Question

Difficulty: MediumResolving Paradoxes and Discrepancies

In 2025, a nationwide logistics firm installed AI-driven route optimization software across its entire delivery fleet to reduce fuel consumption per trip. Over the following year, fuel prices remained completely stable, and the average fuel consumed per delivery dropped by 15 percent. Paradoxically, the firm's total annual fuel expenditure for the fleet increased by more than 10 percent over the same period.

Which of the following, if true, most helps to resolve the apparent discrepancy described above?

  1. The efficiency gained from the software enabled the firm to secure new commercial accounts and complete 40 percent more total deliveries during the year than in the previous year.Answer
  2. B
    The software licensing fees and ongoing IT maintenance expenses exceeded the total financial savings achieved from the reduced fuel consumption per delivery.
  3. C
    The route optimization system frequently rerouted delivery trucks along longer highway bypasses, causing vehicles to cover more miles per delivery.
  4. D
    Drivers operating in rural territories were significantly less likely to follow the software's turn-by-turn recommendations than drivers operating in dense metropolitan zones.
  5. E
    The logistics firm retired several older, fuel-inefficient delivery vans halfway through the year and replaced them with high-efficiency hybrid models.

Answer

The apparent discrepancy is resolved by the option explaining that the efficiency gained enabled the firm to complete 40 percent more total deliveries, increasing total fuel consumption despite lower fuel usage per trip.
The correct answer resolves the discrepancy by introducing a third variable: total delivery volume. Total fuel expenditure equals fuel per trip multiplied by total trips. If the fuel per delivery drops by 15 percent but the total number of deliveries increases by 40 percent, overall fuel consumption and expenditure will increase despite the improved per-trip efficiency.

Step-by-Step Solution

1
Identify the two paradox premises.
Premise 1: Average fuel used per delivery decreased by 15%. Premise 2: Total annual fuel expenditure for the fleet increased by over 10% (with stable fuel prices).
Resolving a paradox requires finding a missing factor that allows both premises to be true simultaneously.
2
Analyze the mathematical relationship between rate and total volume.
Total Fuel Used = (Fuel Consumed per Delivery) × (Total Number of Deliveries).
If fuel per delivery falls, total fuel can only rise if the total number of deliveries increases significantly.
3
Evaluate the options for a factor that expands total volume sufficiently.
A 40% increase in total deliveries accounts for a higher total fuel consumption even when each delivery uses 15% less fuel.
This accounts for both facts without contradicting either premise.

Key Concept

Rate versus Total Volume Discrepancy
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