Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This is a Grouping: Undefined, Numerical Distribution game.

The game scenario establishes that within three development zones (Z1, Z2, and Z3), a maximum of three subzones can be designated for each of three uses (H, I, R):

oct12_game_4_diagram_1.png

This is a somewhat unusual Grouping game, and is clearly the most difficult game on the test. Its difficulty is due to several factors:

• 1. Min/max number of subzones overall. Although subzones can be designated for each use, neither the scenario nor the subsequent rules specify exactly how many subzones must be designated for each use. The word “can” in the second sentence of the scenario is crucial, leaving open the possibility that no subzones are being designated for any use. The rules do nothing to dispel that notion, as each rule represents a prohibition about what cannot be true, rather than an affirmation of what must be true. All we know is that the maximum possible number of subzones designated for each use is 3. The total number of subzones can be anywhere from 0 to 9.
  
  2. Min/max number of subzones per zone. Some students misread the scenario to imply that no more than three subzones of each type were possible within each zone. This is incorrect. The scenario states that no more than three subzones can be designated for each use (H, I, R), not for each zone (Z1, Z2, Z3). In fact, the minimum number of subzones per zone is 0. As a result, there are a lot of possible Numerical Distributions of subzones, as the rules are not restrictive enough to establish a minimum number of subzones per zone. If something seems too laborious, it probably is: a detailed analysis of each distribution is neither required nor encouraged.

With a group being selected, and order not important, this is a Grouping game. Because we are not required to have subzones in any of the zones, the game is Undefined. Let’s examine the rules:

The first rule establishes an R Not Law for Z1:

oct12_game_4_diagram_2.png

The second rule prohibits placing more than two H subzones in any given zone:

• max. 2H/zone

In other words, given the overall maximum of three H subzones, the second rule prohibits placing all three of them within the same zone:

oct12_game_4_diagram_3.png

The third rule establishes that a maximum of one R subzone is allowed in any zone containing an H subzone. This rule is conditional in nature, and can be represented as follows:

• H max. 1R

By the contrapositive, we can infer that any zone containing two or more R subzones cannot have any subzone designated for H:

• H ≥ 2 R

The fourth rule is actually two rules -in -one, and establishes that an I subzone is not allowed in any zone that contains either a subzone designated for H, or 3R subzones. For the sake of clarity, write these relationships out separately:

• I H
  
  I 3R

The second relationship can also be represented as a positive rule:

• I max. 2R

With all the rules properly diagrammed, let’s see if any of them can be combined to provide additional insight into the assignment of subzones to zones. While we cannot make inferences regarding the type of subzones that must (or cannot) be placed within each zone, you should notice that H appears in almost all of the rules, and as such deserves a closer look:

• Since no zone contains more than 2H’s, no zone contains both an H and an I, and no zone with an H contains more than 1R, we can infer that if any zone contains H, that zone can contain a maximum of 3 subzones (H, H, R):

• H max. 3 (H, H, R)

It may also be useful to examine the maximum number of subzones allowed if either of the other two types of subzones (R and I) were designated within any given zone:

• If a zone (other than Z1) contains an R subzone, then it can contain at most two R’s in order to allow as many I subzones as possible to be designated within it. Clearly, that zone will contain no H subzones, because those would limit the total number of subzones to 3 (see discussion above). Thus, if any zone contains R, that zone can contain a maximum of 5 subzones:

• R max. 5 (R, R, I, I, I)

• The same holds true if a zone contains an I subzone. Since I and H cannot be designated within the same zone, the maximum number of subzones allowed in that zone would be five (and not six, due to the last rule in the game):

• I max. 5 (R, R, I, I, I)

Combining all the prior information leads to the final diagram for the game:

oct12_game_4_diagram_4.png

[karlaurrea]

Hello,

I had great difficulty understanding how the rules, and although I think I was in the right track about the diagram I just couldn't comprehend the entirety of the game...

Can you please show me an initial setup followed by the inferences so I can compare and see how the rules to this should be interpreted?

Thanks!!!

[Jon Denning]

Hey karlaurrea - thanks for the question. This was without a doubt the trickiest game on this LSAT, and it gave test takers fits back in October. There are two points of difficulty in this game: first, the rules aren’t very clear about how many subzones can exist, and some students misread the scenario to imply that three subzones of each type were possible within each zone; second, there are a lot of numerical combinations for the subzones (that is, there are a lot of possible Numerical Distributions of subzones). However, test takers who really focused in on the third and fourth rules found that they helped knock out a number of incorrect answers, and made this game more acceptable (not easy, but acceptable).

Truth is there's not really much of a setup possible here. Aside from a not law about R in 1, the rest of it is simply the rules controlling/limiting placement of subzones, and the impact of those restrictions on answer choices. Housing seems to be the most limiting of the three subzones, as it cannot appear in a zone more than twice, cannot appear with more than one R, and cannot appear with I at all.

Take a question like 22 to illustrate the rules' impact: if one subzone in each is I, then H cannot be used at all (H and I never together). So zone 1 has only I, and 2 and 3 can have either 0, 1, or 2 Rs (up to a total of 3 Rs).

