December 2017 LSAT
Section 4
Question 9

# Which one of the following pairs CANNOT be the second and third students to perform, respectively?

Reply

Skylar on December 8, 2019

@Sabrinamc, maybe I can help explain it!First, let's look at the game setup:

We are given 5 students to order: G, H, R, S, T.

Each will perform one at a time and only once, so our diagram looks like: __ __ __ __ __

Now let's breakdown the rules:

#1: H - R. From this, we can deduce that H cannot be last and R cannot be first,

#2: (G - T) -> (R - T and S - T). The contrapositive of this is: (T - R or T - S) -> (T - G).

#3: Either (H - S and H - T) OR (T - H and S - H).

Now, let's look move onto the questions.

QUESTION (1):

G __ __ __ __

Since Gloria is first, we know that G will be before T. According to Rule #2, this also means that R and S have to be before T. According to Rule #1, H has to be before R. Therefore, T has to go in the fifth spot because all of the other variables must come before it. This leaves us with:

G __ __ __ T

This only Gives us three possible ways to fill in spots 2-4, since H has to come before R.

GSHRT is the first possibility, but this is incorrect because, according to rule #3, H either needs to be before both S and T or after both S and T. It cannot be in the middle. This leaves us with only two valid options:

GHRST

GHSRT

Therefore, (D) is the only option that provides a possibility that is shown in one of these two scenarios.

QUESTION (2):

- Immediately, we can eliminate (C) because we know that R cannot be first since, according to Rule #1, it has to come after H.

- This same rule allows us to eliminate (D) because if S is in spot 1 and R is in spot 2, H is not before R.

- We can also eliminate (A) because if G is in spot 1 and T is in spot 2, G is before T but there is no way for R and S to also precede T. This violates Rule #2.

- Lastly, we can eliminate (E) because Rule #3 tells us that we either need both T and S before H, or both T and S after H. Therefore, we cannot have T in spot 1 and H in spot 2 because S would have to go after H.

- So, we are left with (B). HGRST is an example of this.

QUESTION (3):

We are looking for the answer that is impossible to make without violating the rules. A through D have valid examples, as listed below:

(A) HRSGT

(B) TGSHR

(C) HGSRT

(D) HRTSG

(E) is the correct answer because it would force G to be before T, which according to Rule #2, would cause S and R to both be before T as well. This is impossible since the answer choice places T in the fifth spot.

QUESTION (4):

Let's plug each answer choice into the respective spots and see if we can make a valid scenario.

(A) __ G H __ __

In this case, R must be in either spot 4 or 5 because Rule #1 states it must come after H. However, T and S must also fill the two spots after H because Rule #3 states they must both either come before or after H and there is only one open spot before H. So, neither R, T, nor S can fill spot 1. Therefore, this scenario is impossible and (A) is correct.

QUESTION (5):

S __ __ __ __

Let's create a valid scenario and see what we can eliminate: STGHR. This meets all the rules and eliminates (B) and (C).

Let's make another scenario: STHRG. This meets all the rules and eliminates (A) and (D).

Therefore, we are left with (E),

QUESTION (6):

__ __ __ ___ S

Since S is in the last spot and therefore cannot go before T, we need to make sure that G is not before T so that we do not violate Rule #2. We also know that H cannot be in the fourth spot because Rule #3 says H either needs to be before or after both S and T.

With these restrictions in mind, let's make a hypothetical and see what we can eliminate: HRTGS. This eliminates (A), (C), and (E).

Now, let's alter our hypothetical to make: HTGRS. This eliminates (D).

Therefore, we are left with (B).

Does this all make sense? Please reach out with any other questions and best of luck with your studies!