Problem Solving

For a certain race, 3 teams were allowed to enter 3 members each. A team
earned 6-n points whenever one of its members finished in the nth place, where
1<=n<=5. There were no ties, disqualifications or withdrawals. if no team earned
more than 6 points, what is the least possible score a team could have earned.
a) 0
b) 1
c) 2
d) 3
d) 4

For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6-n points whenever one of its members finished in nth places, where 1≤n≤5. there were no ties, disqualifications, or withdrawals. If no team earned more than 6 points, what is the least possible score a team could have earned?
0
1
2
3
4

nth place = 6-n points.
Thus:
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.

Let the 3 teams be A, B and C.

To MINIMIZE the number of points that Team C could earn, we must MAXIMIZE the number of points that Teams A and B earn.
The maximum allowed total per team = 6.
It's possible that Team A wins 1st and 5th places (for a total of 6 points) and that Team B wins 2nd and 4th places (for a total of 6 points) -- the MAXIMUM allowed sum for each team.
Thus, the MINIMUM number of points that could be earned by team C -- winning only 3rd place -- is 3.

The correct answer is D.