Quickly eliminate answers:

B - no housing subzones
C - only 1 I in zone 1
D - would require 2 R in zone 2, and 2 R in zone 3 (cannot have more than 3 of any type and that's 4 Rs)
E - would require 3 R in zone 3, and I and 3 R cannot go together (last rule)

So the answer is A.

Tricky game, but use the rules and their limitations to attack the questions and you should be okay. Thanks!

[imagineer]

Hi,
Ive been working on the questions from the 4th LG game in the section from the October 2012 LSAT (Questions 18-23). I was able to get the first three right, but I think that was due to luck. The wording is quite confusing and and I'm not sure exactly how to set up the diagram to attack the questions. If any of you could help me out with this, I would really appreciate it.
Cheers
Raj

[Jon Denning]

Hey Raj - thanks for the question. This was without a doubt the trickiest game on this LSAT, and it gave test takers fits back in October of last year. There are two points of difficulty in this game: first, the rules aren’t very clear about how many subzones can exist, and some students misread the scenario to imply that three subzones of each type were possible within each zone; second, there are a lot of numerical combinations for the subzones (that is, there are a lot of possible Numerical Distributions of subzones). However, test takers who really focused in on the third and fourth rules found that they helped knock out a number of incorrect answers, and made this game more acceptable (not easy, but acceptable).

Truth is there's not really much of a setup possible here. Aside from a not law about R in 1, the rest of it is simply the rules controlling/limiting placement of subzones, and the impact of those restrictions on answer choices. Housing seems to be the most limiting of the three subzones, as it cannot appear in a zone more than twice, cannot appear with more than one R, and cannot appear with I at all.

Take a question like 22 to illustrate the rules' impact: if one subzone in each is I, then H cannot be used at all (H and I never together). So zone 1 has only I, and 2 and 3 can have either 0, 1, or 2 Rs (up to a total of 3 Rs).

Quickly eliminate answers:

B - no housing subzones
C - only 1 I in zone 1
D - would require 2 R in zone 2, and 2 R in zone 3 (cannot have more than 3 of any type and that's 4 Rs)
E - would require 3 R in zone 3, and I and 3 R cannot go together (last rule)

So the answer is A.

Tricky game, but use the rules and their limitations to attack the questions and you should be okay. Thanks!

[imagineer]

Thanks for the help John. I took this exam last october. My problem with each of the sections was timing. Is there anyway to move faster through the sections? i've tried taking several practice tests and working through the problems. If you could provide any advice I would really appreciate it.
Cheers
Raj

[Jon Denning]

Hey Raj - well, that's a pretty broad question, so I'm going to try to answer it, but I'll have to do so in broad terms. That is, your ability to move quickly is really based on how efficiently you recognize and comprehend the information you're given, and then how quickly you're able to apply the appropriate strategy in response to it. So for example if I'm doing LR and see an argument based on causal reasoning, how well can I spot that (how quickly), and do I have the proper strategies in place to address it as needed: weaken, strengthen, describe a flaw, etc.

Speed, then, is really just a product of comprehension, both in terms of understanding what you're seeing, and in terms of being able to effectively react in an intuitive, consistent, and appropriate manner. Everything that happens on this test, from Games to Reading to LR, and all the elements therein, is predictable to the point that you can prepare yourself very well for it--knowing what you're given AND what to do to beat it--provided you have the right tools in place (proper strategies, generally from a course or books or both) and diligently work to master them through repeated practice. So keep at it, and, again assuming you're working with the right system, you should find that your speed increases as your understanding of the test itself improves.

[Foremostrlty]

Hi instructor,
I have been struggling with the set up in this game, somehow I got the rule question right and two others and just cant figure out how am not getting the other 3 based on my setup, I just feel am missing the interpretation of the statement on the game "….with no subzone designated for more than one use."
Please help me out with this and the 4 rules.
Thanking you for your usual assistance.
Lawrence A

[David Boyle]

Hi instructor,
I have been struggling with the set up in this game, somehow I got the rule question right and two others and just cant figure out how am not getting the other 3 based on my setup, I just feel am missing the interpretation of the statement on the game "….with no subzone designated for more than one use."
Please help me out with this and the 4 rules.
Thanking you for your usual assistance.
Lawrence A

Hello Lawrence A,

The interpretation of that statement should be pretty straightforward: one subzone can't be for housing AND industrial AND retail, or even two of those, but just one.

Besides zero or one, two, or three of any subzone (H, I, R) (and you can have only 2H at maximum, see rule 2), it looks like the possible combos are

2H, 1R;
1H, 1R;
2R, (1, 2, or 3I);
1R, (1, 2, or 3I).

, more or less.
H hates I (rule 4), and H limits R (rule 3), so the most flexibility in combos is when I and R combine, as we see in the combo list above. (Though from rule 4, you can't have 3R and any I.)

One limitation is that the maximum subzones a zone can have is five (three industrial, two retail), see rules 2, 3, 4. This is directly dealt with in question 20.

Hope that helps, and happy holidays,
David

[Foremostrlty]

Dave,
Thanks for your assistance. I got it !!! wishing you and all a happy holidays.

Lawrence A.