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Math Help - Sets Questions with Answer (Need Explanation)

  1. #1
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    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.
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by dumluck View Post
    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.
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