LG Game 1 Setup, by LSATHacks
This is an explanation of the first logic game from Section III of LSAT Preptest 29, the October 1999 LSAT.
An accountant needs to pay seven bills (1, 2, 3, 4, 5, 6, 7) over the next two days: Wednesday and Thursday (W, T). You must determine the possible payment schedule according to the rules.
Game Setup
This is a grouping game, and it illustrates a very important principle. Whenever a rule only allows two possibilities, you can split the game into two scenarios. This is always very useful.
The first rule lets you make two scenarios. Either three or four bills are paid on Wednesday.
Or
You should draw the second rule directly on the diagram. 1 and 5 are never in the same group. Since there are only two groups, that means one of them goes in each group.
Or
I’ve added in the third rule as well: 2 is always paid on Thursday. If you draw it directly on the diagram, you no longer have to waste mental space thinking about it.
By drawing the rule about 2 directly on the diagram, you can also combine it with other rules to make deductions.
For instance: rule four says that 4 and 7 always have to go together. On the diagram with four bills on wednesday, there is only one free space on Thursday. So 4 and 7 have to be paid on Wednesday.
(Three bills on Wednesday)
(Four Bills on Wednesday)
I’m building these diagrams two at a time because this is how I actually set up two scenario games on my own. It’s much faster, and the process is simple: place the rules on the diagram, and look for deductions by focussing on the areas with the most restrictions.
So now our diagram has rules 1-4. The final rule completes the second diagram.
If 6 is paid on Wednesday ➞ 7 is paid on Thursday.
The contrapositive is:
If 7 is paid on Wednesday ➞ 6 is paid on Thursday.
Since 7 is paid on Wednesday in the second diagram, 6 has to be paid on Thursday.
Only 3 is left to be paid, and they fill the last spot on Wednesday.
Or
So we know almost everything if four bills are paid on Wednesday.
If three bills are paid on Wednesday, things are slightly more open ended. You must place 4 and 7 together on either Wednesday or Thursday. There will be two spaces left on the other day, and 3 and 6 have to go there.
Here are the two possibilities for placing 4 and 7 when three bills are paid on Wednesday.
(Three bills on Wednesday)
And here’s the other scenario
(Four Bills on Wednesday)
There are only three possibilities in this game.
- Three bills on Wednesday. 4 and 7 are on Wednesday.
- Three bills on Wednesday. 4 and 7 are on Thursday.
- Four bills on Wednesday.
The main point of uncertainty is where 1 and 5 go. They’re interchangeable, so either one could go on Wednesday or Thursday.
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Further clarification on my comment below.
The contrapositive of:
If 6 is paid on Wednesday ➞ 7 is paid on Thursday.
is:
If 7 is NOT paid on Thursday, 6 is NOT paid on Wednesday
if X, then Y
if NOT Y, then NOT X
but “if Y, then X” is not a contrapositive or “if X, then Y”
Hi there – I’m not understanding how Rule #5 is a contrapositive of “If 7 is paid on Wednesday –> 6 is paid on Thursday”.
The rule states: “If 6 is paid on Wednesday –> 7 is paid on Thursday.”
This rule in and of itself, not taking into account the other rules, does not imply that if 7 is paid on Wednesday, 6 is paid on Thursday. With just rule #5 alone, bills 6 and 7 could both be paid on Thursday.
When taking the other rules into consideration, then yes there is a limitation that makes “If 7 is paid on Wednesday –> 6 is paid on Thursday”, but that limitation is not because of rule #5 it is because of a combination of the rules.
Would you agree that “If 6 is paid on Wednesday –> 7 is paid on Thursday” is NOT a contrapositive of “If 7 is paid on Wednesday –> 6 is paid on Thursday”, when considering just that rule in isolation?
There are only two days, and all variables must be places. Are those the rules you meant? In that case, not Thursday = Wednesday. So, if you take only those two rules, it is the contrapositive. You don’t need any of the rules from the list, other than the basic info from rule 1 that only Wednesday and Thursday are possible days.
>With just rule #5 alone, bills 6 and 7 could both be paid on Thursday.
It actually is true that both can be paid on Thursday. You can always negate a sufficient condition without affecting the necessary.
Is it fair to say that whenever a split is possible, we should pursue it?
If it’s a split between two, I pretty much always do it. If it’s a split more ways than two, I usually don’t. Intuition from past games would let me decide whether to split something three ways.
That may sound like a cop out, but it’s part of the skillset required to get a -0. Doing past games over again and realizing when efficiency potential exists. Then matching those models onto new games.