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# Interesting PS question: combination and arithmatic

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Manager
Joined: 14 Aug 2009
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Interesting PS question: combination and arithmatic [#permalink]

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24 Aug 2009, 06:45
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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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Intern
Joined: 24 Jun 2009
Posts: 39

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Re: Interesting PS question: combination and arithmatic [#permalink]

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24 Aug 2009, 07:38
1
KUDOS
flyingbunny 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

Is it 3. i.e D
since max possible points 15 [(6-1)+ (6-2)+(6-3)+(6-4)+(6-5)] and note that only 5 positions in the race get a point. so position number 6, 7, 8 and 9 are of '0' points.
No team gets more than 6 points. so assume two teams got 6 points sets could be (5,1,0), (2,4,0) and (3,0,0) thus least possible score is 3

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Director
Joined: 01 Apr 2008
Posts: 872

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Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: Interesting PS question: combination and arithmatic [#permalink]

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24 Aug 2009, 08:02
Exactly, idea is to divide 1,2,3,4,5,0,0,0,0 into three groups such that that two groups have the maximum value which is <=6. Whatever is left is the minimum number of points that the third team shall get.

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Manager
Joined: 18 Jul 2009
Posts: 167

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Location: India
Schools: South Asian B-schools
Re: Interesting PS question: combination and arithmatic [#permalink]

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24 Aug 2009, 08:09
OA D = 3

3 teams (T1, T2, T3) with 3 members each with following point system

1 st place = 5 points
2nd place = 4 points
3 rd place = 3 points
4 th place = 2 points
5 th place = 1 point
6th place onwards (ie 6th/7th/8th/9th) = 0 points

Now only refer point table for furthur calculations
( keep in mind that there can be 4 positions with 0 score)

Lets say...T1 has team member with 1st position thus possible scores are ( 510 / 500) with these possible combinations T2 possible combinations are ( 420 / 410 / 400)...(we can see all possibilities in the image attached for clarity only not to be done in exam).....we can understand that T1 & T2 with max scores will lead T3 with Least score hence only possible combination between them is T1 (5,1,0) T2 (4,2,0) => T3 ( 3,0,0)...Hence OA D = 3
Attachments

SCORE.GIF [ 6.68 KiB | Viewed 843 times ]

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Re: Interesting PS question: combination and arithmatic   [#permalink] 24 Aug 2009, 08:09
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