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For a certain race, 3 teams were allowed to enter 3 members each. 28 Mar 2020, 12:55
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Hi Dany11,

The prompt tells us that there are 3 teams with 3 players each - so up to 9 players could enter a race. However, only the first 5 to finish the race scored points. The amount of points rewarded is based on the given formula:

A team scores (6-N) points for each RACER who finishes in Nth place (1 <= N <= 5).

1st = 5 points
2nd = 4 points
3rd = 3 points
4th = 2 points
5th = 1 point
6th - 9th place = 0 points

Total = 15 possible points

Since there are no ties, two RACERS cannot finish in the same 'spot' (for example, two racers cannot both finish in 3rd place). However, that does NOT mean that two TEAMS must have a different total number of points.

We're told that no team scored more than 6 points, but there IS a way for two of the teams to score 6 points each (re: one team finishes 1st and 5th, one team finishes 2nd and 4th). Thus, the remaining 3 points (for 3rd place) would go to the final team - and the MINIMUM number of points that could be earned would be 3.

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For a certain race, 3 teams were allowed to enter 3 members each. 09 Jun 2020, 17:25
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Under what category could one classify this problem? I got it wrong on a practice test and don't really know how to study this type of question because I'm confused what skill it relates to.
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For a certain race, 3 teams were allowed to enter 3 members each. 10 Jun 2020, 00:11
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Under what category could one classify this problem? I got it wrong on a practice test and don't really know how to study this type of question because I'm confused what skill it relates to.

14. Min/Max Problems


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For a certain race, 3 teams were allowed to enter 3 members each. 30 Jul 2020, 23:57
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3(9-n) < 10 : Solve for this
9-n < 10/3
n > 5
Hence minimum value is 6






caiyun
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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For a certain race, 3 teams were allowed to enter 3 members each. 31 Jul 2020, 22:19
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lynnglenda
3(9-n) < 10 : Solve for this
9-n < 10/3
n > 5
Hence minimum value is 6






caiyun
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

Hi lynnglenda,

Can you go into a bit more detail with your explanation? I ask because your answer is not among the 5 choices - and if you can talk me through your 'steps', then we should be able to define the conceptual errors in your thinking.

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For a certain race, 3 teams were allowed to enter 3 members each. 31 Jul 2020, 22:50
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caiyun
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

There are a total of 3 x 3 = 9 members
If a member of a team finishes in:
Position 1 => Points = 5
Position 2 => Points = 4
Position 3 => Points = 3
Position 4 => Points = 2
Position 5 => Points = 1

The other 4 participants got no points

Thus, total points in consideration = 1+2+3+4+5 = 15

Since no team earned more than 6 points, the maximum points they could have earned = 6 points
(There are many ways for that, one such way being: Team-1 has players with 4, 2 and 0 points; Team-2 has players with 5, 1 and 0)

Thus, with 2 teams at 6 points each, the 3rd team will have 15 - 6 - 6 = 3 points (minimum)

Answer D
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For a certain race, 3 teams were allowed to enter 3 members each. 02 Jun 2021, 05:23
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Solution:

Total score=15

6-1 = 5

6-2 = 4

6-3 = 3

6-4 = 2

6-5 = 1

Every team was awarded (6-n) points where 1 ≤ n ≤ 5 , so,we can subtract 1, 2, 3 , 4 and 5 from 6 since each team has to get distinct number of points (as there were no ties, disqualifications or withdrawals)

No team can get more than 6 points, and we need to find the least possible points that a team can have.

=>Try to give maximum points to 2 teams so that the third and the remaining team will have least points.

Max points per team = 6

For two teams, maximum total points = 2 x 6 = 12.

=>The points remaining for team 3 = 15-12 = 3(option d)

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For a certain race, 3 teams were allowed to enter 3 members each. Updated on: 01 Feb 2022, 18:10
Originally posted by otautahi on 01 Feb 2022, 18:00.
Last edited by otautahi on 01 Feb 2022, 18:10, edited 1 time in total.
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Dany11
Hello,
Since the problem clearly states that there were no ties, no two teams could get equal points. Hence the solution must be:
-> team A -6 points
-> team B- 5 points
Hence, team C-> 15-6-5=4 points Answer.

Please correct me if I am wrong.

Your explanation can not be correct because the question states there were no ties that apply to the team members' "place" not the team's "points".


Ref question:
caiyun
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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For a certain race, 3 teams were allowed to enter 3 members each. 01 Feb 2022, 18:07
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scthakur
Plz see below.


I love this visualisation which makes sense. The only thing I'd add to clarify is we need to keep in mind that no team got more than 6 points. So now, whichever way we fill the positions, the least possible score a team could get would be 3.

