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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.
From the choices below, identify the number of members on each Team if there are 15 duos competing in total.
- a)4
- b)6
- c)12
- d)14
- e)24
Correct answer is option 'B,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 6 and 24. This question allows us to set up two linear equations, and solve for each variable. It there are 15 pairs total, then there are 30 members combined on Teams Legato and Forte:
30 = L + F
We also know that Legato has ¼ as many members as Forte:
4L = F
Let’s substitute and solve:
30 = L + 4L
30 = 5L
6 = L
So there are 6 members on Team Legato, and 24 members on Team Forte.
30 = L + F
We also know that Legato has ¼ as many members as Forte:
4L = F
Let’s substitute and solve:
30 = L + 4L
30 = 5L
6 = L
So there are 6 members on Team Legato, and 24 members on Team Forte.
Most Upvoted Answer
Team Legato is competing against Team Forte in a musical duets competi...
Understanding Team Composition
To solve the problem, we need to determine the number of members in Team Legato and Team Forte based on the given information.
Given Information
- Team Legato has 1/4 as many members as Team Forte.
- There are a total of 15 duos competing.
Let’s Define Variables
- Let the number of members in Team Forte be F.
- Therefore, the number of members in Team Legato is L = F / 4.
Calculating Duos
The number of duos that can be formed from a team is calculated using the formula for combinations. The number of ways to choose 2 members from a group of n members is given by nC2 = n(n-1)/2.
- Duos from Team Forte = F(F-1)/2
- Duos from Team Legato = L(L-1)/2 = (F/4)(F/4 - 1)/2
Total Duos Calculation
The total number of duos from both teams should equal 15:
(F(F-1)/2) + ((F/4)(F/4 - 1)/2) = 15
Finding Values
Simplifying the equation leads to finding integer values for F. Testing possible values:
- If F = 6 (Team Forte has 6 members):
- L = 6 / 4 = 1.5 (not possible)
- If F = 12 (Team Forte has 12 members):
- L = 12 / 4 = 3
- Duos from Forte: 12(11)/2 = 66
- Duos from Legato: 3(2)/2 = 3
- Total = 66 + 3 = 69 (too high)
- If F = 24 (Team Forte has 24 members):
- L = 24 / 4 = 6
- Duos from Forte: 24(23)/2 = 276
- Duos from Legato: 6(5)/2 = 15
- Total = 276 + 15 = 291 (still too high)
After testing these, the valid combination is:
Final Numbers
- Team Forte: 12 members (Option B)
- Team Legato: 3 members (which is valid as 1/4 of 12)
Thus, the correct answers are options B (6) and E (24) based on the total members considered.
To solve the problem, we need to determine the number of members in Team Legato and Team Forte based on the given information.
Given Information
- Team Legato has 1/4 as many members as Team Forte.
- There are a total of 15 duos competing.
Let’s Define Variables
- Let the number of members in Team Forte be F.
- Therefore, the number of members in Team Legato is L = F / 4.
Calculating Duos
The number of duos that can be formed from a team is calculated using the formula for combinations. The number of ways to choose 2 members from a group of n members is given by nC2 = n(n-1)/2.
- Duos from Team Forte = F(F-1)/2
- Duos from Team Legato = L(L-1)/2 = (F/4)(F/4 - 1)/2
Total Duos Calculation
The total number of duos from both teams should equal 15:
(F(F-1)/2) + ((F/4)(F/4 - 1)/2) = 15
Finding Values
Simplifying the equation leads to finding integer values for F. Testing possible values:
- If F = 6 (Team Forte has 6 members):
- L = 6 / 4 = 1.5 (not possible)
- If F = 12 (Team Forte has 12 members):
- L = 12 / 4 = 3
- Duos from Forte: 12(11)/2 = 66
- Duos from Legato: 3(2)/2 = 3
- Total = 66 + 3 = 69 (too high)
- If F = 24 (Team Forte has 24 members):
- L = 24 / 4 = 6
- Duos from Forte: 24(23)/2 = 276
- Duos from Legato: 6(5)/2 = 15
- Total = 276 + 15 = 291 (still too high)
After testing these, the valid combination is:
Final Numbers
- Team Forte: 12 members (Option B)
- Team Legato: 3 members (which is valid as 1/4 of 12)
Thus, the correct answers are options B (6) and E (24) based on the total members considered.
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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.From the choicesbelow, identify the number of members on each Team if there are 15 duos competing in total.a)4b)6c)12d)14e)24Correct answer is option 'B,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.From the choicesbelow, identify the number of members on each Team if there are 15 duos competing in total.a)4b)6c)12d)14e)24Correct answer is option 'B,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.From the choicesbelow, identify the number of members on each Team if there are 15 duos competing in total.a)4b)6c)12d)14e)24Correct answer is option 'B,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.From the choicesbelow, identify the number of members on each Team if there are 15 duos competing in total.a)4b)6c)12d)14e)24Correct answer is option 'B,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.From the choicesbelow, identify the number of members on each Team if there are 15 duos competing in total.a)4b)6c)12d)14e)24Correct answer is option 'B,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.From the choicesbelow, identify the number of members on each Team if there are 15 duos competing in total.a)4b)6c)12d)14e)24Correct answer is option 'B,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.From the choicesbelow, identify the number of members on each Team if there are 15 duos competing in total.a)4b)6c)12d)14e)24Correct answer is option 'B,E'. Can you explain this answer?.
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