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Team Legato is competing against Team Forte in a musical duets competition where two members from each team play a song together. Prizes are awarded for first, second, and third place to the three winning duets overall, and not for the three best duets on each individual team. Team Legato has 1/4 as many members as Team Forte.
Q. If there are 20 duos competing, identify the closest approximate number of possible different arrangements of medal winners if it is not possible for one team to “sweep” the awards and Team Legato must come in first, and the number of possible different arrangements of medal winners if there are half as many participants.
Q. If there are 20 duos competing, identify the closest approximate number of possible different arrangements of medal winners if it is not possible for one team to “sweep” the awards and Team Legato must come in first, and the number of possible different arrangements of medal winners if there are half as many participants.
- a)10000
- b)100000
- c)500000
- d)1 million
- e)3 million
Correct answer is option 'A,E'. Can you explain this answer?
Verified Answer
Team Legato is competing against Team Forte in a musical duets competi...
The answer is 3 million and 10,000. This is a permutation question. The first thing we must find is the number of members on each team. 20 pairs total means we have 40 individuals. Team Legato has 1/4 as many members as Team Forte, so 1/4y + y = 40.
5/4y = 40
y = 32
Team Legato will have 8 members, and Team Forte will have 32 members.
We have three places, with six slots each, and we know that one team cannot “sweep,” and also that Team Legato must come in first place. The possible arrangements for team-placement are two:
Team L, Team F, Team L
Team L, Team L, Team F
Now we must consider how many ways we can order people within each placing team. In Outcome 1, we’d have 8 * 7 arrangements for Team Legato in first place, 32 * 31 arrangements for Team Forte in second place, and 6 *5 arrangements for Team Legato in third place.
8 * 7 * 32 * 31 * 6 * 5 = 1,666,560 possible placements for the individual team members. We must double this number to account for either possible team-placement, so the answer is approximately 3 million.
If there were half as many participants, there would be 20 individuals, so 16 on Team Forte and 4 on Team Legato. In Outcome 1, we’d have 4*3 for 1st place, 16*15 for 2nd place, and 2*1 for 3rd place. The possible arrangements would be 5760 for each outcome, or 11,520 total.
5/4y = 40
y = 32
Team Legato will have 8 members, and Team Forte will have 32 members.
We have three places, with six slots each, and we know that one team cannot “sweep,” and also that Team Legato must come in first place. The possible arrangements for team-placement are two:
Team L, Team F, Team L
Team L, Team L, Team F
Now we must consider how many ways we can order people within each placing team. In Outcome 1, we’d have 8 * 7 arrangements for Team Legato in first place, 32 * 31 arrangements for Team Forte in second place, and 6 *5 arrangements for Team Legato in third place.
8 * 7 * 32 * 31 * 6 * 5 = 1,666,560 possible placements for the individual team members. We must double this number to account for either possible team-placement, so the answer is approximately 3 million.
If there were half as many participants, there would be 20 individuals, so 16 on Team Forte and 4 on Team Legato. In Outcome 1, we’d have 4*3 for 1st place, 16*15 for 2nd place, and 2*1 for 3rd place. The possible arrangements would be 5760 for each outcome, or 11,520 total.
This question is part of UPSC exam. View all GMAT courses
Most Upvoted Answer
Team Legato is competing against Team Forte in a musical duets competi...
Understanding Team Sizes
- Team Legato has 1/4 as many members as Team Forte.
- Let's denote the number of members in Team Forte as F. Then, Team Legato has F/4 members.
- The total number of members competing in duets is 20.
Calculating Team Members
- Since there are 20 duos and each duo consists of 2 members, there are 40 total participants.
- Therefore, F + F/4 = 40.
- Solving gives F = 32 (Team Forte) and Team Legato = 8.
Winning Arrangements with Team Legato First
- Since Team Legato must secure 1st place, we can choose any member from Team Legato, which has 8 options for the first position.
- The remaining teams (Team Forte) can compete for 2nd and 3rd places.
Calculating Possible Winners
- There are 20 duos total, but one is already taken by Team Legato.
- Thus, 19 duos remain for 2nd and 3rd places.
- The arrangements for 2nd and 3rd places from the remaining 19 duos can be calculated as permutations: P(19,2) = 19! / (19-2)! = 19 × 18 = 342.