Thank you, scthakur :blushing:
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For a certain race, 3 teams were allowed to enter 3 members each. 12 May 2022, 10:26
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Hi, is there an inherent fault in this question because it clearly states there were no ties, however, two of the teams have to score exactly 6 points each to minimise the score of the third team. 6 points each basically gives a tie... unless we're stating that no two team members can come in first place for example?
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For a certain race, 3 teams were allowed to enter 3 members each. 12 May 2022, 11:02
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A bunch of you got the intended credited response. But just to be a pain in the rear,...the prompt doesn't exclude the possibility of individual runners (who aren't on a team). If some of those are allowed, the minimum a team could score is ZERO. Answer choice A! ;) :P
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For a certain race, 3 teams were allowed to enter 3 members each. 25 Jul 2022, 12:33
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I think a simple solution for the question would be:
Since the number of games to be played is 3, that is each group to give one of its members. It means.

The least position that a member could be is number 5. i.e In a number of points is 6- n hence 6-5 = 1X(3 games for the three players) = 3
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For a certain race, 3 teams were allowed to enter 3 members each. 25 Jul 2022, 15:54
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JohnMuchiri
I think a simple solution for the question would be:
Since the number of games to be played is 3, that is each group to give one of its members. It means.

The least position that a member could be is number 5. i.e In a number of points is 6- n hence 6-5 = 1X(3 games for the three players) = 3

Hi JohnMuchiri,

What you describe does NOT match-up with the information given in the prompt. To start, there is just ONE race - with three teams of three individual people (re: 9 total people) racing in it. Based on the 'scoring system' described, the top 5 finishers earn points for their respective teams (from 5 points for 1st place down to 1 point for 5th place - anyone finishing 6th, 7th, 8th or 9th receives 0 points).

The last piece of information tells us that no team received more than 6 total points - so assuming that two of the three teams received exactly 6 points (which is possible if one team finishes 1st and 5th and the other finishes 2nd and 4th), then the remaining 3 points would have to have been won by the final team (specifically by one person who finishes 3rd). That is why the least possible score is three.

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For a certain race, 3 teams were allowed to enter 3 members each. 06 Dec 2022, 19:39
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KarishmaB
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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

Hi Karishma

In the Ques. we are given there is no tie then how can we assign same score(6) to 2 teams? Please clear this.
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For a certain race, 3 teams were allowed to enter 3 members each. 07 Dec 2022, 17:49
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BansalT
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I3igDmsu
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

Hi Karishma

In the Ques. we are given there is no tie then how can we assign same score(6) to 2 teams? Please clear this.

Hi BansalT,

A TEAM scores (6-N) points for each RACER who finishes in Nth place (1 <= N <= 5).

1st = 5 points
2nd = 4 points
3rd = 3 points
4th = 2 points
5th = 1 point
6th - 9th place = 0 points

Total = 15 possible points

Since there are no ties, two RACERS cannot finish in the same 'spot' (for example, two racers cannot both finish in 3rd place). However, that does NOT mean that two TEAMS must have a different total number of points.

We're told that no team scored more than 6 points, but there IS a way for two of the TEAMS to score 6 points each (re: one team finishes 1st and 5th, one team finishes 2nd and 4th).

GMAT assassins aren't born, they're made,
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For a certain race, 3 teams were allowed to enter 3 members each. 07 Dec 2022, 21:10
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BansalT
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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

Hi Karishma

In the Ques. we are given there is no tie then how can we assign same score(6) to 2 teams? Please clear this.

Request you to please tag me KarishmaB

No ties means no two people got the same rank in the race (so there was only one person at each position from 1 to 9).

But it is possible that 1 member of a team got 1st position (and hence 5 points) and another member of the same team got 5th position and hence 1 point. So this team had total 6 points.
While in another team, one member got 2nd rank and hence 4 points and another member got 4th rank and hence 2 points. So this team also had total 6 points.
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For a certain race, 3 teams were allowed to enter 3 members each. 07 May 2023, 17:38
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KarishmaB
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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

When I read the question, what I inferred was that the team gets 5-n points whenever n is 1-5 (Earning a point is conditional to finishing at nth position) But what if all the 3 team members did not qualify to get the point ie; finished at 7th, 8th and 9th position? Should they all not earn 0,0 and 0 points?
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For a certain race, 3 teams were allowed to enter 3 members each. 08 May 2023, 14:55
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Hi afra94,

Yes, you have correctly interpreted the 'scoring system' in this question (re: only the first 5 members to complete the race receive points). By extension, if three members on the same team finished 7th, 8th and 9th, then that team would receive 0 total points (since none of those racers would have finished in a position that rewards points).

To correctly answer this question though, you have to consider ALL of the information that we are given. There were 3 teams and none of the teams earned more than 6 points. With a little work, you can prove that it's NOT possible for a team's three members to finish 7th, 8th and 9th under those conditions. That team would have to have finished with AT LEAST 3 points (meaning that at least one of the racers finished high-enough to score points).

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For a certain race, 3 teams were allowed to enter 3 members each. 11 May 2025, 21:36
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