Problem Solving

ashg84 wrote:For a certain race, 3 teams were allowed to enter members each. A team earned 6-n points whenever one of its members finished in the nth place, where n belongs to [1,5]. 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 - a
c - 2
d - 3
e - 4

I am finding it difficult to understand the problem. Could anyone please explain the question.

Thanks

As 1 ≤ n ≤ 5, points are only awarded for 1st, 2nd, 3rd, 4th, and 5th place. Hence, the points that can be earned are 1, 2, 3, 4, and 5. Therefore, total points can be earned = (1 + 2 + 3 + 4 + 5) = 15

As there were no ties, disqualifications or withdrawals, no same point are awarded to more than one person.

To minimize the score of a team, we have to maximize the score of the other two teams. Hence, let us assume that other two teams have earned maximum possible score a team can earn, i.e. 6 points.

Therefore, least possible score of a team = (15 - 6 - 6) = 3

The correct answer is D.