""}, "b": {"definition": "random(2..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Amy's copy of Question 5 what is x", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "functions": {}, "ungrouped_variables": ["y"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "a) Line 1 assigns $y=\\var{y}$.
\nLine 2 assigns $x=\\var{y-5}$.
\nLine 3 reassigns $x$ using $x=\\var{y-5}$. Therefore $x=\\var{y+y-5-5}$.
\nb) Line 5 sets $z = x + (x/2)$ but then line 6 reassigns $z$ using the previous $z$ value.
", "rulesets": {}, "parts": [{"displayColumns": 0, "prompt": "What is the value of $x$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": true, "variableReplacements": [], "choices": ["{y+y-10}
", "{y-5}
", "{y}
", "{y-10}
"], "variableReplacementStrategy": "originalfirst", "maxMarks": "1", "distractors": ["", "", "", ""], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}, {"displayColumns": 0, "prompt": "What is the value of $z$?
", "matrix": ["0", 0, 0, "1"], "shuffleChoices": true, "variableReplacements": [], "choices": ["{y-10}
", "{y-5}
", "{y-5+y-5}
", "{3y-10}
"], "variableReplacementStrategy": "originalfirst", "maxMarks": "1", "distractors": ["", "", "", ""], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}], "statement": "> y = {y}
> x = y - 5
> x = x + x
> x
> z = x + (x/2)
> z = z + 5", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"y": {"definition": "random(6..9#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "y", "description": ""}}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "extensions": [], "custom_part_types": [], "resources": []}