PTCB math practice questions

20 pharmacy math questions, each with a worked answer: conversions, weight-based doses, percent and ratio strength, dilutions, alligation and IV flow rates.

On the PTCB exam, calculations are part of Order Entry and Processing, which is 22.5% of the exam under PTCB’s PTCE Content Outline (in effect since January 6, 2026).

Pick an answer to check it. The answer and explanation are under each question.

1. Question 1

   A patient weighs 176 lbs. What is their weight in kilograms?

   1. A40 kg
   2. B58 kg
   3. C88 kg
   4. D80 kg
   Show answer and explanation

   Answer: D. 80 kg

   80 kg. To convert pounds to kilograms, divide by 2.2 (176 ÷ 2.2 = 80 kg).

   From the Pharmacy Calculations flashcards.

2. Question 2

   A physician orders amoxicillin 40 mg/kg/day in 3 divided doses for a child weighing 22 lbs. What is the dose per administration?

   1. A166.7 mg per dose
   2. B133.3 mg per dose
   3. C146.7 mg per dose
   4. D100.0 mg per dose
   Show answer and explanation

   Answer: B. 133.3 mg per dose

   133.3 mg per dose. Convert 22 lbs to 10 kg, multiply by 40 mg = 400 mg/day, then divide by 3 doses = 133.3 mg.

   From the Pharmacy Calculations flashcards.

3. Question 3

   A prescription reads: 'Give 1 tsp of amoxicillin 250 mg/5 mL three times daily for 10 days.' How many milliliters are needed to fill the entire course?

   1. A200 mL
   2. B300 mL
   3. C150 mL
   4. D100 mL
   Show answer and explanation

   Answer: C. 150 mL

   150 mL. One tsp = 5 mL × 3 doses/day × 10 days = 150 mL.

   From the Pharmacy Calculations flashcards.

4. Question 4

   A drug is available as 500 mg/tablet. The prescribed dose is 1.5 g. How many tablets should be dispensed per dose?

   1. A3 tablets
   2. B2 tablets
   3. C6 tablets
   4. D4 tablets
   Show answer and explanation

   Answer: A. 3 tablets

   3 tablets. Convert 1.5 g to 1500 mg, then divide by 500 mg/tablet = 3 tablets.

   From the Pharmacy Calculations flashcards.

5. Question 5

   A physician orders 0.25 mg of digoxin. The available concentration is 0.5 mg/2 mL. How many mL should be administered?

   1. A4 mL
   2. B3 mL
   3. C1 mL
   4. D2 mL
   Show answer and explanation

   Answer: C. 1 mL

   1 mL. Using ratio-proportion: 0.5 mg/2 mL = 0.25 mg/X → X = 1 mL.

   From the Pharmacy Calculations flashcards.

6. Question 6

   A patient is prescribed ibuprofen 10 mg/kg. The patient weighs 66 lbs. What is the correct dose in mg?

   1. A660 mg
   2. B200 mg
   3. C300 mg
   4. D330 mg
   Show answer and explanation

   Answer: C. 300 mg

   300 mg. Convert 66 lbs to 30 kg (66 ÷ 2.2), then multiply 30 kg × 10 mg/kg = 300 mg.

   From the Pharmacy Calculations flashcards.

7. Question 7

   How many grams of dextrose are in 500 mL of D5W (5% dextrose in water)?

   1. A10 grams
   2. B15 grams
   3. C25 grams
   4. D50 grams
   Show answer and explanation

   Answer: C. 25 grams

   25 grams. A 5% w/v solution contains 5 g per 100 mL; 500 mL × 0.05 = 25 g.

   From the Pharmacy Calculations flashcards.

8. Question 8

   How many milligrams of NaCl are in 1 liter of 0.9% Normal Saline?

   1. A9000 mg
   2. B8100 mg
   3. C4500 mg
   4. D900 mg
   Show answer and explanation

   Answer: A. 9000 mg

   9000 mg (9 g). A 0.9% w/v solution contains 0.9 g per 100 mL × 1000 mL = 9 g = 9000 mg.

   From the Pharmacy Calculations flashcards.

9. Question 9

   A pharmacist needs to prepare 200 mL of a 2% solution from a 10% stock solution. What volume of stock solution is required?

   1. A20 mL
   2. B40 mL
   3. C50 mL
   4. D80 mL
   Show answer and explanation

   Answer: B. 40 mL

   40 mL. Using C1V1 = C2V2: 10% × V1 = 2% × 200 mL → V1 = 40 mL.

   From the Pharmacy Calculations flashcards.

10. Question 10

    How many grams of hydrocortisone are needed to prepare 60 g of a 2.5% hydrocortisone cream?

    1. A1.5 g
    2. B2.4 g
    3. C3.0 g
    4. D0.6 g
    Show answer and explanation

    Answer: A. 1.5 g

    1.5 g. 60 g × 0.025 = 1.5 g of hydrocortisone.

    From the Pharmacy Calculations flashcards.

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12. Question 11

    Express 1:200 as a percentage strength.

    1. A2.0 percent
    2. B5.0 percent
    3. C0.5 percent
    4. D0.2 percent
    Show answer and explanation

    Answer: C. 0.5 percent

    0.5%. Divide 1 by 200 and multiply by 100: (1/200) × 100 = 0.5%.

