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- Sat Mar 10, 2012 1:31 pm
#85193
Setup and Rule Diagram Explanation
This is an Advanced Linear: Balanced game.
Whereas the first two games on this test are fairly reasonable, this game is considerably harder. This occurs because the Advanced Linear element is paired with a subdivided selection pool (introductory and advanced). The initial scenario appears as follows:
The first constraint in the game is stated at the end of the game scenario, and stipulates that no textbook is evaluated by both reviewers during the same week:
In the above diagram, “T” stands for textbook, indicating that the same textbook cannot be evaluated by both evaluators during the same week.
The first rule establishes that R cannot evaluate an introductory textbook until J has evaluated that textbook. This should be shown as a sequence, with subscripts for “introductory”:
The A and I subscripts are the easiest way to keep track of the advanced and introductory textbooks since there are already two stacks for Rosenberg and Juarez.
Of course, under this rule, R cannot evaluate an introductory textbook during week 1, and J cannot evaluate an introductory textbook during week 6. Thus, because each textbook is either introductory or advanced, we can infer that R evaluates an advanced textbook during week 1, and J evaluates an advanced textbook during week 6:
The second rule is also sequential, and can be diagrammed as follows:
This rule is really the reverse of the first rule. Under this condition, J cannot evaluate an advanced book during week 1, and R cannot evaluate an advanced book during week 6. Thus, J must evaluate an introductory book during week 1, and R must evaluate an introductory book during week 6:
The third rule indicates that R cannot evaluate any two introductory textbooks consecutively:
This initiates the Separation Principle, and thus for R, the advanced textbooks must separate the introductory textbooks. Because R cannot evaluate any two introductory books consecutively, and because J must evaluate any introductory book before R evaluates it, R must evaluate the introductory textbooks second, fourth, and sixth. Correspondingly, R must evaluate the advanced textbooks first, third, and fifth. Thus, R’s sequence of evaluating textbooks must be A-I-A-I-A-I:
The final rule states that J must evaluate X during week 4, which can be shown directly on the diagram. In addition, because X is an advanced textbook, and from the second rule J cannot evaluate an advanced textbook until R has evaluated it, R must evaluate X first or third, and cannot evaluate X fifth (again, R’s even-numbered book evaluations must be introductory books, so X could not be second, fourth, or sixth). Accounting for this information results in the following diagram:
Note that, due to the second rule, whatever advanced textbook R evaluates in week 5 will be the advanced textbook J evaluates in week 6. This relationship is also true in the reverse: whatever advanced textbook J evaluates in week 6 will be the advanced textbook R evaluates in week 5 (otherwise, the textbook reviewed by R in week 5 would have to be reviewed by J in an earlier week, a violation of the second rule). As this relationship goes both ways, so it will be shown with a double arrow.
Similarly, due to the first rule, whatever introductory textbook R evaluates in week 2 will be the introductory textbook J evaluates in week 1. This relationship also reverses, and so it will also be shown with a double arrow.
These relationships can be shown on the main diagram with arrows, leading to the final diagram:
While R has a fairly limited number of ordering options, J still has a number of options for ordering the introductory and advanced textbooks. For example, J could evaluate the advanced textbooks 2-4-6, 3-4-6, or 4-5-6. However, as each textbook is placed, the interrelationship of the rules and variable sets will quickly limit the number of remaining options.
This is an Advanced Linear: Balanced game.
Whereas the first two games on this test are fairly reasonable, this game is considerably harder. This occurs because the Advanced Linear element is paired with a subdivided selection pool (introductory and advanced). The initial scenario appears as follows:
The first constraint in the game is stated at the end of the game scenario, and stipulates that no textbook is evaluated by both reviewers during the same week:
In the above diagram, “T” stands for textbook, indicating that the same textbook cannot be evaluated by both evaluators during the same week.
The first rule establishes that R cannot evaluate an introductory textbook until J has evaluated that textbook. This should be shown as a sequence, with subscripts for “introductory”:
The A and I subscripts are the easiest way to keep track of the advanced and introductory textbooks since there are already two stacks for Rosenberg and Juarez.
Of course, under this rule, R cannot evaluate an introductory textbook during week 1, and J cannot evaluate an introductory textbook during week 6. Thus, because each textbook is either introductory or advanced, we can infer that R evaluates an advanced textbook during week 1, and J evaluates an advanced textbook during week 6:
The second rule is also sequential, and can be diagrammed as follows:
This rule is really the reverse of the first rule. Under this condition, J cannot evaluate an advanced book during week 1, and R cannot evaluate an advanced book during week 6. Thus, J must evaluate an introductory book during week 1, and R must evaluate an introductory book during week 6:
The third rule indicates that R cannot evaluate any two introductory textbooks consecutively:
This initiates the Separation Principle, and thus for R, the advanced textbooks must separate the introductory textbooks. Because R cannot evaluate any two introductory books consecutively, and because J must evaluate any introductory book before R evaluates it, R must evaluate the introductory textbooks second, fourth, and sixth. Correspondingly, R must evaluate the advanced textbooks first, third, and fifth. Thus, R’s sequence of evaluating textbooks must be A-I-A-I-A-I:
The final rule states that J must evaluate X during week 4, which can be shown directly on the diagram. In addition, because X is an advanced textbook, and from the second rule J cannot evaluate an advanced textbook until R has evaluated it, R must evaluate X first or third, and cannot evaluate X fifth (again, R’s even-numbered book evaluations must be introductory books, so X could not be second, fourth, or sixth). Accounting for this information results in the following diagram:
Note that, due to the second rule, whatever advanced textbook R evaluates in week 5 will be the advanced textbook J evaluates in week 6. This relationship is also true in the reverse: whatever advanced textbook J evaluates in week 6 will be the advanced textbook R evaluates in week 5 (otherwise, the textbook reviewed by R in week 5 would have to be reviewed by J in an earlier week, a violation of the second rule). As this relationship goes both ways, so it will be shown with a double arrow.
Similarly, due to the first rule, whatever introductory textbook R evaluates in week 2 will be the introductory textbook J evaluates in week 1. This relationship also reverses, and so it will also be shown with a double arrow.
These relationships can be shown on the main diagram with arrows, leading to the final diagram:
While R has a fairly limited number of ordering options, J still has a number of options for ordering the introductory and advanced textbooks. For example, J could evaluate the advanced textbooks 2-4-6, 3-4-6, or 4-5-6. However, as each textbook is placed, the interrelationship of the rules and variable sets will quickly limit the number of remaining options.
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Dave Killoran
PowerScore Test Preparation
Follow me on X/Twitter at http://twitter.com/DaveKilloran
My LSAT Articles: http://blog.powerscore.com/lsat/author/dave-killoran
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PowerScore Test Preparation
Follow me on X/Twitter at http://twitter.com/DaveKilloran
My LSAT Articles: http://blog.powerscore.com/lsat/author/dave-killoran
PowerScore Podcast: http://www.powerscore.com/lsat/podcast/
J > R