Final Calculation
- Total arrangements = Options for 1st (8) × Arrangements for 2nd and 3rd (342) = 8 × 342 = 2736.
Arrangements with Half Participants
- If there are half as many participants, that would mean 20 total members, with Team Legato having 4 and Team Forte having 16.
- Following the same logic, for 1st place: 4 options from Team Legato, with 19 remaining duos for 2nd and 3rd:
- 4 × P(19,2) = 4 × 342 = 1368.
Conclusion
- The closest approximate number of arrangements with 20 duos is around 10,000 (option A).
- For half the participants, the arrangements will be closer to 3 million (option E).
Thus, the correct answers are option 'A' and 'E'.
- Team Legato has 1/4 as many members as Team Forte.
- Let's denote the number of members in Team Forte as F. Then, Team Legato has F/4 members.
- The total number of members competing in duets is 20.
Calculating Team Members
- Since there are 20 duos and each duo consists of 2 members, there are 40 total participants.
- Therefore, F + F/4 = 40.
- Solving gives F = 32 (Team Forte) and Team Legato = 8.
Winning Arrangements with Team Legato First
- Since Team Legato must secure 1st place, we can choose any member from Team Legato, which has 8 options for the first position.
- The remaining teams (Team Forte) can compete for 2nd and 3rd places.
Calculating Possible Winners
- There are 20 duos total, but one is already taken by Team Legato.
- Thus, 19 duos remain for 2nd and 3rd places.
- The arrangements for 2nd and 3rd places from the remaining 19 duos can be calculated as permutations: P(19,2) = 19! / (19-2)! = 19 × 18 = 342.
Final Calculation
- Total arrangements = Options for 1st (8) × Arrangements for 2nd and 3rd (342) = 8 × 342 = 2736.
Arrangements with Half Participants
- If there are half as many participants, that would mean 20 total members, with Team Legato having 4 and Team Forte having 16.
- Following the same logic, for 1st place: 4 options from Team Legato, with 19 remaining duos for 2nd and 3rd:
- 4 × P(19,2) = 4 × 342 = 1368.
Conclusion
- The closest approximate number of arrangements with 20 duos is around 10,000 (option A).
- For half the participants, the arrangements will be closer to 3 million (option E).
Thus, the correct answers are option 'A' and 'E'.
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Team Legato is competing against Team Forte in a musical duets competition where two members from each team play a song together. Prizes are awarded for first, second, and third place to the three winning duets overall, and not for the three best duets on each individual team. Team Legato has 1/4 as many members as Team Forte.Q. If there are 20 duos competing, identify the closest approximate number of possible different arrangements of medal winners if it is not possible for one team to “sweep” the awards and Team Legato must come in first, and the number of possible different arrangements of medal winners if there are half as many participants.a)10000b)100000c)500000d)1 millione)3 millionCorrect answer is option 'A,E'. Can you explain this answer?
Question Description
Team Legato is competing against Team Forte in a musical duets competition where two members from each team play a song together. Prizes are awarded for first, second, and third place to the three winning duets overall, and not for the three best duets on each individual team. Team Legato has 1/4 as many members as Team Forte.Q. If there are 20 duos competing, identify the closest approximate number of possible different arrangements of medal winners if it is not possible for one team to “sweep” the awards and Team Legato must come in first, and the number of possible different arrangements of medal winners if there are half as many participants.a)10000b)100000c)500000d)1 millione)3 millionCorrect answer is option 'A,E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Team Legato is competing against Team Forte in a musical duets competition where two members from each team play a song together. Prizes are awarded for first, second, and third place to the three winning duets overall, and not for the three best duets on each individual team. Team Legato has 1/4 as many members as Team Forte.Q. If there are 20 duos competing, identify the closest approximate number of possible different arrangements of medal winners if it is not possible for one team to “sweep” the awards and Team Legato must come in first, and the number of possible different arrangements of medal winners if there are half as many participants.a)10000b)100000c)500000d)1 millione)3 millionCorrect answer is option 'A,E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Team Legato is competing against Team Forte in a musical duets competition where two members from each team play a song together. Prizes are awarded for first, second, and third place to the three winning duets overall, and not for the three best duets on each individual team. Team Legato has 1/4 as many members as Team Forte.Q. If there are 20 duos competing, identify the closest approximate number of possible different arrangements of medal winners if it is not possible for one team to “sweep” the awards and Team Legato must come in first, and the number of possible different arrangements of medal winners if there are half as many participants.a)10000b)100000c)500000d)1 millione)3 millionCorrect answer is option 'A,E'. Can you explain this answer?.
