Tough problem solving - gmac test

[Striver]

GMAC PRACTICE TEST

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 place, where 1 <greater than or equal to> n <less than or equal to> 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
E) 4

[Anurag@Gurome]

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 place, where 1 <greater than or equal to> n <less than or equal to> 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?

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.