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allowed to enter 3

by sanju09 » Thu Mar 22, 2012 1:36 am
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


[spoiler]OA D[/spoiler]
Last edited by sanju09 on Fri Mar 23, 2012 1:41 am, edited 1 time in total.
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by Anurag@Gurome » Thu Mar 22, 2012 2:26 am
sanju09 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 5 points, what is the least possible score a team could have earned?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
1 ≤ n ≤ 5
At the 1st place, n = 1, team earned 6 - 1 = 5 points
At the 2nd place, n = 2, team earned 6 - 2 = 4 points
At the 3rd place, n = 3, team earned 6 - 3 = 3 points
At the 4th place, n = 4, team earned 6 - 4 = 2 points
At the 5th place, n = 5, team earned 6 - 5 = 1 point

Therefore, total # of points earned = 5 + 4 + 3 + 2 + 1 = 15
Noe let us assign maximum possible scores to first two teams, so that the remaining scores is for the 3rd team.
So, possible scores for first two teams = 5 + 5 = 10 points
Hence scores for the third team = 15 - 10 = 5 points, which is not given in the present options.

If the question is: If no team earned more than 6 points, what is the least possible score a team could have earned?, then the maximum possible score for the first two teams = 6 + 6 = 12
So, the least score for the third team = 15 - 12 = 3 points
In that case, the answer would have been D.
Last edited by Anurag@Gurome on Thu Mar 22, 2012 2:53 am, edited 1 time in total.
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by killer1387 » Thu Mar 22, 2012 2:35 am
@Anurag:

thanx for the clarifying,
I solved and ended up with each team scoring 5 as none of the other configurations were possible,
But none of options contained 5.
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by Anurag@Gurome » Thu Mar 22, 2012 2:43 am
killer1387 wrote:@Anurag:

thanx for the clarifying,
I solved and ended up with each team scoring 5 as none of the other configurations were possible,
But none of options contained 5.
You are welcome!
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by sanju09 » Thu Mar 22, 2012 2:51 am
Anurag@Gurome wrote:
sanju09 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 5 points, what is the least possible score a team could have earned?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
1 ≤ n ≤ 5
At the 1st place, n = 1, team earned 6 - 1 = 5 points
At the 1st place, n = 2, team earned 6 - 2 = 4 points
At the 1st place, n = 3, team earned 6 - 3 = 3 points
At the 1st place, n = 4, team earned 6 - 4 = 2 points
At the 1st place, n = 5, team earned 6 - 5 = 1 point

Therefore, total # of points earned = 5 + 4 + 3 + 2 + 1 = 15
Noe let us assign maximum possible scores to first two teams, so that the remaining scores is for the 3rd team.
So, possible scores for first two teams = 5 + 5 = 10 points
Hence scores for the third team = 15 - 10 = 5 points, which is not given in the present options.

If the question is: If no team earned more than 6 points, what is the least possible score a team could have earned?, then the maximum possible score for the first two teams = 6 + 6 = 12
So, the least score for the third team = 15 - 12 = 3 points
In that case, the answer would have been D.
Supplied answer is [spoiler]D[/spoiler]; and the correct wordings are "If no team earned more than 6 points, what is the least possible score a team could have earned?" But, Anurag! Is it just me not getting your explanation or the class is par excellence with both the question and your explanation? Please steer or recommend me take rest.
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by Anurag@Gurome » Thu Mar 22, 2012 2:54 am
sanju09 wrote: Supplied answer is [spoiler]D[/spoiler]; and the correct wordings are "If no team earned more than 6 points, what is the least possible score a team could have earned?" But, Anurag! Is it just me not getting your explanation or the class is par excellence with both the question and your explanation? Please steer or recommend me take rest.
Thanks for pointing that, I have edited my reply.
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by sanju09 » Thu Mar 22, 2012 3:07 am
Anurag@Gurome wrote:
sanju09 wrote: Supplied answer is [spoiler]D[/spoiler]; and the correct wordings are "If no team earned more than 6 points, what is the least possible score a team could have earned?" But, Anurag! Is it just me not getting your explanation or the class is par excellence with both the question and your explanation? Please steer or recommend me take rest.
Thanks for pointing that, I have edited my reply.

