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Difficulty: HardMulti-Statement Boolean Evaluation

The table below details 2025 annual operational metrics for eight commercial container terminals at a regional maritime port hub:

TerminalAnnual Cargo Volume (Thousand TEUs)Automated Crane Ratio (%)Average Berth Dwell Time (Hours)On-Time Vessel Clearance Rate (%)
Terminal A1,25080%18.592%
Terminal B84065%24.085%
Terminal C2,10090%14.296%
Terminal D62040%31.074%
Terminal E1,60075%21.588%
Terminal F95050%26.881%
Terminal G1,85085%16.094%
Terminal H1,10060%22.486%

Based on the table, evaluate the following claim: Exactly two of the three statements below are True.

Statement I: When the terminals are sorted in descending order by Annual Cargo Volume, the median Average Berth Dwell Time for the top 4 terminals is less than 17.017.0 hours.
Statement II: For every terminal where the Automated Crane Ratio is at least 75%75\%, the On-Time Vessel Clearance Rate is greater than 87%87\%.
Statement III: The mean Annual Cargo Volume across all 8 terminals is greater than 1,3501,350 thousand TEUs.

Answer: Answer

Answer

False. Only Statement II is True (Statement I and Statement III are both False). Therefore, exactly one statement is True, making the overall claim False.
Evaluating each component statement reveals that Statement I is False (median is 17.2517.25 hours, which is not less than 17.017.0), Statement II is True (all four terminals with ≥75%\ge 75\% crane automation exceed 87%87\% clearance rate), and Statement III is False (mean cargo volume is 1,288.751,288.75, not greater than 1,3501,350). Because only one statement is True, the claim stating that exactly two statements are True is False.

Step-by-Step Solution

1
Evaluate Statement I by sorting terminals descending by Annual Cargo Volume and finding the median dwell time of the top 4.
Top 4 terminals by volume: Terminal C (2,1002,100), Terminal G (1,8501,850), Terminal E (1,6001,600), and Terminal A (1,2501,250). Their Average Berth Dwell Times are 14.214.2, 16.016.0, 21.521.5, and 18.518.5 hours, respectively. Ordered ascending, these values are 14.2,16.0,18.5,21.514.2, 16.0, 18.5, 21.5. The median is the average of the two middle values: 16.0+18.52=17.25\frac{16.0 + 18.5}{2} = 17.25 hours. Since 17.25>17.017.25 > 17.0, Statement I is False.
Correctly identifying the median of an even set requires ordering the values and taking the midpoint of the two central numbers.
2
Evaluate Statement II by checking the On-Time Vessel Clearance Rate for terminals with an Automated Crane Ratio ≥75%\ge 75\%.
Terminals with Automated Crane Ratio ≥75%\ge 75\% are Terminal A (80%80\%, Clearance 92%92\%), Terminal C (90%90\%, Clearance 96%96\%), Terminal E (75%75\%, Clearance 88%88\%), and Terminal G (85%85\%, Clearance 94%94\%). All four have Clearance Rates strictly greater than 87%87\%. Statement II is True.
Conditional filtering requires verifying every single row that satisfies the specified antecedent condition.
3
Evaluate Statement III by calculating the aggregate arithmetic mean of Annual Cargo Volume across all 8 terminals.
Sum of volume =1250+840+2100+620+1600+950+1850+1100=10,310= 1250 + 840 + 2100 + 620 + 1600 + 950 + 1850 + 1100 = 10,310 thousand TEUs. Mean =10,3108=1,288.75= \frac{10,310}{8} = 1,288.75 thousand TEUs. Since 1,288.75<1,3501,288.75 < 1,350, Statement III is False.
Computing aggregate mean requires dividing total cargo sum by total terminal count.
4
Synthesize the boolean values of the three statements to evaluate the claim.
Statement I = False, Statement II = True, Statement III = False. Exactly 1 statement is True. The claim asserts that exactly 2 statements are True, which is False.
Comparing the count of True statements to the claim's requirement determines the overall boolean result.

Key Concept

Multi-Statement Boolean Evaluation using tabular data sorting, conditional filtering, and descriptive statistics.
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Topics

Multi-Statement Boolean Evaluation

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