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For a certain race, 3 teams were allowed to enter 3 members

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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 05 May 2014, 13:15
Hi Karishma,

Thanks for the explaination, It is very helpful indeed. :)
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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 13 Sep 2014, 04:29
Why is it not Zero?

Since 3 teams were allowed, it is not mandatory that all the teams should participate right?

The stipulation is only on the maximum points, not minimum....what if a team doesn't send any participants? Then it ends up with zero right?
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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 14 Oct 2014, 02:43
2
3
Total scores:
6-1 = 5
6-2 = 4
6-3 = 3
6-4 = 2
6-5 = 1
------------
Total=15
------------

Now, no team can get more than 6 points, and we need to find the least possible points that a team can have. Thus, lets give maximum points to 2 team so that the remaining one team will have least points.
Max points per team = 6
for 2 teams, max total points = 2X6 = 12.
Points remaining for team 3 = 15-12 = 3.

Answer D
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Re: For a certain race, 3 teams were allowed to enter 3 members each. A  [#permalink]

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New post 06 Sep 2015, 22:19
1
VeritasPrepKarishma wrote:
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 6-n 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


Responding to a pm:
Quote:
may i ask you a question about this problem: would it be correct to assume that the least nr of points that team could possibly earn in a race is 1 point (disregarding the case when no racer from a team scores any points), and so much as a result of each race, which yields 3*1=3 points?

I do understand your reasoning, but mine is a bit more straightforward, and I wonder if I am lucky to hit the correct answer with wrong assumption, or is it a valid reasoning?


No, this reasoning is not correct.

Look, there is only ONE race. The rankings in that race are the only points the racers get. The reason some points get added up is that the racers belong to a team.
Team A has three racers: A1, A2, A3.
Similarly, team B and team C.

If A1 gets 4 points and A3 gets 2 points, team A gets 4 + 2 = 6 points.

No team got more than 6 points. So say team A got 6 points and team B got 6 points. This means team C must have got 3 points.
That is the reason 3 points is the minimum any team would have got.
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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 16 Dec 2015, 06:41
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


Its given that no team won more than 6 points. To find the least score a team could earn, lets maximize for others.
5 A
4
3
2
1 A
Third A member comes at a position after 5 in the race.

A cannot win more than 6 points. Similarly assume for B.
5 A
4 B
3
2 B
1 A
Third B member comes at a position after 5 in the race.

Whats left? Just one spot which will be taken up by C. The score is 3.

+Kudos, if this helped!
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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 18 Dec 2015, 07:30
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



and it happened that i was starring at this question in the middle of my GMAT Prep CAT quant section. It made no no sense to me at all and time was running out.
then i did a big picture scan and these numbers were popping up 3, 3, 6, 6... i was kinda.. hei whats with 3s here. so i picked option with 3. i hit D.
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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 24 Jun 2017, 20:13
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


To minimize the score of the third team, we have to maximize the scores of the other two teams. The other teams both scored 6 points, and that's only possible in one way:

Team 1
1st place | 5 points
5th place | 1 point

Team 2
2nd place | 4 points
4th place | 2 points

Thus, since there are only three teams, and someone had to finish in third place, the third team (the one with the minimum score) must have had the third-place runner. It's score is thus 6-3 = 3 points.
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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 22 Jul 2017, 20:53
Kindly help. Why are we adding 1 to the max point of 5 when the max that a team can get is just 5 points. I am not understanding that logic
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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 14 Nov 2017, 08:27
this is how i solved the question and please correct me if my understanding is wrong. Now since each team has 3 members and we are looking for the least or the minimum score that a team can get 6-n has to be the least value. So 6-n is least when n=5 , therefore 6-n = 6-5=1 since there are 3 members in the team the total points is 1+1+1=3. Therefore the answer is D
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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 29 Nov 2017, 05:24
VeritasPrepKarishma wrote:
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.


VeritasPrepKarishma
I solved it liked this.
Score alloted has to be 6-N . There are three members in a team
total scores alloted are from 1 to 5, which means 5 althletes only scored ((( 4 didn't. Others were given a null score
therefore, For the team with least points I tooktwo possiblities First , that one member scored zero . Other came on 5th position , and next on 4th position. Total score being three. or the other possbility that two members of this least scoring team scored zero . but third one cannot come on 5th and 4th position as this will make the scores of other teams more than 6. So,he has to come on third position , scoring 3 points.

Is there a flaw in this logic
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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 12 Feb 2018, 07:39
VeritasPrepKarishma wrote:
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 6-n 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




I am clear with the approach, but have just one doubt. As it is mentioned in the questions that there were no ties and we are allocating 6 points to two team, won't that be considered as a tie?
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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 12 Feb 2018, 22:15
PraktanP wrote:
VeritasPrepKarishma wrote:
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 6-n 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




I am clear with the approach, but have just one doubt. As it is mentioned in the questions that there were no ties and we are allocating 6 points to two team, won't that be considered as a tie?


