Which one of the following could be true?

Skylar on March 16, 2020

@DavidW, happy to help!

Here is our setup:

__ __ __ __ __ __
1 2 3 4 5 6

HLMSTV

Rule #1: S cannot be assigned to 1.
Rule #2: H-L -> M-L
L-M -> L-H
Rule #3: S-V and S-M
Rule #4: (V/H) - T - (H/V)

From these rules, we can make a few deductions to help save us time later:
- S cannot be assigned to 1 (Rule #1), 5, or 6 (Rule #3). Therefore, S can only go in 2-4.
- T cannot be assigned to 1 or 7 (Rule #4). Therefore, T can only go in 2-6.
- The only options for spot 1 are L or H. S is prevented from being assigned to spot 1 by a rule, and M, T, and V all have other antiques that must precede them.

Now, let's move onto the questions.

QUESTION ONE:
To solve this, we can go through each of our rules in order and eliminate answer choices that violate them.
(D) violates Rule #1 because S is in the first spot.
(A) violates Rule #2 because L-M but H-L.
(E) violates Rule #3 because V-S.
(B) violates Rule #4 because H-V-T.
This leaves (C) as the correct answer. We should write out this diagram as a valid arrangement to use for later reference: HSTMLV

QUESTION TWO:
To solve this, we can try each answer choice until we find one that is valid.
(A) __ T L __ __ __
1 2 3 4 5 6
This is an invalid scenario because we know that H is the only option left to go in the first spot, but this would make it so that H-L and it would be impossible to fit M in as to make it so that M-L. Therefore, (A) violates Rule #2 and is incorrect.
(B) __ S V __ __ __
1 2 3 4 5 6
One possibility for arranging this without violating any rules is LSVTHM. Therefore, (B) is correct and we can move onto the next question.

QUESTION THREE:
This question tells us: M-T and V-T.
We can add this with our other rules to get a larger chain: L - S - [(V-M) or (M-V)] - T - H
(D) is the only option that matches the chain, so it is correct.

QUESTION FOUR:
To solve this, we can first look to valid arrangements from past questions and eliminate antiques that were placed in the spot before V. We can eliminate (B) from Question 1, (D) from Question 2, and (C) from Question 3. This leaves us with H and T. Rule #4 tells us that (V/H) - T - (H/V), so we know that it would be impossible for H to be placed immediately before V. Therefore, (A) is the correct answer.

QUESTION FIVE:
Let's work through our answer choices.
(A) __ M __ __ __ __
1 2 3 4 5 6
Rule #3 tells us that S-M, but Rule #1 tells us that S cannot go in the first spot. Therefore, this is invalid.
(B) __ L __ __ __ __
1 2 3 4 5 6
We know from our original deductions that only L or H could go in the first spot. Since L is placed in spot 2 here, H must be assigned to spot 1. However, this would mean H-L, but it would be impossible to arrange it so that M-L. This would violate Rule #2 and make the arrangement invalid.
(C) is incorrect for the same reason that (A) is.
(D) __ __ L __ __ __
1 2 3 4 5 6
Since L is not first, we know that H must be. However, this either violates Rule #2 because H-L and L-M or it violates Rule #3 because M-S. Therefore, it is invalid.
(E) __ __ __ __ M __
1 2 3 4 5 6
One possibility for arranging this without violating any rules is HTSVML. Therefore, (E) is valid and correct.

QUESTION SIX:
Let's work through our answer choices.
(A) is incorrect because we know from our original deductions that S cannot go in the fifth spot because it must precede V and M.
(B) __ __ __ S __ __
1 2 3 4 5 6
One possibility for arranging this without violating any rules is LHTSVM. Therefore, (B) is correct and we are done with the game.

Does that make sense? Please let us know if you have any other questions and best of luck with your studies!

Nishant-Varma on August 14, 2021

Thanks a lot, Skylar!