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

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For a certain race, 3 teams were allowed to enter 3 members [#permalink] New post 06 Nov 2008, 10:03
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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?

A. 0
B. 1
C. 2
D. 3
E. 4
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Re: points--30 [#permalink] New post 06 Nov 2008, 10:25
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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?

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

so got D.
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Re: points--30 [#permalink] New post 06 Nov 2008, 11:11
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?

A. 0
B. 1
C. 2
D. 3
E. 4
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Re: points--30 [#permalink] New post 07 Nov 2008, 06:12
Plz see below.
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Re: points--30 [#permalink] New post 01 Mar 2010, 07:49
Scores are 5,4,3,2 and 1.
Giving maximum score to the first two teams so that the third team has the minimum.
5+1 = 6; 4+2= 6; 3
Hence 3.
Re: points--30   [#permalink] 01 Mar 2010, 07:49
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