LSAT 80, Game 4 Setup, Real Estate Companies, LSATHacks

Game Setup

Time on first attempt: 6:08

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I think this was supposed to be a hard game. It’s certainly an unusual one: I’ve never seen another LSAT game like this.

But it’s actually incredibly easy, once you notice there’s a simple mathematical trick. You can assign each of the buildings a number value.

To explain this, I’ll first give an analogy. Let’s say someone is trading iphones. They have iPhone X’s, iPhone SE’s, and iPhone 4’s. 

• The X is fairly new, and worth $800
• The SE is semi new, and worth $400
• The 4 is old, and only worth $200

You can trade iphones in any combination, as long as the values as equal. So, an iphone X can be traded for two SE’s, or four 4’s.

Rather than using money, we could simplify things by saying that 

• The iPhone 4 has a value of 1
• The iPhone SE has a value of 2
• The iPhone X has a value of 4

So, let’s say someone starts with an iPhone X, and two iphone 4’s. Their iPhone stock has a total value of 6.

They make some phone trades. What kinds of phones can they end up with? For example, can they end up with two iPhone X’s? 

No, that’s too much: two iphone X’s = 8, and this person only started with 6.

So, you can use the number 6 to see if a set of phones is the correct amount. If someone starts with 6, they must end to 6.

You may have figured out that I was making an exact analogy to the buildings. Instead of thinking “Two class 3’s for a class 2”, I want you to think of buildings as having number values. These sets are all equal:

Four class 3 = two class 2 = one class 1

If you make a class 3 worth 1, then each set above is worth 4 in total. 

Let’s look at R’s actual holdings. They have one class 1 (worth 4), and two class 3’s (each worth 1). So, here’s the value of R’s holdings:

Diagram 3

They’re worth 6. But, it will be cleaner to combine the value of the two group three buildings, since they’re always traded in sets of two:

Let’s look at the value of everyone’s set of buildings:

Every group is worth six! This gives us a new rule:

After all trades, each group must still be worth six

Once you know this, it’s easy to see which answers are right or wrong. People can trade as many buildings as they want, but they can never increase or decrease the value of their holdings.

I don’t think any question requires you to think about all the trades that had to happen to produce a new set of buildings. Instead, you only have to think: does this new set of buildings add up to 6?

Note that the letters have an alphabetical order of value. An early alphabet letter is worth 4 (F, G) a middle alphabet letter is worth 2 (K, L, M, O), and a late alphabet letter is worth 1 (Y, Z). This makes the answers faster to calculate.

You may be thinking “I could never come up with this system! I’m going to law school to get away from math!”. There are two things I can saw to that:

1. Repeat this game over and over, without reference to the explanation, trying to replicate this system. This will help make it intuitive.
2. This skill is relevant to law. Lawyers deal with business transactions, and need to be able to do at least some basic, quick mental calculations.

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