Francois and Pierre each owe Claudine money. Today, Francois will make a payment equal to 50% of the amount he...
GMAT Two Part Analysis : (TPA) Questions
Francois and Pierre each owe Claudine money. Today, Francois will make a payment equal to \(50\%\) of the amount he owes Claudine, and Pierre will make a payment equal to \(10\%\) of the amount he owes Claudine. Together, the two payments will be equal to \(40\%\) of the combined amount that Francois and Pierre owe Claudine.
Select for Francois and Pierre amounts that Francois and Pierre could owe Claudine that are jointly consistent with the given information. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Visualization
Let's use a simple table to track the debts and payments:
| Person | Amount Owed | Payment Rate | Payment Made |
| Francois | \(\mathrm{F}\) | 50% | \(0.50\mathrm{F}\) |
| Pierre | \(\mathrm{P}\) | 10% | \(0.10\mathrm{P}\) |
| Total | \(\mathrm{F} + \mathrm{P}\) | - | \(0.50\mathrm{F} + 0.10\mathrm{P}\) |
Key relationship: Combined payment = 40% of combined debt
Phase 2: Understanding the Question
Breaking Down the Complex Statement
The problem tells us:
- "Together, the two payments will be equal to 40% of the combined amount that Francois and Pierre owe Claudine"
Translating to an equation:
\(0.50\mathrm{F} + 0.10\mathrm{P} = 0.40(\mathrm{F} + \mathrm{P})\)
Key Insight
We need to find the mathematical relationship between \(\mathrm{F}\) and \(\mathrm{P}\), then identify which answer choices satisfy this relationship.
Phase 3: Finding the Answer
Solving for the Relationship
Starting with our equation:
\(0.50\mathrm{F} + 0.10\mathrm{P} = 0.40(\mathrm{F} + \mathrm{P})\)
Expanding the right side:
\(0.50\mathrm{F} + 0.10\mathrm{P} = 0.40\mathrm{F} + 0.40\mathrm{P}\)
Rearranging terms:
\(0.50\mathrm{F} - 0.40\mathrm{F} = 0.40\mathrm{P} - 0.10\mathrm{P}\)
\(0.10\mathrm{F} = 0.30\mathrm{P}\)
Simplifying:
\(\mathrm{F} = 3\mathrm{P}\)
Key finding: Francois owes exactly 3 times what Pierre owes.
Checking Answer Choices
Choices: €50, €250, €750, €3,750, €6,750
We need pairs where \(\mathrm{F} = 3\mathrm{P}\):
If Pierre owes €250:
- Then Francois owes: €250 × 3 = €750 ✓ (This is in our choices!)
Stop here - we found our answer.
Verification
Let's confirm this works:
- Francois's payment: 50% × €750 = €375
- Pierre's payment: 10% × €250 = €25
- Total payment: €375 + €25 = €400
- Combined debt: €750 + €250 = €1,000
- 40% of combined debt: 40% × €1,000 = €400 ✓
Phase 4: Solution
Final Answer:
- Francois: €750
- Pierre: €250
These values satisfy our requirement that Francois owes 3 times what Pierre owes, and their partial payments together equal 40% of their combined debt.