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Zorluk: OrtaAnalytical Puzzles and Grouping

Five project managers—Arjun, Bina, Chirag, Divya, and Ekta—are to be assigned to three project teams: Team Alpha, Team Beta, and Team Gamma, according to the following conditions:
1. Each team must contain at least one manager, and Team Alpha must contain exactly two managers.
2. Arjun and Bina are assigned to the same team.
3. Chirag cannot be assigned to Team Beta.
4. Divya and Ekta must be assigned to different teams.
5. Ekta is assigned to Team Gamma.
6. Chirag and Ekta cannot be assigned to the same team.

Which of the following statements is DEFINITELY correct regarding the team assignments?

  1. Chirag and Divya are assigned to Team Alpha.Cevap
  2. B
    Arjun and Bina are assigned to Team Alpha.
  3. C
    Divya is assigned to Team Beta.
  4. D
    Chirag and Ekta are both assigned to Team Gamma.

Cevap

Chirag and Divya are assigned to Team Alpha.
By logical deduction from the given constraints, Chirag must be assigned to Team Alpha because he cannot be in Team Beta or Team Gamma. Arjun and Bina must be in Team Beta to prevent capacity violations or condition conflicts. Divya must join Chirag in Team Alpha to satisfy the requirement of exactly two members in Team Alpha while keeping Divya and Ekta separated.

Adım Adım Çözüm

1
Analyze Ekta's placement and condition restrictions
Ekta is assigned to Team Gamma. Chirag cannot be in Team Beta (condition 3) and cannot be in Team Gamma with Ekta (condition 6). Therefore, Chirag must be in Team Alpha.
Elimination of invalid teams for Chirag leaves only Team Alpha.
2
Determine the placement of Arjun and Bina
Arjun and Bina must be in the same team. If they were in Team Alpha, Team Alpha would reach its maximum capacity of 2 (Arjun and Bina). This would leave Chirag unable to be in Team Alpha, creating a contradiction. If Arjun and Bina were in Team Gamma, Team Gamma would have 3 members, forcing Team Beta to have 0 members, violating condition 1. Thus, Arjun and Bina must be assigned to Team Beta.
Testing possible team assignments for the Arjun-Bina pair shows Team Beta is the only consistent choice.
3
Assign the remaining manager, Divya
Divya cannot be in Team Gamma because Ekta is in Team Gamma (condition 4). Team Beta already has 2 members (Arjun and Bina). Since Team Alpha needs exactly 2 members and currently has Chirag, Divya must join Team Alpha.
Satisfies the team capacity of 2 for Team Alpha and condition 4.
4
Finalize and verify team compositions
Team Alpha: {Chirag, Divya} (2 members), Team Beta: {Arjun, Bina} (2 members), Team Gamma: {Ekta} (1 member). Total = 5 members.
All 6 given conditions are fully satisfied without any contradiction.

Anahtar Kavram

Analytical Grouping and Constraint Satisfaction
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Konular

Analytical Puzzles and Grouping

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