Thread: Sets Questions with Answer (Need Explanation)

2. 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 ≤ 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
E. 4


Answer is:

1. Get total number of points : (6-1) + (6-2) + (6-3) + (6-4) + (6-5) = 5 . 4 . 3 . 2. 1 = 15
2. Max points earned is 6


3. min of 3 teams = 15 - 2 * max of 2 other teams = 15 - 2 * 6 = 3

Step 3 I don't understand, where did the variables come from in the text: I.E. Min of 3 teams, 2 other teams (why is this being substracted from the total points) and why are we multiplying by 6?

Thanks in Advance.

Originally Posted by dumluck

Step 3 I don't understand, where did the variables come from in the text: I.E. Min of 3 teams, 2 other teams (why is this being substracted from the total points) and why are we multiplying by 6?

Thanks in Advance.

I assume you understand how we got to 15 points in total, that's easy enough. I don't know why you want to use sets for this though. It's more of a simple logic problem.

You know the maximum number of points one team can score is 6.

You also know 5 + 4 + 3 + 2 +1 = 15

If team 1 scores 5 + 1 = 6 (the maximum, because we want to assign as many points as possible to the first two teams)
Then team 2 can also score 4 + 2 = 6 (another maximum)

6 + 6 = 12

So we only have 3 points left, since the other teams scored the maximum number of points.

This is the minimum number of points left, and it goes to team 3.