December 2016 LSAT Section 3 Question 20

# Which one of the following CANNOT be true, no matter how many trades are made?

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Shunhe on January 8, 2020

Hi @hannahnaylor5,Thanks for the question! A couple of other people have asked about a video explanation for the problem, so let me help explain this question for you. We have three real estate companies: R, S, and T. They each own buildings with different classes that they can trade for each other. You can either trade 1 building for 1 building if they're the same class, or class 2 buildings are worth two class 3 buildings, and class 1 buildings are worth two class 2 buildings (and hence four class 3 buildings).

The way I like to think of this is to frame everything in terms of class 3 buildings (which we'll call "units"). Each company is going to start off with a certain number of units, and can't increase or decrease its initial number of units by trading. Class 3 buildings are worth 1 unit, class 2 building are worth 2 units, and class 1 buildings are worth 4 units. Thus, R, which owns a class 1 and two class 3s, starts off with 6 units. S, which owns a class 1 and a class 2, starts off with 6 units. T, which owns 3 class 2 buildings, also starts off with 6 units. So each of them start off with 6 units, and they can't gain our lose units by trading.

Take a look at (A). (A) tells us R ends up owning F and G towers. Both of these are class 1 towers, and so if R owns both, (A) would own 8 units of towers. But we've established that trading can't change your number of units, and so we know that (A) must be wrong. Without thinking about this in terms of units, we know that if R already owns tower G, then it basically traded two class 3 towers up for a class 1 tower, and there's no way to do that. You could get one class 2 tower, but you can't trade that for a class 1 tower.

The other answer choices, if you go through them, will all add up to 6 units, and so could be possible. Hope this helps!