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For a certain race, 3 teams were allowed to enter 3 members [#permalink]
06 Nov 2008, 09:03

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Difficulty:

35% (medium)

Question Stats:

58% (02:28) correct
41% (01:25) wrong based on 85 sessions

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?

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

finishing place = 1, 2, 3, 4, and 5.

possible points: 1st place = 6 - 1 = 5 2nd place = 6 - 2 = 4 3rd place = 6 - 3 = 3 4th place = 6 - 4 = 2 5th place = 6 - 5 = 1

so total points = 5+4+3+2+1 = 15 If we assign maximum scores to 2 teams, then the remaining scores is for the remaining team. max scores first 2 teams can have = 6 (6+1) + 6 (4+2) = 12 so the remaining team must have = 3 scores

OK so total runners is 9..but only the first 5 actually get you any points...right

so lets say teams are T1, T2 and T3

T1 gets 1st spot so (6-1)=5, now we are told that no one scores over 6..so then assume that 2nd runner of T1 gets 6-5=1 point so in all T1 has 6 points..the 3rd runner was below 5th so he doesnt carry in points.anyway..

T2 gets 2nd spot so they 4 points from one of their runners, then their other runner gets 4th spot, and thus T2 also get 6 points..

T3 is left with only one runner who is at 3rd spot..so they get 3 points..

D it is

caiyun wrote:

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?

Re: For a certain race, 3 teams were allowed to enter 3 members [#permalink]
27 Jun 2013, 10:48

Since no team scored more than 6 points one team must have 1st, 2nd and 3rd place only otherwise the total will exceed 6. Fourth place will yeild 2 points which cannot go to the team which had a member that placed 1st. Since we are looking at minimizing points for a team, we would place 4th place with the team that also got 2nd place. Similarly, we would also allocate 5th place to the team that got 1st place. Therefore, 3 is the lowest point total possible for a team with this scenario.

Re: For a certain race, 3 teams were allowed to enter 3 members [#permalink]
21 Jul 2013, 22:25

Hi Everyone

My explanation -

Since n is less than equal to 5 and if a player finishes at nth position the team will get 6-n points so the team will get minimum points if all of it's members finish at nth position earning 3(6-n) points As it is a min/max problem the score will be minimum when n=5 so 3(6-5)=3

gmatclubot

Re: For a certain race, 3 teams were allowed to enter 3 members
[#permalink]
21 Jul 2013, 22:25