Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Basic Linear: Balanced, Identify the Templates game.

This game scenario presents a situation where six contract bids each have a different cost, and only one of the bids is accepted. This creates a linear scenario where the six bids are ordered based on cost, with “1” representing the lowest-cost bid and “6” representing the highest-cost bid:

PT54-Jun2008_LGE-G4_srd1.png

The implications of “1” equalling the lowest-cost bid will be discussed later.

The sentence stating that “Exactly one of the bids is accepted” initially causes some students to reasonably wonder if the accepted bid must be the first, or lowest-cost, bid. Fortunately, the first rule eliminates this confusion by establishing that either the second or third bid is the accepted bid.

Within the setup, because there is only one accepted bid, instead of creating a second stack of variables for “accepted” and “not accepted,” we will instead use a sub-A on the second and third positions to designate that one of those bids is accepted:

PT54-Jun2008_LGE-G4_srd2.png

This notation effectively represents the presence of the accepted bid without undue confusion or additional work.

Rule #1. The portion of this rule that states that the accepted bid is second or third lowest in cost has already been addressed. The portion of this rule indicating that K or R is the accepted bid does not mean that K and R are second and third in some order. Instead, the rule means that at least one of K or R is always second or third (and thus K/R dual-options cannot be placed on both the second and third slots). This portion of the rule can be represented as:

PT54-Jun2008_LGE-G4_srd3.png

Rule #2. This rule can be represented as:

PT54-Jun2008_LGE-G4_srd4.png

For some students, this is the point in the game where the lowest-cost bid being first creates a problem. “Lowest” often means “least” or “worst,” so students working through this game have to realize that the test makers have set up the lowest bid as the “best.” This is similar to golf, where lower scores are preferable.

Of course, this sequence generates several Not Laws. H cannot be the fifth or sixth bid, and J and K cannot be the first bid:

PT54-Jun2008_LGE-G4_srd5.png

Rules #3 and #4. Given that these two rules create mutually exclusive situations, we will address them after reviewing the last rule.

Rule #4. This rule creates an R/S dual-option on the fifth space. When combined with the second rule, this causes a problem for the possible placements of H. With the fifth space effectively filled, H can no longer be fourth, otherwise there would be insufficient room for J and K. Hence, an H Not Law can be placed on the fourth space:

PT54-Jun2008_LGE-G4_srd6.png

In essence, filling the fifth space with variables other than H has transferred the H Not Law that used to be on the fifth space to the fourth space.

At this point, we can return to the third and fourth rules.

Rules #3 and #4. The sufficient conditions in these two rules create two separate templates that will cover all possibilities (because J has only two options (fourth or not fourth)). Consequently, the best approach is to examine the templates that occur under each rule.

Rule #3. When J is fourth, both S and T are higher in cost, which can be represented as:

PT54-Jun2008_LGE-G4_srd7.png

Because from the last rule we know that either R or S must be fifth, when the above rule is in force then J is fourth, S is fifth, and T is sixth:

PT54-Jun2008_LGE-G4_srd8.png

The three remaining variables are H, K, and R, and those variables must still meet the requirements of the first and second rules. Thus, H R (meaning that H cannot be third and K cannot be first) and K or R still meets the first rule:

Template #1: J is fourth

PT54-Jun2008_LGE-G4_srd9.png

Rule #4. When J is not fourth, then S and T are less expensive than J:

PT54-Jun2008_LGE-G4_srd10.png

While this relationship may not initially appear to yield any inferences other than standard Not Laws, a closer examination yields that this rule, in combination with the others, has a decisive impact on J.

Under this rule, J cannot be first or second because S and T are both less expensive than J. However, one of the second or third spaces is always filled by either K or R, which effectively adds a space in front of J. For example, if K is accepted and K is the second bid, then S and T still have to be ahead of J, and J cannot be first, second, or third. This same type of reasoning applies to every scenario involving the accepted bid (which is always second or third, and hence presents problems for J). Thus, J can never be first, second or third under the fourth rule. Of course, the rule itself eliminates J from the fourth position, and since the last rule establishes that R or S must be fifth, we can then infer that when J is not fourth, there is no other option than for J to be sixth.

While the combination of the third and fourth rules establishes the inference that J is always fourth or sixth, the templates will also contain this information. The next step is to use the last rule to split the “J not fourth” template into two options, one when R is fifth and one when S is fifth. In each case, J must be sixth.

Template #2: J is not fourth, R is fifth

In this template, J must be sixth (from the inference discussed above), and R is fifth. From the first rule, K must then be the accepted bid, and thus K must be second or third.

From the second rule, H must be less expensive than K, and thus H must be first or second.

With R, J, H, and K accounted for, only S or T can be fourth. The remainder of S and T is one of the first three bids, leading to the following template diagram:

PT54-Jun2008_LGE-G4_srd11.png

Template #3: J is not fourth, S is fifth

In this template, J must be sixth (from the inference discussed previously), and S is fifth. From the first rule, K must then be the accepted bid, and thus K must be second or third.

From the second rule, H must be less expensive than K (H K), and from the first rule K or R must be second or third. This information leads to a template diagram that is considerably more open:

PT54-Jun2008_LGE-G4_srd12.png

The three templates combine to lead to the complete setup for the game:

PT54-Jun2008_LGE-G4_srd13.png

[imagineer]

Hi,
I was working on logic games section (section III) of the June 2008 LSAT exam- it is preptest 54. I have all of the powerscore bibles for all the different sections and have found them very useful. Even after reading the guide though, I struggled with one of the games in the section. If you could provide the diagramming and explain the reasoning behind each of the questions and their answers (18-23- the panel review game), I would really appreciate it. I feel I am either misreading or misinterpreting the first condition, which is causing me to answer the questions incorrectly. If anyone could provide some guidance, I would really appreciate it.
Thank you

[Dave Killoran]

Hi Imagineer,

The key to this game--like so many other games--lies in the setup. Perhaps the most illuminating approach here would be to see what you thought of the rules, and their relative importance. You said the first rule was tripping you up, but the first rule is actually somewhat more straightforward than it looks: it just means that one of K or R is always second or third. There's actually a much more important rule relationship in the game.

