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Race problem

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Race problem

by roy_priya » Mon Feb 04, 2008 12:41 pm
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 teams 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

My answer is B. Could not find the OA. Please let me know if you get the same.
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by cris » Mon Feb 04, 2008 12:55 pm
I think the answer is D) 3.

Here is why: 1st team gets 6 points (with 2 racers), 2nd team gets 6 points (with 2 racers)....so the 3rd team must get 3 (with one racer)
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Re: Race problem

by Stuart@KaplanGMAT » Mon Feb 04, 2008 2:43 pm
roy_priya 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 teams 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

My answer is B. Could not find the OA. Please let me know if you get the same.
Cris is correct, let me explain in a bit more detail.

The points awarded are:

1st - 5
2nd - 4
3rd - 3
4th - 2
5th - 1

So, we have a total of 15 points awarded.

We want to minimize the points earned by one of the teams. On GMAT minimization questions, we want to MAXIMIZE everything else.

We know that no team earned MORE than 6 points. So, let's give teams 1 and 2 their maximum total points, 6 each.

Those two teams account for 12/15 points, which means that team 3 earned the remaining 3 points: choose (D).
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by Topple » Sun Sep 21, 2008 6:36 am
But there are no ties ???
how can u award six to both teams ??
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by cramya » Sun Sep 21, 2008 7:22 am
There are no ties. We are saying that the one of the members in the team with the least points awarded finished 3rd with 3 points.
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by stop@800 » Sun Sep 21, 2008 12:46 pm
The points are 5 4 3 2 1

so we can have
5+1
4+2
3

or any of various other valid possible arrangements
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by scoobydooby » Tue Sep 23, 2008 4:45 am
can we follow this approach?

the team that will score the least possible points will have its 3 members getting the last position each, ie all 3 members come 5th. the total points earned would be therefore: 3*1=3 (the points awarded for 5th position is 1)
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by Stuart@KaplanGMAT » Tue Sep 23, 2008 11:52 am
scoobydooby wrote:can we follow this approach?

the team that will score the least possible points will have its 3 members getting the last position each, ie all 3 members come 5th. the total points earned would be therefore: 3*1=3 (the points awarded for 5th position is 1)
No, because only 1 person finishes in 5th place and earns 1 point.

There are 9 people total in the race (3 people on each of 3 teams), only the top 5 overall finishers earn points.

Also, under your method, one or both of the other two teams would earn more than 6 points, which breaks the rules we're given.
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by sharkss » Tue Sep 23, 2008 1:35 pm
Why can't one team have its members get 7th, 8th and 9th place and therefore get 0 points?
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by sharkss » Tue Sep 23, 2008 1:44 pm
sharkss wrote:Why can't one team have its members get 7th, 8th and 9th place and therefore get 0 points?
NVM - just figured out why --- because if one team scores 0,0,0 points , then one of the other two teams end up with more than 6 points...which is not allowed =D
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by sharkss » Tue Sep 23, 2008 1:45 pm
sharkss wrote:
sharkss wrote:Why can't one team have its members get 7th, 8th and 9th place and therefore get 0 points?
NVM - just figured out why --- because if one team scores 0,0,0 points , then one of the other two teams end up with more than 6 points...which is not allowed =D
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