# Lesson 14; game 2

• June 16, 2016 at 1:33 pm #2060
jareddevore
Participant

Hi, I just have a quick question about why D is the answer to number 1. For some reason, I found E to be the answer, and can’t really figure out why its not.

Thanks!

• June 16, 2016 at 2:42 pm #2061
LSAT Dan
Participant

This game is generating quite a bit of interest!

Let’s start with (D). If K is on the bottom shelf, the L is on the middle shelf (third rule).

Since there is at least one book on the middle shelf, the distribution of books must be 1 on the top, 3 in the middle, and 2 on the bottom. That’s the only way the first rule can be satisfied; 2 books on the bottom shelf and one on the top. The other way that it might have been satisfied originally is with 4 on the bottom and 2 on the top, but in that variation, there aren’t any books on the middle shelf. As long as the middle shelf isn’t empty, it must be 1 on the top, 3 on the middle, and 2 on the bottom.

So far, testing answer choice (D), it’s:
Top: 1 book
Middle: 3 books, including L
Bottom: 2 books, including K.

G and J must be on the same shelf, and at this point, the only shelf with enough vacant spaces for both of them is the middle shelf, so they’re with L. Now it’s:

Top: 1 book
Middle: G, J, and L
Bottom: K and one other book.

The last two books are F and H; one is on the top shelf, and the other is on the bottom shelf, and we have no flexibility, because of the last rule: F is never on the top shelf. So if K is on the bottom shelf, there’s only one valid layout:

Top: H
Middle: GJL
Bottom: FK

So now let’s look at (E), which starts with G on the bottom shelf. J goes with G, so we know that both G and J are on the bottom shelf. Nothing else seems immediately forced from here. Here are two possible arrangement that satisfy (E):

Top: KL
Middle: (none)
Bottom: GJFH

Top: K
Middle: FHL
Bottom: GJ

Since at least two valid layouts can be created with G on the bottom shelf, (E) cannot be correct; placing G on the bottom shelf does not completely determine the arrangement.

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