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- Fri Jan 21, 2011 12:00 am
#27437
Setup and Rule Diagram Explanation
This is a Grouping Game: Undefined.
This game has always been considered by students to be very challenging. The difficulty arises because the store carries ten CDs, but the number of CDs for sale is Undefined. As discussed in Lesson Six, Undefined Grouping games can at times present a severe challenge. Increasing the complexity of the game, four of the rules involve a double conditional. The variables can be listed as follows:
One critical inference involves identifying UO as a random. Because NO is not on sale, and none of the rules involve UO, questions about the CDs that must or cannot be on sale are not likely to involve O. For example, #8 (C), #10 (A), (B), and (C), and #12 (B) each focus on O in a Must be True or Cannot be True question. Because we know nothing about the actions of UO, these answers are likely to be incorrect. A similar line of reasoning can be used to attack question #11. Question #11 asks for what Must be True EXCEPT. Thus, each incorrect answer Must be True, and the correct answer is Not Necessarily True. At first glance, answer choice (A), which addresses UO, is very likely to be correct because we know nothing about the actions of UO and thus almost anything is possible, the opposite of Must be True. Note that, in question #13, the restrictions in the question stem are so severe as to ultimately affect UO.
The diagramming of the rules presents some choices. The second, third, fourth, and fifth rules contain multiple sufficient or necessary conditions. For example, the third rule can be diagrammed as follows:
Some students, however, may find this notation cumbersome. An alternate representation would be to diagram the rule as follows:
While this representation is easier to digest, because the rules vary between “and” and “or” conditions, some consideration must be given to the impact of those differences. For example, the conditions involving “all,” “both,” or “neither” could appear with an NU (new and used) designator:
Rules involving “either,” or contrapositives involving “or” could be diagrammed without designators, thus indicating that the presence of either the new or used type of music would enact the rule.
Ultimately, either representation presents drawbacks: showing each type of music separately is cluttered, whereas using subscripts could be confusing. On the next page we will show both types of diagrams.
Please note that the second and fourth rules in the game are modified above to reflect the fact that UP must be on sale.
In attacking the game, we choose to use the second set of representations, but if you feel more comfortable with the first set of representations, you can certainly use those instead.
The relationships above lead to several inferences. For example, the second and fourth rules of the game can be combined:
This combination leads to the following inference
This inference answers question #10, and eliminates answer choices (D) and (E) in question #11.
The last rule and the extended contrapositive of the second rule can be combined:
This combination reduces to:
On some of the questions, a simple application of the contrapositive can be sufficient to answer the question. For example, question #8 can be answered by applying the contrapositive of the second rule.
Largely, solving this game requires a simple application of the rules. However, because there are so many variables and the rules are complex in nature, that application takes time. In addition, the lack of definition makes the game more difficult. Students would have been best served by recognizing that this is an Undefined game with a large number of variables and then pushing this game to last on that basis.
This is a Grouping Game: Undefined.
This game has always been considered by students to be very challenging. The difficulty arises because the store carries ten CDs, but the number of CDs for sale is Undefined. As discussed in Lesson Six, Undefined Grouping games can at times present a severe challenge. Increasing the complexity of the game, four of the rules involve a double conditional. The variables can be listed as follows:
One critical inference involves identifying UO as a random. Because NO is not on sale, and none of the rules involve UO, questions about the CDs that must or cannot be on sale are not likely to involve O. For example, #8 (C), #10 (A), (B), and (C), and #12 (B) each focus on O in a Must be True or Cannot be True question. Because we know nothing about the actions of UO, these answers are likely to be incorrect. A similar line of reasoning can be used to attack question #11. Question #11 asks for what Must be True EXCEPT. Thus, each incorrect answer Must be True, and the correct answer is Not Necessarily True. At first glance, answer choice (A), which addresses UO, is very likely to be correct because we know nothing about the actions of UO and thus almost anything is possible, the opposite of Must be True. Note that, in question #13, the restrictions in the question stem are so severe as to ultimately affect UO.
The diagramming of the rules presents some choices. The second, third, fourth, and fifth rules contain multiple sufficient or necessary conditions. For example, the third rule can be diagrammed as follows:
Some students, however, may find this notation cumbersome. An alternate representation would be to diagram the rule as follows:
While this representation is easier to digest, because the rules vary between “and” and “or” conditions, some consideration must be given to the impact of those differences. For example, the conditions involving “all,” “both,” or “neither” could appear with an NU (new and used) designator:
Rules involving “either,” or contrapositives involving “or” could be diagrammed without designators, thus indicating that the presence of either the new or used type of music would enact the rule.
Ultimately, either representation presents drawbacks: showing each type of music separately is cluttered, whereas using subscripts could be confusing. On the next page we will show both types of diagrams.
Please note that the second and fourth rules in the game are modified above to reflect the fact that UP must be on sale.
In attacking the game, we choose to use the second set of representations, but if you feel more comfortable with the first set of representations, you can certainly use those instead.
The relationships above lead to several inferences. For example, the second and fourth rules of the game can be combined:
This combination leads to the following inference
This inference answers question #10, and eliminates answer choices (D) and (E) in question #11.
The last rule and the extended contrapositive of the second rule can be combined:
This combination reduces to:
On some of the questions, a simple application of the contrapositive can be sufficient to answer the question. For example, question #8 can be answered by applying the contrapositive of the second rule.
Largely, solving this game requires a simple application of the rules. However, because there are so many variables and the rules are complex in nature, that application takes time. In addition, the lack of definition makes the game more difficult. Students would have been best served by recognizing that this is an Undefined game with a large number of variables and then pushing this game to last on that basis.
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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
PowerScore Podcast: http://www.powerscore.com/lsat/podcast/
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/
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