PTCB Practice Question Walkthrough: Calculations

Mastering Pharmacy Calculations for the PTCB Exam

Pharmacy calculations are among the most feared topics on the PTCB exam, but they are entirely manageable with practice and the right approach. This walkthrough demonstrates step-by-step solutions to common calculation types you will encounter on the 90-question certification exam.

Question 1: Day Supply Calculation

A prescription reads: Amoxicillin 250 mg/5 mL suspension, 150 mL, take 5 mL by mouth three times daily. What is the day supply?

Solution:

• Daily usage: 5 mL x 3 times = 15 mL per day
• Day supply: 150 mL / 15 mL per day = 10 days

Explanation: Day supply calculations divide the total quantity dispensed by the daily usage amount. This is one of the most common calculation types on the PTCB exam and is also essential for insurance billing, as incorrect day supply can cause claim rejections.

Question 2: Dosage Based on Weight

A physician orders amoxicillin 25 mg/kg/day divided into 3 doses for a child weighing 44 pounds. What is the dose per administration?

Solution:

• Convert weight: 44 lbs / 2.2 = 20 kg
• Total daily dose: 25 mg/kg x 20 kg = 500 mg per day
• Dose per administration: 500 mg / 3 = 166.7 mg per dose (approximately 167 mg)

Explanation: Weight-based dosing requires converting pounds to kilograms (divide by 2.2), then multiplying by the mg/kg dose. Always check whether the dose is per day or per administration, and whether it needs to be divided. This is a critical distinction on the PTCB exam.

Question 3: Concentration and Dilution

How many milliliters of a 70% isopropyl alcohol solution are needed to prepare 500 mL of a 30% solution?

Solution:

• Use the dilution equation: C1 x V1 = C2 x V2
• 70% x V1 = 30% x 500 mL
• V1 = (30 x 500) / 70
• V1 = 15000 / 70 = 214.3 mL

Explanation: The dilution equation (C1V1 = C2V2) is one of the most important formulas for the PTCB exam. It works for any concentration dilution problem. You would take 214.3 mL of the 70% solution and add enough water (about 285.7 mL) to reach a final volume of 500 mL.

Question 4: Percentage Strength

How many grams of hydrocortisone powder are needed to prepare 120 g of a 2.5% hydrocortisone cream?

Solution:

• Percentage strength: 2.5% = 2.5 g per 100 g
• Amount needed: (2.5 / 100) x 120 g = 3 g

Explanation: Percentage w/w (weight-in-weight) means grams of active ingredient per 100 grams of total preparation. This is a straightforward proportion calculation. For a 2.5% cream, there are 2.5 grams of drug in every 100 grams. Scale up proportionally for 120 grams.

Calculation Tips for Exam Day

• Write it down: Always set up the problem on your scratch paper before calculating
• Label units: Write out the units at every step to avoid conversion errors
• Check reasonableness: Does your answer make sense? A 10,000 mg dose for a child should raise a flag.
• Practice daily: Do at least 5 calculation problems every day during your study period
• Know your conversions: 1 kg = 2.2 lbs, 1 tsp = 5 mL, 1 tbsp = 15 mL, 1 oz = 30 mL, 1 grain = 65 mg

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