    From the Pharmacy Calculations flashcards.

13. Question 12

    A technician prepares 1 liter of a solution containing 40 mEq of potassium chloride. KCl has a molecular weight of 74.5 g/mol and is monovalent. How many grams of KCl were added?

    1. A5.96 g
    2. B1.49 g
    3. C3.72 g
    4. D2.98 g
    Show answer and explanation

    Answer: D. 2.98 g

    2.98 g. For a monovalent ion, mEq = mmol; 40 mmol × 74.5 mg/mmol = 2980 mg = 2.98 g.

    From the Pharmacy Calculations flashcards.

14. Question 13

    A physician orders 1000 mL of NS to infuse over 8 hours. What is the flow rate in mL/hr?

    1. A167 mL/hr
    2. B200 mL/hr
    3. C125 mL/hr
    4. D100 mL/hr
    Show answer and explanation

    Answer: C. 125 mL/hr

    125 mL/hr. 1000 mL ÷ 8 hours = 125 mL/hr.

    From the Pharmacy Calculations flashcards.

15. Question 14

    An IV is set to infuse at 50 mL/hr using tubing with a drop factor of 15 gtt/mL. What is the drip rate in gtt/min?

    1. A20.8 gtt/min
    2. B18.75 gtt/min
    3. C10.0 gtt/min
    4. D12.5 gtt/min
    Show answer and explanation

    Answer: D. 12.5 gtt/min

    12.5 gtt/min (≈ 13 gtt/min). (50 mL/hr × 15 gtt/mL) ÷ 60 min = 12.5 gtt/min.

    From the Pharmacy Calculations flashcards.

16. Question 15

    A patient is receiving dopamine at 5 mcg/kg/min. The patient weighs 70 kg. The dopamine bag contains 400 mg in 250 mL D5W. What is the infusion rate in mL/hr?

    1. A13.125 mL/hr
    2. B10.500 mL/hr
    3. C16.406 mL/hr
    4. D21.875 mL/hr
    Show answer and explanation

    Answer: A. 13.125 mL/hr

    13.125 mL/hr. Dose = 5 × 70 = 350 mcg/min = 21,000 mcg/hr = 21 mg/hr. Concentration = 400 mg/250 mL = 1.6 mg/mL. Rate = 21 ÷ 1.6 = 13.125 mL/hr.

    From the Pharmacy Calculations flashcards.

17. Question 16

    A heparin infusion is ordered at 1200 units/hr. The bag contains 25,000 units in 500 mL NS. What is the infusion rate in mL/hr?

    1. A48 mL/hr
    2. B30 mL/hr
    3. C20 mL/hr
    4. D24 mL/hr
    Show answer and explanation

    Answer: D. 24 mL/hr

    24 mL/hr. Concentration = 25,000 units/500 mL = 50 units/mL. Rate = 1200 units/hr ÷ 50 units/mL = 24 mL/hr.

    From the Pharmacy Calculations flashcards.

18. Question 17

    How much water must be added to 100 mL of a 70% alcohol solution to make a 40% solution?

    1. A30 mL of water
    2. B43 mL of water
    3. C75 mL of water
    4. D57 mL of water
    Show answer and explanation

    Answer: C. 75 mL of water

    75 mL of water. C1V1 = C2V2: 70% × 100 = 40% × V2 → V2 = 175 mL total; 175 − 100 = 75 mL water.

    From the Pharmacy Calculations flashcards.

19. Question 18

    Using the alligation method, how many mL of 20% dextrose and 5% dextrose are needed to prepare 1000 mL of 10% dextrose?

    1. A250.0 mL of 20% and 750.0 mL of 5%
    2. B400.0 mL of 20% and 600.0 mL of 5%
    3. C500.0 mL of 20% and 500.0 mL of 5%
    4. D333.3 mL of 20% and 666.7 mL of 5%
    Show answer and explanation

    Answer: D. 333.3 mL of 20% and 666.7 mL of 5%

    333.3 mL of 20% and 666.7 mL of 5%. Alligation gives 5 parts of 20% and 10 parts of 5% = 15 total parts. (5/15) × 1000 = 333.3 mL; (10/15) × 1000 = 666.7 mL.

    From the Pharmacy Calculations flashcards.

20. Question 19

    A prescription requires 1:10 dilution of a stock solution to be made into 60 mL total. How much stock solution is needed?

    1. A10 mL of stock solution
    2. B6 mL of stock solution
    3. C12 mL of stock solution
    4. D30 mL of stock solution
    Show answer and explanation

    Answer: B. 6 mL of stock solution

    6 mL of stock solution. A 1:10 dilution means 1 part concentrate in 10 parts total; 60 mL × (1/10) = 6 mL.

    From the Pharmacy Calculations flashcards.

21. Question 20

    A prescription has an AWP of $80.00. The insurance pays AWP minus 15% plus a $2.00 dispensing fee. What does the insurance reimburse?

    1. A$70.00 in total
    2. B$68.00 in total
    3. C$72.00 in total
    4. D$64.00 in total
    Show answer and explanation

    Answer: A. $70.00 in total

    $70.00. AWP − 15% = $80.00 − $12.00 = $68.00 + $2.00 dispensing fee = $70.00.

    From the Pharmacy Calculations flashcards.

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