How can a team possibly earn 6 points under the following conditions?

A team earned 6 - n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5.
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by killer1387 » Thu Mar 22, 2012 7:56 am
sanju09 wrote:
Anurag@Gurome wrote:
sanju09 wrote: Supplied answer is [spoiler]D[/spoiler]; and the correct wordings are "If no team earned more than 6 points, what is the least possible score a team could have earned?" But, Anurag! Is it just me not getting your explanation or the class is par excellence with both the question and your explanation? Please steer or recommend me take rest.
Thanks for pointing that, I have edited my reply.

How can a team possibly earn 6 points under the following conditions?

A team earned 6 - n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5.
its definitely possible suppose three members come at 3rd,4th and 5th then the total score a team gets is (6-3)+(6-4)+(6-5)=6.

the question stem clearly states this thing for scoring. But if maximum is 5, we can never ever make a race for three teams with three members each, involved in the race, getting different scores other than each getting 5.

hence IMO: No offence but this question with presented options is not correct. We need to add an option with numeral 5 for this question to stand.
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by ubhanja » Thu Mar 22, 2012 10:00 am
why can't it be zero? 3 teams with 3 members each. It could happen that one team has all the 3 members in 7,8,9 position. what would be the score? since
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by sanju09 » Fri Mar 23, 2012 1:45 am
killer1387 wrote:
sanju09 wrote:
Anurag@Gurome wrote:
sanju09 wrote: Supplied answer is [spoiler]D[/spoiler]; and the correct wordings are "If no team earned more than 6 points, what is the least possible score a team could have earned?" But, Anurag! Is it just me not getting your explanation or the class is par excellence with both the question and your explanation? Please steer or recommend me take rest.
Thanks for pointing that, I have edited my reply.

How can a team possibly earn 6 points under the following conditions?

A team earned 6 - n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5.
its definitely possible suppose three members come at 3rd,4th and 5th then the total score a team gets is (6-3)+(6-4)+(6-5)=6.

the question stem clearly states this thing for scoring. But if maximum is 5, we can never ever make a race for three teams with three members each, involved in the race, getting different scores other than each getting 5.

hence IMO: No offence but this question with presented options is not correct. We need to add an option with numeral 5 for this question to stand.
Thanks killer1387, happy to see you writing beyond IMOs. I have already come clean with the needed correction in the stem, in the court of Anurag Sir. In fact all of you collectively rocked in making me understand the question finally.
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by killer1387 » Fri Mar 23, 2012 1:58 am
sanju09 wrote:
killer1387 wrote:
sanju09 wrote:
Anurag@Gurome wrote:
sanju09 wrote: Supplied answer is [spoiler]D[/spoiler]; and the correct wordings are "If no team earned more than 6 points, what is the least possible score a team could have earned?" But, Anurag! Is it just me not getting your explanation or the class is par excellence with both the question and your explanation? Please steer or recommend me take rest.
Thanks for pointing that, I have edited my reply.

How can a team possibly earn 6 points under the following conditions?

A team earned 6 - n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5.
its definitely possible suppose three members come at 3rd,4th and 5th then the total score a team gets is (6-3)+(6-4)+(6-5)=6.

the question stem clearly states this thing for scoring. But if maximum is 5, we can never ever make a race for three teams with three members each, involved in the race, getting different scores other than each getting 5.

hence IMO: No offence but this question with presented options is not correct. We need to add an option with numeral 5 for this question to stand.
Thanks killer1387, happy to see you writing beyond IMOs. I have already come clean with the needed correction in the stem, in the court of Anurag Sir. In fact all of you collectively rocked in making me understand the question finally.
Its nice we finally arrived a consensus for the question after this long discussion.
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