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Difficulty: HardAnalytical Puzzles and Grouping

Seven researchers—Aarav, Brinda, Chetan, Divya, Ekta, Faisal, and Gautam—are to be assigned to three project teams: Alpha, Beta, and Gamma, adhering strictly to the following conditions:

1. Each team must contain at least two researchers.
2. Aarav and Brinda must be assigned to the same team.
3. Chetan cannot be in the same team as Divya or Ekta.
4. Faisal and Gautam must be assigned to different teams.
5. Team Alpha consists of exactly three members, one of whom is Faisal.
6. Ekta is assigned to Team Beta.

Based on these conditions, which of the following statements are correct?

  1. Divya is assigned to Team Beta.Answer
  2. Gautam and Chetan are both assigned to Team Gamma.Answer
  3. C
    Aarav is assigned to Team Beta.
  4. D
    Chetan is assigned to Team Alpha.

Answer

The correct statements are that Divya is assigned to Team Beta and that Gautam and Chetan are both assigned to Team Gamma.
Systematic elimination of impossible team size configurations dictates that Team Alpha must contain Aarav, Brinda, and Faisal; Team Beta must contain Ekta and Divya; and Team Gamma must contain Chetan and Gautam. Therefore, the statement that Divya is assigned to Team Beta and the statement that Gautam and Chetan are both assigned to Team Gamma are both unequivocally true.

Step-by-Step Solution

1
Determine the team size distribution.
Team Alpha has 3 members. Since there are 7 researchers in total and every team must have at least 2 members, the team size distribution must be 3 (Alpha), 2 (Beta), and 2 (Gamma).
Partitioning 7 into 3 sets with each set size ≥ 2 yields (3, 2, 2) as the only valid distribution.
2
Determine the placement of paired researchers Aarav and Brinda.
Aarav and Brinda must be assigned to Team Alpha.
If Aarav and Brinda were placed in Team Beta (which already contains Ekta) or Team Gamma, that team would reach a size of 3, leaving the remaining team with only 1 member and violating the minimum capacity constraint.
3
Determine the complete membership of Team Alpha.
Team Alpha consists of Aarav, Brinda, and Faisal.
Team Alpha has a fixed size of 3 and already contains Faisal. Adding Aarav and Brinda fills Team Alpha completely.
4
Deduce assignments for Chetan, Divya, Ekta, and Gautam.
Team Beta consists of Ekta and Divya; Team Gamma consists of Chetan and Gautam.
Chetan cannot be in Team Beta with Ekta and cannot enter full Team Alpha, so Chetan is in Team Gamma. Divya cannot be in Team Gamma with Chetan, so Divya goes to Team Beta. Gautam cannot be with Faisal in Team Alpha, so Gautam joins Chetan in Team Gamma.

Key Concept

Multi-Constraint Analytical Grouping and Deduction
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Topics

Analytical Puzzles and Grouping

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