The table below presents operational data for seven regional flight routes operated by an airline during Q1 2026:
| Route Code | Distance (miles) | Flights Scheduled | On-Time Arrival Rate | Average Passenger Load Factor | Fuel Consumption (gallons/flight) |
|---|---|---|---|---|---|
| R-101 | 450 | 120 | 88% | 82% | 1,400 |
| R-102 | 820 | 90 | 75% | 86% | 2,300 |
| R-103 | 1,250 | 60 | 92% | 78% | 3,600 |
| R-104 | 310 | 150 | 84% | 74% | 1,100 |
| R-105 | 960 | 80 | 80% | 90% | 2,850 |
| R-106 | 1,500 | 45 | 94% | 85% | 4,200 |
| R-107 | 680 | 110 | 85% | 88% | 1,950 |
Match each of the following statements to its corresponding truth value and evaluation justification based on the table.
- Statement I: For all routes with a distance greater than 800 miles, the median On-Time Arrival Rate is greater than 85%.Evaluates to True because the median On-Time Arrival Rate for the four qualifying routes (75%, 80%, 92%, 94%) is 86%.
- Statement II: The route with the highest Average Passenger Load Factor also has the fewest total number of scheduled flights.Evaluates to False because the route with the highest load factor (R-105 with 90%) scheduled 80 flights, whereas R-106 scheduled the fewest (45 flights).
- Statement III: The ratio of Fuel Consumption per flight to Distance is strictly decreasing as Route Distance increases across all seven routes.Evaluates to False because the fuel-to-distance ratio increases from R-102 (approximately 2.80 gallons per mile) to R-105 (approximately 2.97 gallons per mile).
Answer
Statement I matches with the evaluation of True (median rate is 86%). Statement II matches with the evaluation of False (R-105 has 80 flights while minimum is 45). Statement III matches with the evaluation of False (the ratio increases from R-102 to R-105).
Each statement is evaluated against the quantitative data provided in the table. Statement I correctly identifies the four routes exceeding 800 miles and calculates their median as 86%. Statement II correctly identifies that R-105 has the highest load factor (90%) but 80 flights, whereas R-106 has the minimum flights (45). Statement III correctly identifies a counterexample where the fuel-to-distance ratio increases from R-102 to R-105.
Step-by-Step Solution
Key Concept
Multi-statement boolean verification requiring subset filtering, descriptive statistics (median of even-sized set), cross-column extrema matching, and rate trend testing.