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I must be missing something.
The three highest placing teams in a high school debate tournament are teams from Fairview Gillom and Hilltop high schools. Each team has exactly two members. The individuals are M, N, O , P S and T.

S is on the team from Gillom
T is on the second place team
M and P are not on the same team
P's team places higher than N's
Gillom places higher than Hilltop.

Since Gillom Places higher than Hilltop. That means Hilltop will never be first. So the order of teams is either Fairview Gillom Hilltop or Gillom Hilltop Fairview.

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

This is what I diagramed. If I put p ahead of n in the bottom grid, that would put mp and P together and would break a rule. I can not get the answer. What am I missing?

M P N
S T O
G H F

S
M T
F G H

If M places higher than H, you essentially have 2 possibilities. Either M places first or M places second.


A can't be true since F must be second or third.
B can't be true since G must be first.
C can't be true since N must be third.
D can't be true since O must be third.
E could be true, as verified by Diagram 1.

What it the Fairview team was first? Sorry if i am being stupid. I understand your diagram

S will always be on the first place team so therefore G must be the first place team.

flounder wrote:What it the Fairview team was first? Sorry if i am being stupid. I understand your diagram

If you put F first, G would have to go second and H would have to go third.
F G H
_ _ _
_ T _
1 2 3

Because G is second, S would have to go second.
F G H
_ S _
_ T _
1 2 3

Since M has to be higher than H, M would have to go first.
F G H
_ S _
M T _
1 2 3

P can't be last since it has to be higher than N, hence P has to go first.
F G H
P S _
M T _
1 2 3

P and M are on the same team which is not allowed by the rules and therefore it can't be true since it results in a contradiction.

I think I got stuck on the fact that GH are may not nescessarily go 12 or 23. I did not consider 13