If Mei is on a team that places higher than the Hilltop team, then which one of the following could be true?

Mida on August 20, 2020

Please help

I thought A could be the answer because of a different scenario. But I also found that E too could be an answer. Why would choosing A be wrong over E.

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Victoria on August 21, 2020

Hi @maonuo,

Happy to help!

We know that there are three teams which have placed the highest in a high school debate tournament: F, G, and H.

Each team has exactly two members out of: M, N, O, P, S, and T.

We know that these teams have placed the highest tournament, so we must have a team in each of 1st, 2nd, and 3rd place.

Rule 5 tells us that Team G placed higher than Team H. This gives us three possible scenarios.

Option 1: F1 G2 H3

Option 2: G1 F2 H3

Option 3: G1 H2 F3

Rules 1 and 2 definitively place S and T within our outlined options above. We know that S is on Team G and T is on the team that comes in 2nd place.

Option 1

G2: S T

Option 2

G1: S
F2: T

Option 3

G1: S
H2: T

We also know that M and P cannot be on the same team and that P's team places higher than N's team. The only scenario that this severely restricts is Option 1.

Team G is full; therefore, P must be on Team F and N must be on Team H to satisfy Rule 4.

Option 1

F1: P
G2: S T
H3: N

Notice that we run into a problem here. M and P cannot be on the same team. This means that M must be on Team H. However, the stimulus tells us that M is on a team that places higher than Team H. This means that M cannot be on Team H.

These two things cannot both be true. Therefore, it cannot be true that Team F places first because we run into this problem.

To demonstrate that something could be true, we simply need to find one instance where it is true. Let's try Option 2 to see if P could be on the first-place team.

G1: S P
F2: T M
H3: N O

This scenario meets all of our conditions:

- S is on Team G
- T is on Team F which is in 2nd place
- M and P are not on the same team
- P's team places higher than N's team
- Team G places higher than Team H
- M is on Team F which places higher than Team H

Therefore, it could be true that P is on the first-place team, making (E) the correct answer.

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