This is an explanation of the third logic game from Section II of LSAT preptest 63, the June 2011 LSAT.
Six company vehicles – a hatchback, a limousine, a pickup, a roadster, a sedan, and a van (H, L, P, R, S, V) – will be serviced during a week. One vehicle will be serviced each day, from Monday to Saturday (M, Tu, W, Th, F, S). You must use the rules to determine the possible orders of the vehicles.
I made almost no deductions on the setup when I first did this. But as I was going through the questions, I saw I had missed a major deduction. I’ll first show you the standard setup, then I’ll show you how to make the deduction.
(I still did fine on this game. I figured out the deduction on the first question where it was useful, and so I was able to use the deduction on all the questions where it mattered. )
Here’s the standard setup. I combined rules one and two:
We don’t know who is after H, but someone is, so you should draw that.
The third rule, I drew as an “Or” statement. This is an exclusive or, unlike most “Or’s” on the LSAT. Since both “Or’s” in this game are exclusive, I just memorized that detail.
Most people draw the fourth rule wrong
The fourth rule is very common on modern linear games. Most students just draw this:
This is incomplete. The rule says “but not both”. If the sedan is before the pickup, then it can’t be before the limousine. That means the sedan is after the limousine. Likewise, if the sedan is before the limousine, then it can’t be before the pickup, so the sedan is after the pickup. Here’s the full rule:
Always draw the full rule.
Deduction: Only L or P can go last
Now, the three diagrams I’ve drawn above are enough to solve the game. It’s what I drew when I first did this game – but I made a big deduction on question 14: only the pickup or the limousine can go last.
I’ll explain how I figured that out. It’s possible to make this deduction upfront. You can do this by looking at the most restricted space. In this case, the last space is very restricted.
- The van and the roadster can’t go last, because they’re before the hatchback.
- The first rule says the hatchback can’t go last.
- The sedan can’t go last, because it’s in between the pickup and the limousine.
You can draw these restrictions as “not” rules under the final space:
That’s four variables that can’t go last. So only the limousine and the pickup can go last. You can turn this into two diagrams:
Remember, the order has to be P – S – L or L – S – P. Having P or L last determines the order of this group in both diagrams. I’ve drawn this.
We know that the pickup needs to be beside either the sedan or the van. In the second scenario, only the sedan can go fifth. That’s because the van is before the roadster and the hatchback. (You can’t deduce anything new in the first scenario):
Next, you should draw the remaining variables on each diagram. This helps to visualize possibilities:
The commas indicate that variables are interchangeable. For instance, P – S could go before V – R – H in the first scenario, or after, or in between.
In the initial setup, I drew V – R – H – __ . I haven’t drawn a space after H here because the rule just says H can’t go last, and both diagrams now have someone last. So the first rule is automatically fulfilled in both diagrams.
There are only two main scenarios
Only the third rule isn’t on the diagram now. That still applies to the first scenario. I drew it up and right as a reminder:
This is exactly what my diagram looked like the second time I did the game. It was much faster. I recommend you try this game with both the rules based approach and the scenario based approach. Personally, I find the scenarios much faster, but I don’t always see them up front.
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