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Re: For a certain race, 3 teams were allowed to enter 3 members [#permalink]
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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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20 Jun 2014, 06:10
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
Experts, can you please evaluate my solution/approach.
Team has to earn 6n points. And 1 ≤ n ≤ 5 To minimize the total points, select maximum value of n i.e. 5 (for each of team's 3 participants). 3 is the answer.



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Re: For a certain race, 3 teams were allowed to enter 3 members [#permalink]
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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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14 Oct 2014, 02:43
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Total scores: 61 = 5 62 = 4 63 = 3 64 = 2 65 = 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 = 1512 = 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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06 Sep 2015, 22:19
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 6n 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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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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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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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 thirdplace runner. It's score is thus 63 = 3 points.



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Re: For a certain race, 3 teams were allowed to enter 3 members [#permalink]
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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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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 6n has to be the least value. So 6n is least when n=5 , therefore 6n = 65=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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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. VeritasPrepKarishmaI solved it liked this. Score alloted has to be 6N . 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 Bunuel VeritasPrepKarishma



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Re: For a certain race, 3 teams were allowed to enter 3 members [#permalink]
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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 6n 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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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 6n 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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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 (6N) 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). Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: For a certain race, 3 teams were allowed to enter 3 members [#permalink]
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17 Mar 2018, 07:45
n Team Points 6n ====================== 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
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Re: For a certain race, 3 teams were allowed to enter 3 members [#permalink]
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21 Mar 2018, 08:39
VeritasPrepKarishma Bunuel chetan2uApart from below part of solution which I did not understand , can you help me to understand below queries? 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 1. Do we not need to know total no of games played? 2. Why did you took two scores to maximize, can there be not only one winner?
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Re: For a certain race, 3 teams were allowed to enter 3 members
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