# If Roil is shown in both the second and fourth weeks, which one of the following could be true?

zia305 on May 30, 2020

Explanation

Replies

Skylar on May 31, 2020

@zia305, happy to help!

Let's go through each answer choice by assigning R to both the 2nd and 4th weeks (as the question calls for) and testing out possible scenarios.

(A) O: G __ __ __
W: __ R __ R
1 2 3 4
We know that each painting must be placed, and Rule #2 says that G cannot be shown in the same week as P. Therefore, the only spot we can place P is Week 3. This leaves S to fill Week 1. However, Rule #3 says that if we have S, we must also have H in that same week. We have G in the Week 1 instead of H, so this situation violates the rules and is invalid. (A) is incorrect.

(B) O: __ H __ __
W: __ R __ R
1 2 3 4
If we have H in the second week, we know from the contrapositive of Rule #4 that I must be in the first week. Rule #3 says that if S is placed in a week, H must also be there. We only have Week 1 and 3 open as options for S, and we just placed I in Week 1. So, we place S in Week 3 along with H. However, this means that H is in both the 2nd and 3rd weeks, which violates the Rule #1. Therefore, the scenario is invalid and (B) is incorrect.

(C) O: __ __ __ H
W: __ R __ R
1 2 3 4
We know that all paintings must be shown, so we need to place S. Rule #3 says that H must be shown in whatever week S is placed in. The only open spots to place S (along with H because of Rule #3) are Weeks 1 or 3. If we place S and H in Week 1, we violate Rule #4. If we place S and H in Week 3, we violate Rule #1. Therefore, the scenario is invalid and (C) is incorrect.

(D) O: __ I __ __
W: __ R __ R
1 2 3 4
As all paintings must be shown, we need to place S. Rule #3 says that there must be an H in the same week that we place S. So, what weeks could we place both S and H? Again, only Weeks 1 and 3 have two open spots. However, I is in Week 2, which means I cannot be in Week 1, and following Rule #4 we know that this means H must be in either Week 3 or Week 4. Therefore, we place H and S in Week 3. This leaves P to be placed in Week 1. From Rule #1, we know that I cannot be in Week 1 since it is already in Week 2. From Rule #2, we know that G cannot be placed in the same week as P, so G cannot be in Week 1. From Rule #4, we know that H cannot be placed in Week 1. Therefore, there are no oil paintings that can be placed in Week 1, so the scenario is invalid and (D) is incorrect.

(E) O: __ __ __ I
W: __ R __ R
1 2 3 4
Let's draw out a scenario using this framework:
O: I G H I
W: P R S R
1 2 3 4
This is a valid scenario that does not break any of the rules. Therefore, (E) could be true and is the correct answer.

Does that make sense? Please let us know if you have any other questions!

zingzang123 on July 26, 2020

This is the method I use, but I always find it lengthy and too time consuming to go through the answer choices one by one. Is there a way to go faster?

MichaelKoss on July 17, 2021

How does placing S and H in Week 3 violate Rule #1 when evaluation Answer Choice C and then become a valid placement to get the correct answer in Answer Choice E?

Emil-Kunkin on April 25 at 06:56PM

Because the reason we can't place S in week three in C is that H is in week four. H is not in week four in E.