gmatt1476 wrote:
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?
(1) No team was awarded more than a total of 6 points.
(2) No pair of teammates finished in consecutive places among the top five places.
DS08602.01
The values of points 5, 4, 3, 2, and 1 must be distributed among the three teams. The original question: Was each team awarded at least 1 point?
1) We know that no team was awarded more than a total of 6 points, so any two teams combined weren't awarded more than a total of 12 points. Since the sum of all values of points is 15, two teams are not enough to take all the points. Thus, the answer to the original question is a definite Yes. \(\implies\)
Sufficient2) It's possible that one team got the points 5, 3, 1, another team got the points 4 and 2, while the third team got no points. However, it's also possible that one team got the points 5 and 3, another team got the points 4 and 2, and the third team got the point 1. Thus, we can't get a definite answer to the original question. \(\implies\)
InsufficientAnswer: A