vannu wrote:
The participants in a race consisted of 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 one 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.
1st place = 6-1 = 5 points
2nd place = 6-2 = 4 points
3rd place = 6-3 = 3 points
4th place = 6-4 = 2 points
5th place = 6-5 = 1 point
Total number of points = 5+4+3+2+1 = 15
Statement 1:
Maximum number of points for 2 teams = 2*6 = 12, with the result that the number of points for the 3rd team = 15-12 = 3
Implication:
Every team must get at least 1 point.
SUFFICIENT.
Statement 2:
Case 1:
Team A could be 1st, 3rd, 5th.
Team B could be 2nd, 4th.
Here, only 2 teams get at least one point.
Case 2:
Team A could be 1st, 3rd, 5th.
Team B could be 2nd.
Team C could be 4th.
Here, all 3 teams get at least 1 point.
INSUFFICIENT.