Question

Difficulty: MediumAnalytical Puzzles and Grouping

Six delegates—Alan, Bina, Farah, George, Harish, and Indu—are to be divided into two committees, Committee X and Committee Y, with exactly three members in each committee. The assignment must satisfy the following conditions:
1. Alan and Bina cannot be assigned to the same committee.
2. If Farah is assigned to Committee X, then George must be assigned to Committee Y.
3. Harish and Indu must be assigned to the same committee.
4. Alan is assigned to Committee X.

Which of the following delegates MUST be assigned to Committee X?

  1. HarishAnswer
  2. B
    Bina
  3. C
    Farah
  4. D
    George

Answer

Harish must be assigned to Committee X.
Because Alan is in Committee X, Bina must be in Committee Y. If Harish and Indu were placed in Committee Y, Committee Y would be full with Bina, Harish, and Indu. That would force Farah and George into Committee X. However, placing Farah in Committee X requires George to be in Committee Y, which creates a contradiction. Therefore, Harish and Indu must be in Committee X.

Step-by-Step Solution

1
Determine Bina's committee assignment using Condition 1 and Condition 4.
Alan is in Committee X. Since Alan and Bina cannot be together, Bina must be assigned to Committee Y.
Direct placement from explicit conditions.
2
Analyze the placement of Harish and Indu using Condition 3.
Harish and Indu must be placed in the same committee (either both in X or both in Y).
Condition 3 forces Harish and Indu as a unit.
3
Test the assumption that Harish and Indu are in Committee Y.
If Harish and Indu were in Committee Y, Committee Y would have three members: Bina, Harish, and Indu. This would leave Alan, Farah, and George in Committee X. But if Farah is in Committee X, Condition 2 requires George to be in Committee Y, creating a contradiction.
Proof by contradiction eliminates placing Harish and Indu in Committee Y.
4
Conclude the valid committee assignments.
Harish and Indu must both be in Committee X. Therefore, Committee X consists of Alan, Harish, and Indu, while Committee Y consists of Bina, Farah, and George.
Complete placement satisfying all conditions.

Key Concept

Analytical Grouping and Constraint Satisfaction
Estimated Time:1m 30s
Rate this question