Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Balanced, Advanced Linear Game.

This game is discussed in detail in our podcast recap of PT1 Logic Games at https://www.powerscore.com/lsat/podcast/104/


This Advanced Linear game contains multiple variable sets, and choosing the base can be difficult. The four numbered offices and the three years both have an inherent sense of order, so you must look beyond that element in choosing the base. Ultimately, the four offices are the best base because with the offices as the base, you can show the connection of each computer and printer to that office in an organized fashion. The years can then be used “inside” the diagram:

PT1-Jun1991 game 2 setup diagram 1.png

The first rule is a difficult rule to represent, and is ultimately the rule that causes the greatest number of issues in the game.

C ≥ P

This representation captures the idea that the computer in each office was purchased in an earlier year or the same year as the printer in that office. Note: if you designated this rule as P ≥ C, that's fine too. It all depends on how you define “earlier.” To me, 1990 > 1991 designated that 1990 is “earlier” than 1991. That said, it doesn’t actually matter the exact designation as long as you know the computers are the same year or older.

The second rule should be diagrammed internally, as in on the diagram:

PT1-Jun1991 game 2 setup diagram 2.png

The third rule should also be diagrammed internally:

PT1-Jun1991 game 2 setup diagram 3.png

The fourth rule should also be diagrammed internally:

PT1-Jun1991 game 2 setup diagram 4.png

The last rule fixes two of the machines to an exact date:

PT1-Jun1991 game 2 setup diagram 5.png

The final rule, in conjunction with first rule, allows us to infer that the printer in office 1 cannot have been purchased in 1987, and therefore must have been purchased in 1988 or 1989. We can also infer that the computer in office 3 cannot have been purchased in 1989, and therefore must have been purchased in 1987 or 1988. Both dual-options should be shown on the diagram:

PT1-Jun1991 game 2 setup diagram 6.png

From the second rule, then, we can infer that the computer in office 2 was purchased in 1988 or 1989:

PT1-Jun1991 game 2 setup diagram 7.png

And from the third rule, we can infer that the printer in office 4 was purchased in 1987 or 1988:

PT1-Jun1991 game 2 setup diagram 8.png

Finally, by reapplying the first rule, we can determine that the printer in office 2 cannot have been purchased in 1987, and therefore must have been purchased in 1988 or 1989, and that the computer in office 4 cannot have been purchased in 1989, and must have been purchased in 1987 or 1988. These two inferences lead to the final diagram:

PT1-Jun1991 game 2 setup diagram 9.png

The only considerations remaining are the exact years of each machine (determined in part by the action of the first rule) and the fourth rule about the computers in offices 2 and 3.

[MaryamAfzal]

Hi! I was wondering what the optimal setup is for this game. I scribbled around and I think I finally got to a pretty good one, but I wanted to know what set up you recommend.

Thanks!
Maryam

[Dave Killoran]

Hi Maryam,

This Advanced Linear game contains multiple variable sets, and choosing the base can be difficult. The four numbered offices and the three years both have an inherent sense of order, so you must look beyond that element in choosing the base. Ultimately, the four offices are the best base because with the offices as the base, you can show the connection of each computer and printer to that office in an organized fashion. The years can then be used “inside” the diagram:

• C: 7 8 9: __ __ __ __
  P: 7 8 9: __ __ __ __
  Offices: 1   2   3 4

The second third and fourth rules can then be diagrammed internally, right inside the setup above (not easy to do in this Forum).

When you analyze the various rules, there's a sort of chain reaction of connections that occurs that occurs, which ultimately limits the options in each position. That begins when you apply the final rule, which forces an "8" for the computer in office 1 and the printer in office 3.

For example, from there you can deduce that the printer in office 1 was purchased in either 8 or 9 (from the first rule), and that the computer in office 3 was purchased in 7 or 8 (again, from the first rule). From there, you can use the other rules to begin connecting the possibilities in other offices, ultimately resulting in the following setup:

• C: 7 8 9: 8  8/9 7/8 7/8
  P: 7 8 9: 8/9 .....8/9 8 7/8
  Offices: 1    2      3   4

You still need to track the second, third, and fourth rules throughout the game, but the setup above makes it very easy to do so (especially once you internally diagram those three rules).

