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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:

55% (hard)

Question Stats:

62% (02:24) correct
38% (01:51) wrong based on 292 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

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

Re: For a certain race, 3 teams were allowed to enter 3 members [#permalink]
23 Apr 2014, 04:36

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aniketb wrote:

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. _________________

Re: For a certain race, 3 teams were allowed to enter 3 members [#permalink]
20 Jun 2014, 05:10

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

Experts, can you please evaluate my solution/approach.

Team has to earn 6-n points. And 1 ≤ n ≤ 5 To minimize the total points, select maximum value of n i.e. 5 (for each of team's 3 participants). 3 is the answer.

Now, no team can get more than 6 points, and we need to find the least possible points that a team can have. Thus, lets give maximum points to 2 team so that the remaining one team will have least points. Max points per team = 6 for 2 teams, max total points = 2X6 = 12. Points remaining for team 3 = 15-12 = 3.

Answer D _________________

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Re: For a certain race, 3 teams were allowed to enter 3 members
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