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Difficulty: Very hardResolving Paradoxes and Discrepancies

A major commercial airline implemented a fleet-wide routing and weight-optimization program that successfully reduced average fuel consumption per passenger-mile by 12 percent across its international operations over a two-year period. However, financial and operational audits revealed that during the exact same two-year period, the airline's total fuel expenditure for international flights increased by 18 percent, even though global jet fuel prices remained completely unchanged throughout this timeframe.

Which of the following statements, if true, help to resolve the apparent discrepancy described above? Select all that apply.

  1. The airline substantially expanded its international route offerings and increased total flight frequency, resulting in a 35 percent increase in total passenger-miles flown over the two-year period.Answer
  2. The airline replaced smaller jets on high-density routes with much larger aircraft that operated at full seating capacity, lowering fuel burn per passenger-mile while consuming significantly more total fuel per flight segment.Answer
  3. C
    Passenger demand for international routes declined sharply during the period, forcing the airline to fly many of its long-distance routes with less than half of their seats filled.
  4. D
    The airline's domestic division experienced a parallel 15 percent increase in total operational costs due to rising labor expenditures and airport landing fees.
  5. E
    Engineers predict that future iterations of fuel-efficient turbine engines will require higher upfront capital investment for maintenance overhaul cycles.

Answer

The discrepancy is resolved by statements showing that total flying volume increased substantially despite per-unit efficiency gains, or that aircraft size shifts improved per-passenger metrics while increasing aggregate fuel consumption.
The paradox centers on how per-unit efficiency (fuel per passenger-mile) improved while aggregate consumption (total fuel expenditure) increased under constant fuel prices. The first correct statement resolves this by showing a large increase in total volume (passenger-miles flown), which offsets the unit efficiency gain. The second correct statement resolves it by showing a shift to larger, fully-filled aircraft, which optimizes the per-passenger ratio while increasing total fuel burned per flight segment.

Step-by-Step Solution

1
Identify the two contradictory facts in the passage
Fact 1: Fuel consumption per passenger-mile decreased by 12%. Fact 2: Total international fuel expenditure increased by 18%, with fuel prices constant.
Resolving a paradox requires finding an explanation that allows both facts to be simultaneously true without denying either.
2
Analyze mathematical relationship between rate, total volume, and aggregate cost
Total Fuel Expenditure = (Fuel per Passenger-Mile) × (Total Passenger-Miles) × (Fuel Price per Gallon).
Since fuel price was constant and fuel per passenger-mile dropped, total fuel expenditure could only rise if Total Passenger-Miles increased by a percentage larger than the rate decrease.
3
Evaluate candidate resolution statements
An increase in total passenger-miles by 35% directly accounts for higher total fuel expenditure despite better per-mile efficiency. Similarly, deploying larger aircraft that run at full capacity improves the per-passenger metric while burning more total fuel in aggregate.
Both explanations reconcile the lower unit rate with higher total consumption without contradicting premise facts.

Key Concept

Rate vs. Aggregate Volume Discrepancy
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Topics

Resolving Paradoxes and Discrepancies

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