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For a certain race, 3 teams were allowed to enter 3 members [#permalink]

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06 Nov 2008, 09:03

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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 each. A [#permalink]

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31 May 2009, 12:59

if both teams earned 6 the last team would earn the least.

Since 6 is the limit, and the total points awarded is 15, then 6+6+3=15. if one scored 5, it would be 6+5+4, and the least score would be 4, and vice versa, so that if both teams score 6 you get the least possible score for the last team

Re: For a certain race, 3 teams were allowed to enter 3 members each. A [#permalink]

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01 Jun 2009, 04:44

Consider a team member comes last gets last point, that will be 5 in our case, the team will earn 6-5 = 1 point, Similarly the minimum possibility is that the team lasted in all the 3 events. so 3* 1 = 3 points is the minimum.

If this answer is not in OA, then we need to substitite with different combinations.

Re: For a certain race, 3 teams were allowed to enter 3 members each. A [#permalink]

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05 Dec 2010, 15:50

I3igDmsu wrote:

I am struggling with this one, it may be that I don't understand the question and information given.

If there are 3 teams of 3 members each (9 people total), wouldn't the possible finishes for each member of the teams be 1st, 2nd, 3rd,..., 9th?

How is it that 1 <= n <= 5 when there are 9 racers? Do racers 6 through 9 just get 0 points?

Try thinking of this as only the top 5 individuals from the teams can earn points for their teams, the rest of the 4 people who didn't place in the top 5 don't matter.

I am struggling with this one, it may be that I don't understand the question and information given.

If there are 3 teams of 3 members each (9 people total), wouldn't the possible finishes for each member of the teams be 1st, 2nd, 3rd,..., 9th?

How is it that 1 <= n <= 5 when there are 9 racers? Do racers 6 through 9 just get 0 points?

Yes, a racer gets points only when he/she ranks 1 - 5.

Break down the question to get a handle on it: For a certain race, 3 teams were allowed to enter 3 members each. This means 9 racers.

A team earned 6-n points whenever one of its members finished in nth place, where 1<= n<=5, there were no ties, or withdraw. Since n varies from 1 to 5, only when a member finishes in one of those positions, does he score something. That something is 6 - n. So person who finishes first, gets 5 points, person who finishes 2nd gets 4 points and so on till the person who finishes 5th gets 1 point. So in all, 5+4+3+2+1 = 15 points were given

If no team earned more than 6 points, what is the least possible score a team could have owned? No team got more than 6 points. We have to find the minimum score of a team. Since the total is 15 and one score has to be minimized, we should try to maximize the other two scores. Maximum score is 6 so other two teams get 6 points each maximum (e.g. One team gets 5 + 1, another gets 4+2). Then the third team will get a minimum score of 15 - 2*6 = 3
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Re: For a certain race, 3 teams were allowed to enter 3 members [#permalink]

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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]

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21 Jul 2013, 22:25

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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

Re: For a certain race, 3 teams were allowed to enter 3 members [#permalink]

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22 Apr 2014, 22:38

Minimum possible score which team can earn through each member is 1. There are 3 members in each team. So, minimum possible score for a team is 1+1+1=3.

thats how i thought it to be. Experts please let me know if its correct.

Minimum possible score which team can earn through each member is 1. There are 3 members in each team. So, minimum possible score for a team is 1+1+1=3.

thats how i thought it to be. Experts please let me know if its correct.

From what I understand from your explanation, I don't think your method is correct.

Note that only one person will get a score of 1. There are 3 teams with 3 athletes each so there are a total of 9 athletes competing in the race. The first 5 positions, will be given points 5, 4, 3, 2 and 1. So theoretically, a team could gather a max of 5+4+3 = 12 points if its three athletes get positions 1st, 2nd and 3rd. Also, theoretically, a team could get 0 points if its 3 athletes occupy the last 3 positions!

There are a total of 5+4+3+2+1 = 15 points up for grabs among the 9 athletes.

But you are given that the max points a team got was 6. Say, its two athletes got ranks 1st and 5th and hence scored 5 and 1 respectively. To give minimum points to one team, we need to give max points to the other team too i.e. 6 (say, its two athletes got ranks 2nd and 4th). So out of a total of 15 points, 6 each are allotted to two teams leaving you with 3 points for the third team (one of its athletes came in 3rd)

That is the reason 3 is the minimum points a team could get.
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