The 9 participants in a race were divided into 3 teams with 3 runners on each team. A team was awarded 6 – n points if one of its runners finished in nth place, where 1 ≤ n ≤ 5. If all of the runners finished the race and if there were no ties, was each team awarded at least 1 point?
My approach --
We have 3 teams with 3 participants per team:
Team 1: A, B, C
Team 2: D, E, F
Team 3: G, H, I
Each participant receives 6-n points for achieving nth place. For example: 5 points for achieving 1st place.
Was each team awarded at least one point?
(1) No team was awarded more than a total of 6 points.
The 1st 5 people will receive a certain amount of points. (5+4+3+2+1 = 15 points)
If no team was awarded more than 6 points, we can maximize two teams by awarding them each 6 points. We're then left with 3 points, which must go to the 3rd team. SUFFICIENT.
(2) No pair of teammates finished in consecutive places among the top five places.
1ST: Team 1
2ND: Team 2
3RD: Team 1
4TH: Team 2
5TH: Team 1
In this situation, Team 3 did not receive any points.
1ST: Team 1
2ND: Team 2
3RD: Team 3
4TH: Team 1
5TH: Team 2
In this situation each team received at least one point. INSUFFICIENT.
Answer is A.
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