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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?
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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.
Most Upvoted Answer
Team Legato is competing against Team Forte in a musical duets competi...
Win all three prizes.
Let's assume that Team Forte has x members. Since Team Legato has 1/4 as many members as Team Forte, Team Legato has (1/4)x members.
Since each duo consists of one member from Team Legato and one member from Team Forte, the total number of duos is equal to the smaller of the two team sizes.
Therefore, if there are 20 duos competing, we can write the equation:
20 = min(x, (1/4)x)
To solve for x, we can set up and solve the equation:
20 = min(x, (1/4)x)
20 = x (since (1/4)x is always smaller than x)
Therefore, x = 20.
This means that Team Forte has 20 members and Team Legato has (1/4)x = (1/4)(20) = 5 members.
Now, let's consider the arrangements of the medal winners.
For the first-place duo, there are 20 possible choices.
For the second-place duo, there are 19 possible choices remaining.
For the third-place duo, there are 18 possible choices remaining.
Therefore, the total number of possible arrangements of medal winners is 20 * 19 * 18 = 6840.
So, the closest approximate number of possible different arrangements of medal winners is 6840.
Let's assume that Team Forte has x members. Since Team Legato has 1/4 as many members as Team Forte, Team Legato has (1/4)x members.
Since each duo consists of one member from Team Legato and one member from Team Forte, the total number of duos is equal to the smaller of the two team sizes.
Therefore, if there are 20 duos competing, we can write the equation:
20 = min(x, (1/4)x)
To solve for x, we can set up and solve the equation:
20 = min(x, (1/4)x)
20 = x (since (1/4)x is always smaller than x)
Therefore, x = 20.
This means that Team Forte has 20 members and Team Legato has (1/4)x = (1/4)(20) = 5 members.
Now, let's consider the arrangements of the medal winners.
For the first-place duo, there are 20 possible choices.
For the second-place duo, there are 19 possible choices remaining.
For the third-place duo, there are 18 possible choices remaining.
Therefore, the total number of possible arrangements of medal winners is 20 * 19 * 18 = 6840.
So, the closest approximate number of possible different arrangements of medal winners is 6840.
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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?
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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? 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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