The table below presents 2025 operational performance and cost metrics for eight regional commercial biofuel production facilities: | Facility Name | Feedstock Type | Annual Output (Million L) | Operating Cost (/L) | Carbon Intensity Reduction (%) | Capacity Utilization Rate (%) | |---|---|---|---|-

The table below presents 2025 operational performance and cost metrics for eight regional … — GMAT

The table below presents 2025 operational performance and cost metrics for eight regional commercial biofuel production facilities:

Facility Name	Feedstock Type	Annual Output (Million L)	Operating Cost ($/L)	Carbon Intensity Reduction (%)	Capacity Utilization Rate (%)
BioAlpha	Cellulosic	85	0.72	68%	88%
EcoEthanol	Corn Stover	120	0.55	45%	92%
GreenFuel X	Algae	40	1.10	82%	75%
PureBio	Used Cooking Oil	95	0.64	74%	95%
TerraFuel	Cellulosic	110	0.68	65%	82%
Vanguard Bio	Algae	60	0.98	85%	80%
SunFuel North	Corn Stover	150	0.50	42%	90%
NextGen Fuel	Used Cooking Oil	75	0.76	70%	85%

Based on the data provided, evaluate whether the following overall assertion is True or False:

"Exactly two of the three statements below are True:
- Statement 1: The median Annual Output among facilities with a Carbon Intensity Reduction of at least 70% is 67.5 Million Liters.
- Statement 2: For all facilities utilizing Cellulosic or Algae feedstock, the Operating Cost per Liter is strictly greater than $0.65.
- Statement 3: The facility with the highest Capacity Utilization Rate incurred a lower total annual operating cost (calculated as Annual Output × Operating Cost) than the facility with the lowest Capacity Utilization Rate."

Cevap: Cevap

Cevap

True. Statements 1 and 2 are True, while Statement 3 is False, meaning exactly two of the three statements are True.

Evaluating the individual statements reveals that Statement 1 is True (the median of {40, 60, 75, 95} is 67.5), Statement 2 is True (operating costs for Cellulosic and Algae facilities are

0.72,

1.10,

0.68, and

0.98, all greater than

0.65), and Statement 3 is False (PureBio's total cost of

60.8 Million exceeds GreenFuel X's total cost of $44.0 Million). Since exactly two statements are True, the overall compound assertion is True.

Adım Adım Çözüm

Evaluate Statement 1: Identify facilities with Carbon Intensity Reduction ≥ 70% and calculate their median Annual Output.

Facilities satisfying the condition are GreenFuel X (82%), PureBio (74%), Vanguard Bio (85%), and NextGen Fuel (70%). Their outputs are 40, 95, 60, and 75 Million Liters, respectively. Ordering these values: 40, 60, 75, 95. The median of an even set of four numbers is

(60 + 75) / 2 = 67.5

Million Liters. Thus, Statement 1 is True.

Correctly filtering by the conditional threshold (70%) and sorting the output values is required to calculate the median of an even dataset.

Evaluate Statement 2: Filter for facilities using Cellulosic or Algae feedstock and compare their Operating Costs to $0.65.

Facilities matching Cellulosic or Algae feedstock are BioAlpha (

0.72), GreenFuel X (

1.10), TerraFuel (

0.68), and Vanguard Bio (

0.98). Every single one of these operating costs is strictly greater than $0.65. Thus, Statement 2 is True.

A universal condition ('for all') requires checking every matching row to ensure no counterexample exists.

Evaluate Statement 3: Identify facilities with the highest and lowest Capacity Utilization Rates, compute their total annual operating costs, and compare.

Highest Capacity Utilization Rate: PureBio (95%). Total annual operating cost =

95 \text{ Million L} \times \$0.64/\text{L} = \$60.8 \text{ Million}

. Lowest Capacity Utilization Rate: GreenFuel X (75%). Total annual operating cost =

40 \text{ Million L} \times \$1.10/\text{L} = \$44.0 \text{ Million}

. Since

\$60.8 \text{ Million} > \$44.0 \text{ Million}

, the highest utilization facility did NOT incur a lower cost. Thus, Statement 3 is False.

Row-level product calculations must be performed accurately for both extreme values before evaluating the inequality.

Synthesize the truth values of the three statements to evaluate the overall assertion.

Statement 1 = True, Statement 2 = True, Statement 3 = False. Total number of True statements = 2. Therefore, the assertion 'Exactly two of the three statements below are True' is True.

The top-level boolean logic requires assessing whether the count of True individual statements equals 2.

Anahtar Kavram

Multi-Statement Boolean Evaluation

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