#23 - Global, Justify

[Dave Killoran]

Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?f=157&t=1677)

The correct answer choice is (E)

The question stem requests an additional piece of information that will fully determine the grants for each quarter. Because the numbers in this game allow for different results, the answer must address the numbers in some fashion, and the correct answer will definitively affect the total number of grants, and the quarters for each grant.

Answer choices (A) and (B) specify that two grants are awarded to T and Y, respectively. While this sets the grants-to-areas distribution at 2-2-1-1, there is still a wide variety of options for the grants-to-quarters, and thus neither of these answer choices satisfies the requirement of the question stem.

Answer choices (C), (D), and (E) indicate that there are three grants in one quarter, and thus one in each of the other quarters (the 3-1-1-1 grants-to-quarters distribution). Thus, there are also six total grants, determining the grants-to-areas distribution at 2-2-1-1. Therefore, any of these three answers has the potential to provide the correct answer; the question now is which specific quarter produces the proper result.

Answer choice (C): If three grants are awarded in the first quarter, those three grants must be for M, T, and Y. However, the second M grant could be in the third or fourth quarter, so answer choice (C) does not definitively determine which grants are awarded each quarter.

Answer choice (D): As shown by the hypothetical in question #21 (A) and (B), and the discussion of question #22 (A), the second quarter can have three grants of differing compositions, and thus three grants in the second quarter is not determinative. Answer choice (D) is therefore incorrect.

Answer choice (E): This is the correct answer choice. If three grants are awarded in the third quarter, those three grants must be for M, T, and Y (from the third rule, W cannot be awarded a grant in the third quarter). The second M grant must then be awarded in the first quarter (again, from the third rule). The fourth quarter must also be awarded a grant, and thus the sixth and final grant must be W in the fourth quarter. Thus, this answer choice fully determines the grants for each quarter, and is therefore correct.

[demk26]

Hi PS,

Can you please provide an explanation for #23 (Justify Question) of this game?

Thank you!

[Rachael Wilkenfeld]

Hi demk,

To start off here, we want to think about what would drive knowledge about the game. The idea of consecutive quarters cannot have the same areas granted really can drive this game. If we pile a bunch of areas in either slot 2 or 3, we might be able to find a really limited solution.

We know we have at least 5 grants (2Ms, plus one of T, Y and W) but at most 6 grants (2Ms, plus one of T, Y, and W, and a second of T, Y or W). In order to have all the quarters have at least one grant, we can have at most 3 grants in a single quarter (3 in one quarter, 1 in each of the other three, would total our maximum of six grants).

So let's try and fill up slot 2, and see if we can figure out a full solution based on that.

If slot 2 is full, it must have W, but we don't know what else it would have. It could have M (with the other M in 4), or it could have Y/T or both. There's a lot we don't know about what a solution here. Hopefully putting 3 grants in slot 3 works out better for us.

If we put 3 grants in 3, they must be M, T and Y. This is because W is in 2, and you can't have the same grant in two consecutive quarters. Whew. This is already looking a bit better. Now I know that we have W in quarter 2 alone, MTY in quarter 3. We still need to place one more M. That can't go in 4 because M is in quarter 3. That places M in one. And now we need some grant for quarter 4. It can't be any of those grants from quarter 3, so that leaves only W as an option.

So if we put 3 grants in quarter 3, we know the grants look as follows:

Q1:M
Q2: W
Q3: MTY
Q4: W

That's fully solved. And it's answer choice (E).

Hope that helps!
Rachael