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Difficulty: HardAnalytical Puzzles and Grouping

Five officers — Arjun, Bina, Chandan, Deepa, and Ehsaan — represent five different departments: Finance, Health, Home, Revenue, and Transport. They are assigned to three committees: Committee X, Committee Y, and Committee Z such that each committee has at least one officer and at most two officers. The following conditions apply:

• Arjun is assigned to Committee X, but he is not from the Finance or Health department.
• The officer from the Revenue department is in the same committee as Bina.
• Chandan is from the Transport department and is assigned to Committee Z.
• Deepa is not assigned to Committee X and is not from the Finance department.
• The officer from the Health department is in Committee Y along with the officer from the Home department.
• Ehsaan is from the Health department.

Which of the following statements is definitely correct?

  1. Arjun belongs to the Revenue department and is assigned to Committee X along with Bina.Answer
  2. B
    Bina belongs to the Home department and is assigned to Committee Y along with Ehsaan.
  3. C
    Arjun belongs to the Finance department and is assigned to Committee X.
  4. D
    Deepa belongs to the Revenue department and is assigned to Committee Z.

Answer

Arjun belongs to the Revenue department and is assigned to Committee X along with Bina.
By systematically evaluating committee capacities and negative constraints, Committee Y consists of Ehsaan (Health) and Deepa (Home). Committee Z consists solely of Chandan (Transport). Committee X consists of Arjun (Revenue) and Bina (Finance). Thus, the statement asserting Arjun is from Revenue and in Committee X with Bina is uniquely correct.

Step-by-Step Solution

1
Identify known assignments and committee constraints.
Ehsaan is from Health. The Health officer (Ehsaan) and the Home officer are together in Committee Y. Thus, Committee Y has 2 officers: Ehsaan (Health) and [Home officer]. Chandan is from Transport and in Committee Z.
Direct deduction from clues regarding Ehsaan, Health, Home, and Chandan.
2
Determine the identity of the Home officer in Committee Y.
Deepa is the Home officer in Committee Y.
Arjun is in Committee X, Chandan is in Committee Z, and Ehsaan is Health in Y. The Home officer must be either Bina or Deepa. If Bina were the Home officer in Y, the Revenue officer would also have to be in Y (by clue 2), creating 3 members in Y which violates the maximum committee size of 2. Thus, Bina cannot be in Y, making Deepa the Home officer in Y.
3
Place Bina and determine committee distributions.
Bina is assigned to Committee X.
Committee Y is full with 2 members (Ehsaan and Deepa). If Bina were in Committee Z with Chandan (Transport), the Revenue officer would also be in Z, making Bina the Revenue officer. But then Arjun (in X) would have to be Finance, which violates clue 1. Hence, Bina must be in Committee X.
4
Assign remaining departments (Finance and Revenue) to Committee X officers (Arjun and Bina).
Arjun is from Revenue and Bina is from Finance, both in Committee X.
Clue 1 states Arjun cannot be from Finance. Therefore, Arjun is from Revenue, leaving Bina to be from Finance.

Key Concept

Multi-Constraint Matrix Elimination & Grouping
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Topics

Analytical Puzzles and Grouping

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