Each team has provided 3 runners. No tie means no two runners get the same position (and hence the same number of points out of 1/2/3/4/5). 2 teams get 6 points which would be split as 1+5 and 2+4 which means 2 of their runners got points for them.
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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 09 Mar 2018, 16:17
Hi All,

This is essentially a "limit" question; to figure out the LEAST number of points that any team could score, we have to MAXIMIZE what the other 2 teams scored.

Since a team scores (6-N) points for each racer who finishes in Nth place (1 <= N <= 5). This means that ONLY 5 racers get points:
1st = 5 points
2nd = 4 points
3rd = 3 points
4th = 2 points
5th = 1 point
Total = 15 possible points

We're told that none of the 3 teams scored more than 6 points.

IF we can find a way for two of the teams to score 6 points each, then the third team would have the remaining 3 points. There IS a way for that to occur (one team finishes 1st and 5th, one team finishes 2nd and 4th).

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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 17 Mar 2018, 07:45
n Team Points 6-n
======================
1 A 6 5
2 A 5 4
3 A 4 3 Team A Total 12 Max Score
4 B 3 2
5 B 2 1
6 B 1 0 Team B Total 3 Min Score
7 C 0 0
8 C 0 0
9 C 0 0 Team C Total 0
Total Points 15
Attachments

File comment: Question: What is the least possible score or what is the lowest amount of points > 0
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For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 11 Jun 2018, 20:06
VeritasPrepKarishma gmatbusters niks18 pushpitkc

Please see my comments in red

For a certain race, 3 teams were allowed to enter 3 members each.
This means 9 racers.

Quote:
A team earned 6-n 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

But a team has only 3 players? Why do we care beyond score that more than 3 players get?

Quote:
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


q stem says: A team earned 6 – n points but n can take maximum value of 5, also all teams score UNIQUE scores at the end, since there are no ties.
I am not able to understand total score calculated by points scored by individual players from team.

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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 11 Jun 2018, 22:03
adkikani wrote:
VeritasPrepKarishma gmatbusters niks18 pushpitkc

Please see my comments in red

For a certain race, 3 teams were allowed to enter 3 members each.
This means 9 racers.

Quote:
A team earned 6-n 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

But a team has only 3 players? Why do we care beyond score that more than 3 players get?

Quote:
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


q stem says: A team earned 6 – n points but n can take maximum value of 5, also all teams score UNIQUE scores at the end, since there are no ties.
I am not able to understand total score calculated by points scored by individual players from team.


Hey adkikani

There are a total of 3 teams and 3 racers each. Since, we are concerned with the overall score of
the team, we take into account the points of all the players. The overall score of the team involves
the score of the individual players.

We are told that a team earned 6-n points whenever one of its members finished in nth place. It
has been given that 1<= n<= 5, so we are concerned about the first 5 positions overall.

So, the guy who finishes first will get 1st, gets 6-1 = 5 points. Similarly, the person who finishes 2nd
finishes 4 points and so on. Since we need to minimize the score of a team, the other two teams must
get a maximum score(which according to the question stem is 6).

Let's say
Team-A has the players who come 1st and 5th, get 5+1 or 6 points.
Team-B has the players who come 2nd and 4th, get 4+2 or 6 points.
Team-C will have the player who came 3rd and get 3 points.

Hope this helps you!
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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 28 Aug 2018, 11:52
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?


There weren't any ties in the terms of the position of the athletes, but not in the terms of the score the teams scored. Here the two teams which scored them in this fashion:
Team 1: One Athlete ended at 1st position, scoring 6-1 = 5 points.
Second Athlete finished 5th, scoring 6-5 = 1 point.
Team 1 scored 5+1 = 6 points

Team 2: One Athlete ended at 2nd position, scoring 6-2 = 4 points.
Second Athlete finished 4th, scoring 6-4 = 2 points.
Team 2 scored 4+2 = 6 points
This way the positions occupied by Team 1 and Team 2 members were (1st, 2nd, 4th, and 5th)
Hence the only position left for Team 3 member to occupy is 3.
Score 6-3 = 3
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Re: For a certain race, 3 teams were allowed to enter 3 members  [#permalink]

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New post 28 Aug 2018, 11:58
mvraditya wrote:
Why is it not Zero?

Since 3 teams were allowed, it is not mandatory that all the teams should participate right?

The stipulation is only on the maximum points, not minimum....what if a team doesn't send any participants? Then it ends up with zero right?

The score isn't zero because of the following reasons:
1. Total score awarded = 15 {(6-5)+(6-4)+(6-3)+(6-2)+(6-1)}
2. None of the team scored more than 6. Hence max score scored by any team is 6.
So, even if 2 teams scored the max, 1 still would be awarded the leftover.
Re: For a certain race, 3 teams were allowed to enter 3 members &nbs [#permalink] 28 Aug 2018, 11:58

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