Question

Difficulty: HardRatio, Proportion, and Percent Calculations

The table below presents energy and cost metrics for six commercial data center facilities operated by a cloud computing provider in fiscal year 2025.

FacilityIT Load Capacity (MW)Renewable Energy Used (GWh)Total Energy Consumption (GWh)Operational Cost ($M)
Alpha4018024036.0
Beta6531239054.6
Gamma2510016022.4
Delta8036048072.0
Epsilon5022530042.0
Zeta9048654075.6

Statement: If the operational cost of facility Beta increases by 15% in 2026 while its IT load capacity remains unchanged, its 2026 operational cost per megawatt (MW) of IT load capacity will exceed the 2025 operational cost per megawatt of facility Alpha by more than 8%.

Answer: Answer

Answer

The statement is False because facility Beta's 2026 operational cost per MW (0.966M/MW)exceedsfacilityAlphas2025operationalcostperMW(0.966M/MW) exceeds facility Alpha's 2025 operational cost per MW ( 0.900M/MW) by approximately 7.33%, which is less than 8%.
The correct evaluation is False. Facility Alpha's unit operational cost is 0.900MperMW(0.900M per MW ( 36.0M / 40 MW). Facility Beta's unit cost in 2025 is 0.840MperMW(0.840M per MW ( 54.6M / 65 MW). A 15% increase brings Beta's 2026 unit cost to 0.966MperMW.ComparingBetas2026rate(0.966M per MW. Comparing Beta's 2026 rate ( 0.966M) to Alpha's 2025 rate (0.900M)givesarelativeincreaseof(0.900M) gives a relative increase of ( 0.966 - 0.900)/0.900) / 0.900 = 7.33%, which does not exceed 8%.

Step-by-Step Solution

1
Calculate facility Alpha's 2025 operational cost per MW of IT load capacity.
Facility Alpha cost per MW = 36.0M/40MW=36.0M / 40 MW = 0.900M per MW.
Establishes the base value against which the 2026 rate will be compared.
2
Calculate facility Beta's 2025 operational cost per MW and its updated 2026 rate after a 15% increase.
Facility Beta 2025 rate = 54.6M/65MW=54.6M / 65 MW = 0.840M per MW. Facility Beta 2026 rate = 0.840M×1.15=0.840M × 1.15 = 0.966M per MW.
Applies the 15% growth rate to Beta's cost per unit capacity.
3
Compute the percentage change (excess) of facility Beta's 2026 rate relative to facility Alpha's 2025 rate.
Percentage excess = (0.966M0.966M - 0.900M) / $0.900M = 0.066 / 0.900 = 7.33%.
Evaluates whether the percentage difference exceeds the 8% threshold requested in the statement.

Key Concept

Unit Rate Calculations and Percentage Change Base Selection
Rate this question