A plumbing contractor is scheduling plumbers on her crew to work at five job sites next week - an apartment...
GMAT Two Part Analysis : (TPA) Questions
A plumbing contractor is scheduling plumbers on her crew to work at five job sites next week - an apartment complex, a department store, an office building, a restaurant, and a school. Because of the proximities of and projected workloads at the various job sites, she has decided on the following requirements:
- Each plumber working on the apartment complex must also work on either the department store or the school
- A plumber must work on the office building if that plumber works on the restaurant
- Any plumber working on the restaurant but not on the school must also work on the department store
- Of the plumbers working on the department store, those who work on the school must also work on the office building
Any plumber working on the 1 must also work on the 2. Select for 1 and 2 the two job sites that would complement the statement in a way that would accurately reexpress one of the requirements
Solution: Two-Part Analysis - Plumbing Contractor Scheduling
Visual Representation
Job Sites:
- A: Apartment complex
- D: Department store
- O: Office building
- R: Restaurant
- S: School
Requirements (as logical statements):
- \(\mathrm{A} \to (\mathrm{D} \lor \mathrm{S})\): If plumber works on A, then must work on D or S
- \(\mathrm{R} \to \mathrm{O}\): If plumber works on R, then must work on O
- \((\mathrm{R} \land \neg\mathrm{S}) \to \mathrm{D}\): If plumber works on R but not S, then must work on D
- \((\mathrm{D} \land \mathrm{S}) \to \mathrm{O}\): If plumber works on both D and S, then must work on O
Understanding the Question
We need to find two job sites that complete: "Any plumber working on the [1] must also work on the [2]"
This statement has the form: \(\mathrm{X} \to \mathrm{Y}\) (If X then Y)
Processing the Solution
Analyzing Each Requirement
Requirement 1: \(\mathrm{A} \to (\mathrm{D} \lor \mathrm{S})\)
- Cannot be expressed as simple "\(\mathrm{X} \to \mathrm{Y}\)" because conclusion has OR condition
- Would need: "Any plumber working on A must work on D or S"
Requirement 2: \(\mathrm{R} \to \mathrm{O}\)
- Perfect match!
- Can be expressed as: "Any plumber working on R must also work on O"
- This is exactly the format requested
Requirement 3: \((\mathrm{R} \land \neg\mathrm{S}) \to \mathrm{D}\)
- Cannot fit because premise has compound condition
- Would need: "Any plumber working on R but not on S must work on D"
Requirement 4: \((\mathrm{D} \land \mathrm{S}) \to \mathrm{O}\)
- Cannot fit because premise requires working on BOTH sites
- Would need: "Any plumber working on both D and S must work on O"
Critical Insight
Only Requirement 2 can be expressed in the simple "If X then Y" format without additional conditions or qualifiers.
Final Solution
Answer:
- Column 1: restaurant
- Column 2: office building
Verification: "Any plumber working on the restaurant must also work on the office building" accurately reexpresses Requirement 2.
Key Exam Strategy
When asked to reexpress requirements:
- First convert all requirements to logical notation
- Identify which can fit the requested format without modification
- Requirements with OR conditions, NOT conditions, or AND conditions in the premise typically cannot be simplified to basic "If X then Y" statements