Please let me know if that helps. Thanks!

[ryan89]

Hello,

I know it's difficult to type out, but is there an effective way to represent the first rule? I wrote it out as:

Cx
Px or x+1

It worked for me, but I'm curious if you had any recommendations for a representation that is easier to see visually?

Thanks!
Ryan

[James Finch]

Hi Ryan,

The way I personally represented it when I was writing down the rules was with this:

C ≤ P

However, while that diagram captures the idea of the rule, the more important representation would be either as not laws, so that you understand that the printer row must always be an 8 or 9, and the computer row must always be a 7 or 8, or literally writing in 8/9 across the four printer slots and 7/8 across the computer slots. Either way, the important thing is that you remember to apply the rule and any inferences you can draw from it.

Hope this helps!

[Shelbyhenderson86]

DO you think it would have been worthwhile to make templates? I was originally confused with his game but I split the game into four templates and was able to answer all the questions...

[Jeremy Press]

Hi Shelby,

Great question!

It's entirely possible to split this game into its templates and diagram the possibilities before you dive into the questions. As with all such games, it's a question of the benefit that strategy will get you versus the time it takes to do it. If diagramming the possibilities did not take you an inordinately long time (maybe 2-3 minutes once you noticed that it was possible?), then I'd say go for it. If you worried that diagramming out each option would take significantly longer than that, then I think Dave's initial diagram (which relies heavily on "Dual Options") is the way to go. With that diagram you can efficiently see the various possible "directions" the solutions could take, without necessarily diagramming each one separately. And many times that's just as good as having everything laid out in full. It does take a bit of practice to get used to "seeing" the answers to questions within a setup populated with "Dual Options," but I'd encourage you to take one pass through this game with Dave's setup and try that out. See if you can make it work for you, because it could save you just a bit of time on the front end, with no sacrifice of accuracy on the back end.

Let me know if this triggers any other questions for you!

Jeremy

[CodeyD29]

Hi Ryan,

The way I personally represented it when I was writing down the rules was with this:

C ≤ P

However, while that diagram captures the idea of the rule, the more important representation would be either as not laws, so that you understand that the printer row must always be an 8 or 9, and the computer row must always be a 7 or 8, or literally writing in 8/9 across the four printer slots and 7/8 across the computer slots. Either way, the important thing is that you remember to apply the rule and any inferences you can draw from it.

Hope this helps!

Hello sir, isn't it possible for printer four to be a 7/8? Therefore it's not true that the printer row can only consist of 8 and 9. Am I misunderstanding something? I had an issue with this rule: it always took me a little longer to process than I would have liked. I was wondering if there was an easier way of thinking about and diagramming that controlling rule.

[KelseyWoods]

Hi Codey!

You are correct, it's not as simple as saying that the printers must all be in 8 or 9 and the computers must all be in 7 or 8. Printer 4 could be 1987, computer 2 could be 1989. But James's basic point about making sure the rule is diagrammed within the diagram is an important one. Check out how Dave set up his diagram above:

C: 7 8 9:       8       8/9      7/8       7/8
P: 7 8 9:      8/9      8/9       8      7/8
Offices:      1         2           3        4

You'd still have to keep track of the rule as you're going through (e.g., if computer 4 is 1988, then printer 4 must be 1988 as well). But having the options written right on the diagram will make it easier to track.

Hope this helps!

Best,
Kelsey

[menkenj]

I set this game up like a matching grid and it worked really well for my brain. I found the suggested setup confusing.

In my grid, I have the offices across the top and the years along the side. I deduced that no c/p can be in 87 for office 1 or 2 and no c/p can be in 89 for office 3 or 4. So my grid had Xs where spaces were empty. I found this helpful because there were two ordered variables.

I tried to type up my grid but I'm seriously struggling with the formatting here.