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# race

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race [#permalink]  31 May 2009, 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, or withdraw. If no team earned more than 6 points, what is the least possible score a team could have owned?
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Re: race [#permalink]  31 May 2009, 09:09
should be 3 points.

the teams scored 6 - n points for each prize won.

this results in 5 points for first, 4 for second, etc.

The total number of points given for the race is 5 + 4 + 3 + 2 + 1, or 15 points awarded to all 3 teams combined.

since no team was awarded more than 6, then to get the least possible score, assume two teams earned 6 points.

15 - 2 (6) = 3

there are only 3 more points to be awarded, so the least possible score for the losing team would be 3.
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Re: race [#permalink]  31 May 2009, 10:36
since no team was awarded more than 6, then to get the least possible score, assume two teams earned 6 points.

how is it infered
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Re: race [#permalink]  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
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Re: race [#permalink]  31 May 2009, 13:30
hello vcbabu,

Could you please post OA and source for this question.
Nice one.
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Re: race [#permalink]  31 May 2009, 13:31
And yes , answer must be 3.
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Lahoosaher

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Re: race [#permalink]  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.

Thanks,
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Re: race [#permalink]  01 Jun 2009, 09:17
A team earned 6-n points whenever one of its members finished in nth place, where 1<= n<=5,

from the above maximum points limit , i think , is 5 . how 6 ?
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Re: race [#permalink]  01 Jun 2009, 12:10
each team has three members, so it could place 1st and 5th to get 6 points, or second and fourth.

Team 1: 1st and 5th - 5+1= 6 points
Team 2: 2nd and 4th - 4+2=6 points

Team 3: 3rd place - 3 points

the least possible score team 3 could have would be 3 points.
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Re: race [#permalink]  07 Jun 2009, 17:06
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?
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Re: race [#permalink]  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.
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Re: race [#permalink]  05 Dec 2010, 18:44
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Expert's post
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?

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: race   [#permalink] 05 Dec 2010, 18:44
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