kingflo wrote:
In a certain sport, teams receive 3 points for each win, 1 point for each draw, and no points for losses. In a five-team tournament in this sport, in which each of teams G, H, J, K, and L played each other team exactly once, did team L finish the tournament with the highest point total?
(1) Team L finished with 8 points.
(2) The sum of all five teams’ point totals for the tournament was 23 points.
The maximum total points any team can make is by winning all the 4 matches = 4*3 = 12 points. The next maximum point can be by a team, which loses one match and wins the next three = 3*3 = 9 points. By the same logic, the total maximum points is 12+9+6+3+0 = 30 points.
From F.S 1 ,we know that Team L got 8 points. Let's assume that all the teams won the maximum points available = 12,9,6,3,0.
We redistribute the points, assuming that the team which had won all 3 matches didn't will all 3, rather had a tie in 2 matches : 12,9-2-2,6+1,3+1,0 = 12,5,7,4,0. Again, let the team with 12 points instead have a tie with the team which has 7 points = 12-2,5,7+1,4,0= 10,5,8,4,0.We see that there is a scenario where team L with 8 points doesn't end with the highest points. Again, we can have a different scenario where the team which had one 4 matches instead had 2 ties = 12-2-2,9,6+1,3+1,0 = 8,9,7,4,0 = Again, the team which had won all three matches instead had one tie = 8,9-2,6,4+1,0 = 8,7,6,5,0. Thus, there is a scenario possible where team L does have the highest points. As we get two different answers. Insufficient.
From F.S 2, we have to make the total sum as 23. We started with 12,9,6,3,0 = 30 points, and we need to get rid of 7 points. This can happen if we have 7 mathches as tie( Each tie redistributes the points as -2 and +1, giving a net decrease of 1 point). Thus, we can assume that the team which had won all 4 matches instead had 4 ties = 12-2-2-2-2,9+1,6+1,3+1,0+1 = 4,10,7,4,1. We have to get rid of 3 more points = 3 more draws = 4,10-2-2-2,7+1,4+1,1+1 = 4,4,8,5,2 = 23 points. Now, any team could be team L. Insufficient.
Combining both statements together, we see that team L does have the maximum points in the end,Sufficient.
C.
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