So, as a LG analysis exercise, please take a look at those rules again, and let me know the order of the rules that you think matches their importance (for example, 1, 5, 2, 3, 4 etc) and why. If we can get the rule importance (and subsequent impact) right, that should make it much easier for you to solve this game (and future games, which is where it really matters ).

Once I see what you think is important here, we can discuss why it is important and what direction that should send you in.

Thanks!

[imagineer]

Hi Dave,
Thank you very much for your prompt response.

Based on all my diagramming and re- doing the questions, I would rank the conditions in the following order:

1st Condition: After having overread the condition and reading too much into it, I understand why its so simple. (I get a bit confused because i thought that if R is 2nd or 3rd, then K could be anywhere according to the rules and vice versa). Am I understanding your explanation correctly? I would rank this as the 45h most important rule.

2nd Condition- 2nd most important rule- because it restricts movement of "H" in the remaineder of the game.

3rd and 4th condition- 3rd most important rule- J virtually controls the game and the placement of the other variables, but it does not provide any certainty as to where they could be placed.

5th condition- most important rule- restricts what can go into the 5th spot.

I think the reason I had so much trouble with this question is because I was trying to combine the conditions and solidify the variables that had only a few spots to go into. If you could provide a diagram of some sort of how I should work through this problem, I would really appreciate it.

I feel like all the variables were moving throughout the game and there weren't enough variables with restrictions on their movement to make correct decisions.

If you could help me out, I would really appreciate it.

Best Regards
Raj

[Dave Killoran]

Hi Raj,

Thanks so much for replying, and giving me your thoughts. Let me first say that it can at times be pretty difficult to assess which rule is the most important because all the rules obviously work together, and sometimes a rule is made more important by that interaction. So, I know I gave you a tough job

To me, the third and fourth rules are actually the most important, because they send the game in two distinct directions:

1. When J is 4th, then:

S
J > - - - -
T

2. When J is not 4th, then:

S
- - - - > J
T

So, combined, these two rules separate the game into two directions. I think you saw this too, as you said, "J virtually controls the game and the placement of the other variables."

After that, the second and fifth rules become extremely important, and then the first rule has to be accounted for as well.

So, if we have a game that seems to be going in very different directions, the best approach is often to create Templates. That's what should be done here--the first template shows J in 4 (which is then very restricted since S and T have to be fifth and sixth, respectively, and the first three bids are then H > K and R.

When J is not in 4th, two very open templates result, one with R fifth and the other with S fifth. The one with R fifth end up with S/T fourth, and J sixth; the one with S fifth has J sixth.

Going back to our original point, is that first rule important? Definitely. For example, note how using the first rule and fifth rule together easily answer question #21. That rule also plays a role in the templates.

If you don't mind, please take a closer look at those templates, and then check out the questions again--I think you may find them much easier (especially a question like #22, which is tailor-made for the template approach).

Please let me know if that helps. Thanks!

[imagineer]

Hi Dave,
Thanks so much for the explanation. I really appreciate it. I'm really glad I chose powerscore over any of the other test prep companies. Your books and insight have been great. Thanks again.
Best Regards
Raj

[Nadia0702]

Hi PowerScore
This game tripped me up a bit the first time around, and the second time around I realized it was because I didn't immediately recognize the "if and only if" rule. I'd like to get some comments on my diagram and set-up to see if I missed any key inferences that would have made this game go a lot quicker.

1) K/R 2/3 (winning bid)
2) H>J/K
3)J4 J>S/T
4)J4 S/T>J
3+4)
J4 J>S/T
J4 S/T>J
5) R/S 5

My inferences were that J, K cannot be in 1, J cannot be in 2, J cannot be in 3, H cannot be in 4, H cannot be in 6.

I think the key inference was that J could only be in 4 and 6.
I also recognized the implication of R being the winning big (S=5)

Some specific questions:
Did I miss any key inferences that would have made the game go forward more quickly?
Is there a more appropriate way of diagramming rule 1? I didn't put it in my diagram at all (just wrote down the rule) and just relied on remembering it.

Thanks,
Nadia

[Dave Killoran]

Hi Nadia,

You look like you have a good handle on what's going on The one other thing I would have done is that, given all those rules and restrictions (and especially the way the third and fourth rules operate), I would have taken the extra step of writing down a few templates. These templates would be be based on J being fourth or not, and when J is not fourth, whether R or S is fifth. That leads to three templates that capture a lot of the truth in this game and make the information easier to process.

As for the fourth rule, I'd note part of the rule on the diagram itself with subscripts:


1 2A 3A 4 5 6


Then, you could note that the accepted bid is K/R like this: A2/3 K/R

But overall, good job!

[Nadia0702]

Thanks Dave! I struggled with the decision for making templates, but now see that it would've probably been a good idea. Thanks for the tip on diagramming the 1st rule.

Nadia

[lsatstudier]

Hi!

I was wondering if someone could please explain how you decide the base for this question's diagram. Specifically, in the rule that states "If J is the fourth lowest in cost, then J is lower....," how do you determine which way is lower if I have a base numbering 1 through 6? Do you put S and T to the right or left of J? I tried setting up the diagram horizontally and vertically but still seem to be missing something.

Please let me know. Thank you so much!