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For a certain race, 3 teams were allowed to enter 3 members
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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: For a certain race, 3 teams were allowed to enter 3 members each. A
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05 Dec 2010, 19:44
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 6n 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: points30
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06 Nov 2008, 10:25
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: points30
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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 (61)=5, now we are told that no one scores over 6..so then assume that 2nd runner of T1 gets 65=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: points30
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07 Nov 2008, 06:12
Plz see below.
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Re: For a certain race, 3 teams were allowed to enter 3 members each. A
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31 May 2009, 10:09
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: For a certain race, 3 teams were allowed to enter 3 members each. A
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31 May 2009, 13:59
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: For a certain race, 3 teams were allowed to enter 3 members each. A
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01 Jun 2009, 05:44
Consider a team member comes last gets last point, that will be 5 in our case, the team will earn 65 = 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.
Please post the OA!!
Thanks,



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Re: For a certain race, 3 teams were allowed to enter 3 members each. A
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01 Jun 2009, 13:10
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: For a certain race, 3 teams were allowed to enter 3 members each. A
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07 Jun 2009, 18:06
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: points30
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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.



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Re: For a certain race, 3 teams were allowed to enter 3 members each. A
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05 Dec 2010, 16:50
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: For a certain race, 3 teams were allowed to enter 3 members
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26 Jun 2013, 01:19
Is this a combination and probability question?



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Re: For a certain race, 3 teams were allowed to enter 3 members
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26 Jun 2013, 01:31
fozzzy wrote: Is this a combination and probability question? No, it's min/max problem.
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Re: For a certain race, 3 teams were allowed to enter 3 members
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27 Jun 2013, 11:48
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.
Answer: D



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Re: For a certain race, 3 teams were allowed to enter 3 members
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21 Jul 2013, 15:34
This wording of this problem is still misleading because how can Team 1 and 2 both get 6 points total if it says there were no ties?



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Re: For a certain race, 3 teams were allowed to enter 3 members
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21 Jul 2013, 22:17
shriyasp wrote: This wording of this problem is still misleading because how can Team 1 and 2 both get 6 points total if it says there were no ties? "No ties" means that there were no ties between members/runners not between teams.
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Re: For a certain race, 3 teams were allowed to enter 3 members
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21 Jul 2013, 23:25
Hi Everyone My explanation  Since n is less than equal to 5 and if a player finishes at nth position the team will get 6n points so the team will get minimum points if all of it's members finish at nth position earning 3(6n) points As it is a min/max problem the score will be minimum when n=5 so 3(65)=3



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Re: For a certain race, 3 teams were allowed to enter 3 members
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22 Apr 2014, 23:38
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.



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Re: For a certain race, 3 teams were allowed to enter 3 members
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23 Apr 2014, 05:36
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.
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Re: For a certain race, 3 teams were allowed to enter 3 members
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