Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping/Linear Combination game.

There are three variable sets in this game: the songs, the vocalists, and the performance order. The performance order should be chosen as the base, and the other two variable sets stacked on top:

O96_Game_#4_setup_diagram 1.png

The first two rules can be combined to make a super sequencing chain:

O96_Game_#4_setup_diagram 2.png

The only song not addressed in the sequence is X, which can be played at any point in the performance order. Thus, because Y must be performed before four other songs, only X or Y can be played first, and Y must be played first or second. We can also draw a number of other Not Laws from the sequence:

O96_Game_#4_setup_diagram 3.png

Note that with three Not Laws on the sixth performance, we can infer that T, X, or Z performs last.

The third and fourth rules establish the songs that each vocalist can sing:

O96_Game_#4_setup_diagram 4.png

In examining the songs each vocalist can sing, some notable observations can be made:

• Because Y and Z appear only on George’s list, Y and Z must be performed by George.
  
  Because T appears only on Helen’s list, T must be performed by Helen.
  
  Because O appears only on Leslie’s list, O must be performed by Leslie.
  
  Because P appears on Helen’s and Leslie’s lists, P must be performed by Helen or Leslie.
  
  Because X appears on all three vocalist’s lists, X can be performed by any of the vocalists.

The facts above can be shown as subscripts:

O96_Game_#4_setup_diagram 5.png

The subscripts can be attached to the super-sequence created by the first two rules:

O96_Game_#4_setup_diagram 6.png

The final rule indicates that the same vocalists cannot perform both first and last

O96_Game_#4_setup_diagram 7.png

Also, because the same vocalists cannot perform both first and last and George performs both Y and Z, if Y is performed first, Z is not performed last, and via the contrapositive, if Z is performed last, Y is not performed first:

O96_Game_#4_setup_diagram 8.png

Combining all of this information results in the final diagram for the game:

O96_Game_#4_setup_diagram 9.png

[lathlee]

Hi. Guys, How can I set up the rules and inferences the diagram in this case, i am simply lost cuz i never done this kind of set up. I am sure the one I had was inefficient

[Clay Cooper]

Hi lathlee,

Thanks for your question. Generally speaking, we need a bit more input from you before we delve into a discussion of a particular logic game. Ultimately, it won't be us who are taking the test; it's you! Our goal is to help you cultivate the analytical ability to approach these games on your own, which is why you need to help us help you first.

Here's what I'd like you to do:

1. Describe your approach to the setup. Were you able to determine what type of game it is? What the variable sets are?

2. Were you able to diagram any of the rules, or make any inferences?

I am confident that you will get more out of our help if we start with an understanding of how you approached the game and what you found difficult about it.

Thanks.

[lathlee]

Hi. I am just making the first condition,

IF both G and S are reduced, W is also reduced.

everyone knows G and S W

(-)W -G or -S

only one or can it both

as in when - W occurred, and I do not have any information about G and S,

should I assume that both of them are not reduced (which can happen, according to LSAT bible) or if I see one of them negated, aka: not reduced, (G or S) I assume that another is not reduced, Not negated.

[James Finch]

Hi Lathlee,

Are you sure you're posting in the right thread? This is for the October 1996 LSAT (Preptest 20), Section #3, Game #4, Questions #19-24. It's a hybrid linear/grouping game that uses 6 songs (OPTXYZ) and 3 singers (GHL) as variables.

[AJH]

Hello,

I am having trouble figuring out how I should diagram this game. Initially I thought to put G,H, and L as the base and assign two slots for each and fill in with the songs. I didn't set it up that way because I did not want to assume G, H and L preformed in that order with their respective songs. I decided to try using 1-6 as a base for the respective performances and then one slot above for the song that would be assigned to each. I used the rules to figure out which songs could and could not be sung at certain times (or in the 1-6 performances). However, I am stumped now in trying to figure out who sings which song. I know there are several rules with this information, but it still seems like there are too many possibilities to narrow it down and answer questions like # 20.

Thank you!

[Adam Tyson]

Thanks for the question, AJH! I handled this one with an advanced linear setup, with 6 slots and two rows (one for the songs, one for the singers). I also listed my variables in groups by singer, like this, per rules 3 through 5:

G: XYZ
H: TPX
L: OPX

I then went a step further and wrote out a few blocks that told me about certain fixed relationships based on unique pairs created by those three rules. For example, G is the only one that can sing either Y or Z, so since every song is sung exactly once I can be sure that G sings both of those. I did those as vertical blocks to match my advanced linear setup (where I put the singers on the bottom), like this:

Y | Z | T | O
G | G| H | L

That left only P and X unassigned, because P could be sung by either H or L and X could be sung by any of the three (and notice that there is no requirement that they each sing twice, so G could sing all three of his options and one of the others would then only sing once).

The first two rules gave me a sequence to work with, one that pushed Y up to the front of the order (first or second) and Z towards the back of the order (no earlier than 4th).

Y O P Z

and

Y T

(imagine those two sequences merged together, branching out from Y - I'm having trouble making that happen in this post)

For the last rule, I did a double-not-arrow for 1 and 6:

1 6

and I made note to myself that if Y was first, Z could not be last (since G sings both of those), and therefore either T or X would have to be last, and if Z was last, Y could not be first and so X would be the only option for first and Y, because of the sequence, would necessarily be second.

From there, I headed into the questions.

You asked specifically about question 20, and you can see from this setup that it is already answered: H performs T. This is because nobody else can perform T, and T must be performed.

Take another look at those unique pairs, created by the restrictions in rules 3 through 5, and I bet you'll find this game to be much easier than you realized. Good luck!

[alexis.la]

Hi Powerscore. My struggle with combination games and advanced linear has been that I get flustered trying to figure out the setup sometimes. My set up is a little different than the solution that was posted in this thread. Instead of putting the initial of the vocalist, I have a different row for each of them, and I would put the initial of a song on the corresponding vocalists row. I added what they COULD sing next to their row, and circled what I knew they HAD to sing.

My question is whether it's okay if my set-up doesn't match yours, if it got the job done. I did actually understand this game and moved pretty quickly through the questions. Let me know!

[Adam Tyson]

The question of whether you can use an alternate setup is best answered by saying "if it worked well for you, sure!" Our way is not necessarily the only way to do a game, alexis!

That said, I do have a concern about your choice here, and that is that it suggests that each person will be singing 6 songs in some order, rather than that there are six songs total. To set up rows for each singer makes it look like the first song has three different people singing it, when what we really want in that first position is a space for the song being sung and a second space for the person singing it. Two rows, not three, and a row for the singer because the three singers G, H, and L are a single variable set. You want one row per variable SET, not one row per VARIABLE.

If this setup worked for you, and you got a perfect score on the game in good time, then you do you! But if you struggled at all, consider the concepts that led us to do it the way we did, with one row per variable set, and see if it could be a better choice for you. We find that it's a better choice for us, so maybe you'll like it, too?