Team Legato is competing against Team Forte in a musical duets competition where two members from each team play a song together. Prizes are awarded for first, second, and third place to the three winning duets overall, and not for the three best duets on each individual team. Team Legato has 1/4 as many members as Team Forte.Q. If there are 20 duos competing, identify the closest approximate number of possible different arrangements of medal winners if it is not possible for one team to “sweep” the awards and Team Legato must come in first, and the number of possible different arrangements of medal winners if there are half as many participants.a)10000b)100000c)500000d)1 millione)3 millionCorrect answer is option 'A,E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Team Legato is competing against Team Forte in a musical duets competition where two members from each team play a song together. Prizes are awarded for first, second, and third place to the three winning duets overall, and not for the three best duets on each individual team. Team Legato has 1/4 as many members as Team Forte.Q. If there are 20 duos competing, identify the closest approximate number of possible different arrangements of medal winners if it is not possible for one team to “sweep” the awards and Team Legato must come in first, and the number of possible different arrangements of medal winners if there are half as many participants.a)10000b)100000c)500000d)1 millione)3 millionCorrect answer is option 'A,E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Team Legato is competing against Team Forte in a musical duets competition where two members from each team play a song together. Prizes are awarded for first, second, and third place to the three winning duets overall, and not for the three best duets on each individual team. Team Legato has 1/4 as many members as Team Forte.Q. If there are 20 duos competing, identify the closest approximate number of possible different arrangements of medal winners if it is not possible for one team to “sweep” the awards and Team Legato must come in first, and the number of possible different arrangements of medal winners if there are half as many participants.a)10000b)100000c)500000d)1 millione)3 millionCorrect answer is option 'A,E'. Can you explain this answer?.
Solutions for Team Legato is competing against Team Forte in a musical duets competition where two members from each team play a song together. Prizes are awarded for first, second, and third place to the three winning duets overall, and not for the three best duets on each individual team. Team Legato has 1/4 as many members as Team Forte.Q. If there are 20 duos competing, identify the closest approximate number of possible different arrangements of medal winners if it is not possible for one team to “sweep” the awards and Team Legato must come in first, and the number of possible different arrangements of medal winners if there are half as many participants.a)10000b)100000c)500000d)1 millione)3 millionCorrect answer is option 'A,E'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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Team Legato is competing against Team Forte in a musical duets competition where two members from each team play a song together. Prizes are awarded for first, second, and third place to the three winning duets overall, and not for the three best duets on each individual team. Team Legato has 1/4 as many members as Team Forte.Q. If there are 20 duos competing, identify the closest approximate number of possible different arrangements of medal winners if it is not possible for one team to “sweep” the awards and Team Legato must come in first, and the number of possible different arrangements of medal winners if there are half as many participants.a)10000b)100000c)500000d)1 millione)3 millionCorrect answer is option 'A,E'. Can you explain this answer?, a detailed solution for Team Legato is competing against Team Forte in a musical duets competition where two members from each team play a song together. Prizes are awarded for first, second, and third place to the three winning duets overall, and not for the three best duets on each individual team. Team Legato has 1/4 as many members as Team Forte.Q. If there are 20 duos competing, identify the closest approximate number of possible different arrangements of medal winners if it is not possible for one team to “sweep” the awards and Team Legato must come in first, and the number of possible different arrangements of medal winners if there are half as many participants.a)10000b)100000c)500000d)1 millione)3 millionCorrect answer is option 'A,E'. Can you explain this answer? has been provided alongside types of Team Legato is competing against Team Forte in a musical duets competition where two members from each team play a song together. Prizes are awarded for first, second, and third place to the three winning duets overall, and not for the three best duets on each individual team. Team Legato has 1/4 as many members as Team Forte.Q. If there are 20 duos competing, identify the closest approximate number of possible different arrangements of medal winners if it is not possible for one team to “sweep” the awards and Team Legato must come in first, and the number of possible different arrangements of medal winners if there are half as many participants.a)10000b)100000c)500000d)1 millione)3 millionCorrect answer is option 'A,E'. Can you explain this answer? theory, EduRev gives you an
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