#8 - Local, Could Be True

[Administrator]

Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=15461)

The correct answer choice is (C)

The question stem stipulates that three dishes—1, 2, and 3—are all stored on the same shelf. Thus, the 2-2-2 distribution is impossible, and only the 3-3-0 or 3-2-1 distributions could apply. However, from our analysis of the 3-3-0 distribution, each group of three under that scenario must contain one dish from the 1-4 pair, one dish from the 5-6 pair, and one dish from the 2-3 pair. Thus, the alignment in this question violates those requirements, meaning that the 3-3-0 distribution cannot apply. Therefore, in this question, the 3-2-1 distribution must be in effect.

With the 3-2-1 distribution established, the “3” shelf is fully occupied by dishes 1, 2, and 3. Because dishes 5 and 6 must be on separate shelves, they occupy a space on the other two shelves (which then means that the shelf with two dishes and the shelf with one dish must be consecutive; in other words, the shelf with three dishes is not the middle shelf. More on this in a moment):

PT69_Game_#2_#8_diagram 1.png

Thus, the only remaining dish that is unassigned is dish 4, and dish 4 must be on the shelf with two dishes:

PT69_Game_#2_#8_diagram 2.png

With the composition of each shelf largely determined, we can examine the effect of the rules on the shelves. The group of three contains dish 2, which from the first rule must be on the middle or top shelf. But, because dishes 5 and 6 are in the groups of one dish and two dishes, one of those groups must be the middle shelf, and thus the group of three cannot be stored on the middle shelf. Consequently, in this question the group of three must be stored on the top shelf. The group of one and two are the bottom and middle shelves, in some order (this information is the justification for answer choice (C)).

Now, we can quickly identify the correct answer. Answer choices (A) and (B) can be eliminated because they attempt to place the group of one or the group of two on the top shelf, a violation.

Answer choices (D) and (E) can be eliminated because they attempt to place the group of three on a shelf other than the top shelf.

Because the group of two could be stored on the bottom or middle shelf, answer choice (C) could be true and is therefore correct.

[tnafisi]

I do not understand how answer C is correct I chose A but I thought A,B and C could work. we do not have much information about the limitations of where the dishes could be so it did not help. I know that 6 can not be with 5 so it had to be in-between 2 and 5 since 5 was not with 2 in this question but from what I understood 4 can be with 6 or 5 I did not find any limitations for it. please explain why the answer is as so, thank you.

[Dave Killoran]

Hi T,

There's actually a lot going on in this question--it's a tough one! With all three of dishes 1, 2, and 3 assigned to the same shelf, it initially appears as if the dishes are in the 3-3-0 or 3-2-1 distributions. But, the 3-3-0 is impossible in this question because it would force dishes 5 and 6 onto the same shelf. So, we actually know that you are in the 3-2-1

With the 3-2-1 distribution established, the “3” shelf is fully occupied by dishes 1, 2, and 3. Because dishes 5 and 6 must be on separate shelves, they occupy a space on the other two shelves:

• Shelf of 3 dishes: 1 2 3
  
  
  Shelf of 2 dishes: 5/6
  
  
  Shelf of 1 dish: 6/5

Thus, the only remaining dish that is unassigned is dish 4, and dish 4 must be on the shelf with two dishes:

• Shelf of 3 dishes: 1 2 3
  
  
  Shelf of 2 dishes: 5/6 4
  
  
  Shelf of 1 dish: 6/5

With the composition of each shelf largely determined, we can examine the effect of the rules on the shelves. The group of three contains dish 2, which from the first rule must be on the middle or top shelf. But, because dishes 5 and 6 are in the groups of one dish and two dishes, one of those groups must be the middle shelf, and thus the group of three cannot be stored on the middle shelf. Consequently, in this question the group of three must be stored on the top shelf. The group of one and two are the bottom and middle shelves, in some order. Since the group of two dishes can be stored on the middle shelf, answer choice (C) could be true and is therefore correct.

Overall, there is a lot of numerical information in this game, and that info, when combined with the rules, actually limits what can occur.

Please let me know if that helps. Thanks!