Which one of the following could be the order in which the artifacts are displayed, from case 1 to case 7?

Skylar on May 18, 2020

@mg123, I do not believe there is a video explanation currently posted. However, I am happy to provide a written explanation.

GHJMNPS

<- __ __ __ __ __ __ __ ->
1 2 3 4 5 6 7

We are told that the display cases are arranged in a circle. Don't let this throw you off! We can still draw a linear diagram for clarity, but I recommend putting arrows on the end to remind yourself of the circular arrangement. The key is that we know case 1 and case 7 are next to each other.

Rule #1: spot 7 = H/J
Rule #2: N < M
Rule #3: HM or MH
Rule #4: NOT SP and NOT PS
Rule #5: NOT PJ and NOT JP and NOT SJ and NOT JS

<- __ __ __ __ __ __ (H/J) ->
1 2 3 4 5 6 7

QUESTION 1:
The best approach to this type of question is to go through rule by rule and eliminate answer choices with violations.
- (C) violates Rule #1.
- (A) violates Rule #2.
- (D) violates Rule #3.
- (E) violates Rule #5. Remember, 7 and 1 are next to each other.
- This leaves (B) as the correct answer. We should write out the arrangement to the side as a free hypothetical to be used for later questions.

QUESTION 2:
We know that G is 6th. Let's write this out with our two scenarios for the 7th spot.
<- __ __ __ __ __ G H ->
1 2 3 4 5 6 7
- Under this scenario (when H is 7th), M must be 1st. This is because Rule #3 states that H and M must be next to each other and G is in the other spot adjacent to H.
- However, this poses a problem because if M is in the first spot, it is impossible for N to be in a lower-numbered spot. Therefore, this setup violates Rule #2.
- So, H cannot be 7th. Let's look at the alternate scenario.
<- __ __ __ __ __ G J ->
1. 2 3 4 5 6 7
- Rule #5 says that neither P nor S can be next to J. Remember, spots 1 and 7 are next to each other since the cases are arranged in a circle. Therefore, neither P nor S can be 1st.
- Rule #3 says that M and H must be next to each other and Rule #2 says that M must be in a higher-numbered case than N. Therefore, neither M nor H can be 1st.
- This leaves only N to be 1st, which is answer choice (C).

QUESTION 3:
We know that S is 3rd. Let's write this out with our two scenarios for the 7th spot.
<- __ __ S __ __ __ H ->
1 2 3 4 5 6 7
- Rule #3 says that M and H must be next to each other and Rule #2 says that M must be in a higher-numbered case than N. Therefore, M must be 6th.
- Rules #4 and #5 say that S, P, and J must all be separated. This means that either P or J needs to go 1st and the other needs to go 5th.
- This leaves either N or G to fill spot 2 and the other to fill spot 4.
<- (P/J) (N/G) S (G/N) (J/P) M H ->
1 2 3 4 5 6 7
- Before we try to write out the scenario where J is 7th instead of H, let's check in with our answer choices and see if we can already answer the question.
- The question asks what "must be true," and there is only one answer choice that is definite in our diagram - (C). So, (C) is correct and M must be 6th.

QUESTION 4:
We are asked which answer choice could be true. We should start out by looking for past hypotheticals that prove one of the answer choices could work.
- The hypothetical we just drew in Question 3 shows that P could be 1st.
- So, (D) is correct.

QUESTION 5:
Like the previous question, we are asked what could be true and we should first start by checking for past hypotheticals that may correspond with one of the answer choices.
- The hypothetical we drew in Question 3 shows that J could be 1st while S is 3rd.
- Therefore, (E) is correct.

QUESTION 6:
We know that P is 2nd. Let's write this out with our two scenarios for the 7th spot.
<- __ P __ __ __ __ H ->
1 2 3 4 5 6 7
- We know that in order to fulfill Rule #2 and Rule #3, M would have to be 6th.
- However, Rule #4 and Rule #5 say that P, S, and J must all be separated. This is not possible in the current arrangement.
- So, H cannot be 7th. Let's look at the alternate scenario.
<- __ P __ __ __ __ J ->
1 2 3 4 5 6 7
- In order to separate P, S, and J like Rules #4 and #5 call for, S must be placed either 4th or 5th. Remember that the 7th spot is next to the 1st spot.
- Let's try putting S 4th first.
<- __ P __ S __ __ J ->
1 2 3 4 5 6 7
- Rule #3 says that M and H must be next to each other. The only two adjacent open spots for them are 5 and 6.
- This means that either G or N would go in spot 1, and the other would go in spot 3.
- Let's check in with our answer choices at this point.
- M could be 6th, so (D) is correct.

Hope this helps. Please let us know if you have any other questions!