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urooj.khan
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Post subject: for a certain race, 3 teams were allowed to enter  Posted: Sat Jun 13, 2009 6:33 pm |
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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 the 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
d) 4
the correct answer is D.
this is how i got this answer......
since there are 3 teams, each team would come in either first, second or third. the team that comes in third will be the one with the least points.. the points would equal 6 - 3 for this team, which is 3.
is this the correct rationale?
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stock.mojo11
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Post subject: Re: for a certain race, 3 teams were allowed to enter Posted: Sun Jun 14, 2009 10:33 am |
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Posts: 43
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urooj.khan 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 the 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
d) 4
the correct answer is D.
this is how i got this answer......
since there are 3 teams, each team would come in either first, second or third. the team that comes in third will be the one with the least points.. the points would equal 6 - 3 for this team, which is 3.
is this the correct rationale? I am not sure I understood what you did. Here is what I did 9 members in race. no points for standing 6th-9th positions in race. That means 5 points for first place and 1 point for 5th place 5,4,3,2,1 respectively. To minimize the number of points for one team max others. no team scored more than 6. 5+1 and 4+2 max two teams score. 3 is left out, the min other team could score.
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RonPurewal
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Post subject: Re: for a certain race, 3 teams were allowed to enter Posted: Mon Jun 15, 2009 11:00 pm |
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| ManhattanGMAT Staff |
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Posts: 6765
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the main takeaway here is the same as the main takeaway from the "voltage readings" problem, also posted by you today:
TAKEAWAY:
when you have numbers with a fixed sum or product:
if you want to MINIMIZE A QUANTITY, then you must MAXIMIZE ALL OTHER QUANTITIES in the sum or product.
if you want to MAXIMIZE A QUANTITY, then you must MINIMIZE ALL OTHER QUANTITIES in the sum or product.
--
in this problem:
as the above poster has mentioned, the given description of the point system is cryptic, but you should decode it:
the numbers of points awarded are 5, 4, 3, 2, and 1.
therefore, there is a TOTAL OF 15 POINTS.
we want to MINIMIZE the number of points awarded to any one team.
according to the above takeaway, this means that we should MAXIMIZE the number of points awarded to the OTHER teams.
per the restrictions given, the other teams can receive a maximum of 6 points apiece, so, 15 - 6 - 6 = 3.
(you should probably verify that this is indeed possible, as the above poster has done.)
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rockrock
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Post subject: Re: for a certain race, 3 teams were allowed to enter Posted: Sat Aug 28, 2010 7:33 pm |
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Posts: 38
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for this problem i just added the "minimum" amount of points one team could receive --- so if each team member got 5th place...it would be 6-5=1 times 3.. is this method flawed?
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sandeep.19+man
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Post subject: Re: for a certain race, 3 teams were allowed to enter Posted: Tue Aug 31, 2010 2:22 am |
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rockrock wrote: is this method flawed? Yes. The question says "There were no ties"
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RonPurewal
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Post subject: Re: for a certain race, 3 teams were allowed to enter Posted: Thu Sep 16, 2010 7:29 am |
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| ManhattanGMAT Staff |
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Posts: 6765
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sandeep.19+man wrote: rockrock wrote: is this method flawed? Yes. The question says "There were no ties" yep. in fact, if you ever think that the solution to an official problem is this simple, then you are pretty much always going to be wrong; this is just not the way in which the problems are written, even at the most elementary levels. therefore, if you encounter a “solution” that is this simple, you should think twice before picking that answer.
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