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Difficulty: MediumQuantitative Data Reconciliation Across Sources

Tab 1: Biopharmaceutical Batch Processing Log
- Initial Harvest Volume: 2,000 Liters2,000\text{ Liters}
- Active Pharmaceutical Ingredient (API) Concentration: 50 mg/mL50\text{ mg/mL}
- Purification Loss: 15%15\% of initial liquid volume lost during filtration

Tab 2: Encapsulation & Quality Inspection Audit
- Total Capsules Manufactured: 400,000 units400,000\text{ units}
- API Dosage per Unit: 200 mg200\text{ mg}
- Inspection Rejection Rate: 5%5\% of manufactured units destroyed due to quality variance

Based on the information provided in Tab 1 and Tab 2, evaluate the following statement as True or False:

*Statement: The total mass of API contained in all accepted (non-rejected) manufactured capsules represents exactly 76%76\% of the total API present in the initial raw harvest batch.*

Answer: Answer

Answer

True. The total mass of API contained in the accepted capsules (76 kg) is exactly 76% of the initial raw harvest API mass (100 kg).
The evaluation of True is correct because the initial API mass from Tab 1 (2,000,000 mL×50 mg/mL=100 kg2,000,000\text{ mL} \times 50\text{ mg/mL} = 100\text{ kg}) when reconciled with the net accepted capsule output from Tab 2 (400,000×0.95×200 mg=76 kg400,000 \times 0.95 \times 200\text{ mg} = 76\text{ kg}) confirms a precise ratio of 76 kg100 kg=76%\frac{76\text{ kg}}{100\text{ kg}} = 76\%.

Step-by-Step Solution

1
Calculate the total initial API mass harvested prior to purification using Tab 1.
Initial Volume =2,000 L=2,000,000 mL= 2,000\text{ L} = 2,000,000\text{ mL}. Initial API Mass =2,000,000 mL×50 mg/mL=100,000,000 mg=100 kg= 2,000,000\text{ mL} \times 50\text{ mg/mL} = 100,000,000\text{ mg} = 100\text{ kg}.
Establishing the baseline quantity of active compound from the source data.
2
Calculate the number of accepted capsules following quality inspection using Tab 2.
Accepted Capsules =400,000×(1−0.05)=380,000 units= 400,000 \times (1 - 0.05) = 380,000\text{ units}.
Accounting for the packaging quality rejection loss to isolate usable units.
3
Calculate the total API mass contained in accepted capsules.
Accepted API Mass =380,000 units×200 mg/unit=76,000,000 mg=76 kg= 380,000\text{ units} \times 200\text{ mg/unit} = 76,000,000\text{ mg} = 76\text{ kg}.
Determining the net yield of active constituent delivered in final accepted products.
4
Reconcile the accepted API mass against the initial harvest baseline.
Percentage =76 kg100 kg×100%=76%= \frac{76\text{ kg}}{100\text{ kg}} \times 100\% = 76\%.
Comparing final output to initial input across tabs to verify the target statement.

Key Concept

Quantitative Data Reconciliation Across Sources
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Topics

Quantitative Data Reconciliation Across Sources

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