Syscorp occupies three floors of an office building, the first floor, the second floor, which is immediately above the first...
GMAT Two Part Analysis : (TPA) Questions
Syscorp occupies three floors of an office building, the first floor, the second floor, which is immediately above the first floor, and the third floor, which is immediately above the second floor, but no other floors. These three floors house only the following corporate departments: Administrative, Finance, Human Resources, Information Technology, Legal, and Marketing. Each department is on exactly one floor, and each floor houses at least one department. Exactly three of the departments are on the second floor. The Legal and Administrative departments are both on the floor immediately below the Finance department. The Human Resources department is on the floor immediately below the Marketing department.
In the table select for First Floor an allocation of departments to the first floor and for Third Floor an allocation of departments to the third floor such that the two allocations are jointly compatible with the information provided. Make only two selections, one in each column.
Solution for TPA Floor Allocation Problem
Visual Representation
Building Structure:
- Floor 3 (top)
- Floor 2 (middle) - must have exactly 3 departments
- Floor 1 (bottom)
Departments to allocate:
- Administrative (A)
- Finance (F)
- Human Resources (H)
- Information Technology (I)
- Legal (L)
- Marketing (M)
Key Constraints:
- Each department on exactly one floor
- Each floor has at least one department
- Exactly 3 departments on floor 2
- L and A are both on the floor immediately below F
- H is on the floor immediately below M
Drawing Immediate Inferences
From Constraint 4:
- Legal and Administrative must be together on the same floor
- Finance must be exactly one floor above them
- Possible positions:
- If F is on floor 2 → L and A are on floor 1
- If F is on floor 3 → L and A are on floor 2
- F cannot be on floor 1 (nothing below)
From Constraint 5:
- Marketing must be exactly one floor above HR
- Possible positions:
- If M is on floor 2 → H is on floor 1
- If M is on floor 3 → H is on floor 2
- M cannot be on floor 1 (nothing below)
Strategic Analysis
Testing Finance on Floor 3:
If F is on floor 3:
- L and A must be on floor 2 (2 departments on floor 2 so far)
- Need exactly 1 more department on floor 2
Case 1: If M is on floor 3 with F:
- H must be on floor 2 (with L and A)
- Floor 2 now has: L, A, H (3 departments) ✓
- Floor 1 gets: I
- Floor 3 has: F, M
Case 2: If M is on floor 2:
- H must be on floor 1
- Floor 2 has: L, A, M (3 departments) ✓
- Floor 1 has: H
- Floor 3 has: F, I
Testing Finance on Floor 2:
If F is on floor 2:
- L and A must be on floor 1
- Floor 2 has F (needs 2 more departments)
Case 3: If M is on floor 3:
- H must be on floor 2
- Floor 2 has: F, H (needs 1 more)
- I goes to floor 2
- Floor 2 has: F, H, I (3 departments) ✓
- Floor 1 has: L, A
- Floor 3 has: M
Matching with Answer Choices
Examining our valid configurations against the answer choices:
Configuration from Case 2:
- First floor: H only → matches "The Human Resources Department only"
- Third floor: F and I → matches "The Finance and Information Technology departments only"
Final Answer
First Floor: The Human Resources Department only
Third Floor: The Finance and Information Technology departments only
Key Insights
- Paired constraints create rigid structures: When L and A must be together below F, this creates a two-floor unit that significantly constrains the solution
- The "exactly 3" constraint on floor 2 is critical: This forces specific distributions
- Answer choices provide validation: Not all mathematically valid configurations match the given options
- Exam strategy: Start with the most constrained elements (paired departments) and build around them