Comprehensive pharmacy review: Pharmaceutical Calculations

Question 1

Directions for questions 1–30: Each question, statement,
or incomplete statement in this section can be correctly
answered or completed by one of the suggested answers or
phrases. Choose the best answer.
1. If a vitamin solution contains 0.5 mg of fl uoride ion in
each milliliter, then how many milligrams of fl uoride ion
would be provided by a dropper that delivers 0.6 mL?
(A) 0.30 mg
(B) 0.10 mg
(C) 1.00 mg
(D) 0.83 mg

Answer 1

(A) 0.30 mg

Question 2

2. How many chloramphenicol capsules, each containing
   250 mg, are needed to provide 25 mg/kg/d for 7 days
   for a person weighing 200 lb?
   (A) 90 capsules
   (B) 64 capsules
   (C) 13 capsules
   (D) 25 capsules

Answer 2

(B) 64 capsules

Question 3

3. If 3.17 kg of a drug is used to make 50000 tablets, how
   many milligrams will 30 tablets contain?
   (A) 1.9 mg
   (B) 1900 mg
   (C) 0.0019 mg
   (D) 3.2 mg

Answer 3

(B) 1900 mg

Question 4

4. A capsule contains ⅛ gr of ephedrine sulfate, ¼ gr of
   theophylline, and ¹⁄16 gr of phenobarbital. What is the
   total mass of the active ingredients in milligrams?
   (A) 20 mg
   (B) 8 mg
   (C) 28 mg
   (D) 4 mg

Answer 4

(C) 28 mg

Question 5

5. If 1 fluid ounce of a cough syrup contains 10 gr of
   sodium citrate, how many milligrams are contained in
   10 mL?
   (A) 650 mg
   (B) 65 mg
   (C) 217 mg
   (D) 20 mg

Answer 5

(C) 217 mg

Question 6

6. How many capsules, each containing ¼ gr of
   phenobarbital, can be manufactured if a bottle
   containing 2 avoirdupois ounces of phenobarbital is
   available?
   (A) 771 capsules
   (B) 350 capsules
   (C) 3500 capsules
   (D) 1250 capsules

Answer 6

(C) 3500 capsules

Question 7

7. Using the formula for calamine lotion, determine the
   amount of calamine (in grams) necessary to prepare 240 mL of lotion.
   calamine 80 g
   zinc oxide 80 g
   glycerin 20 mL
   bentonite magma 250 mL
   calcium hydroxide sufficient quantity to
   topical solution make 1000 mL
   (A) 19.2 g
   (B) 140.0 g
   (C) 100.0 g
   (D) 24.0 g

Answer 7

(A) 19.2 g

Question 8

8. From the following formula, calculate the amount of white wax required to make 1 lb of cold cream.
   Determine the mass in grams.

cetyl esters wax 12.5 parts
white wax 12.0 parts
mineral oil 56.0 parts
sodium borate 0.5 parts
purified water 19.0 parts
(A) 56.75 g
(B) 254.24 g
(C) 54.48 g
(D) 86.26 g

Answer 8

The answer is C [see II; III.A].
Th e formula tells the pharmacist that white wax (W.W.)
represents 12 parts out of the total 100 parts in the prescription.
What we wish to determine is the mass of
white wax required to prepare 454 g (1 lb) of the recipe.

Question 9

9. How many grams of aspirin should be used to prepare 1.255 kg of the powder?

Aspirin 6 parts
phenacetin 3 parts
caffeine 1 part

(A) 125 g
(B) 750 g
(C) 175 g
(D) 360 g

Answer 9

(B) 750 g

Question 10

10. A solution contains 1.25 mg of a drug per milliliter. At what rate should the solution be infused (drops per minute) if the drug is to be administered at a rate of 80 mg/hr? (1 mL = 30 drops)
    (A) 64.00 drops/min
    (B) 1.06 drops/min
    (C) 32.00 drops/min
    (D) 20.00 drops/min

Answer 10

(C) 32.00 drops/min

Question 11

11. Th e recommended maintenance dose of aminophylline for children is 1.0 mg/kg/hr by injection. If 10 mL of a 25-mg/mL solution of aminophylline is added to a 100-mL bottle of 5% dextrose, what should be the rate of delivery in mL/hr for a 40-lb child?
    (A) 2.30 mL/hr
    (B) 8.00 mL/hr
    (C) 18.90 mL/hr
    (D) 18.20 mL/hr

Answer 11

(B) 8.00 mL/hr

Question 12

12. For children, streptomycin is to be administered at a dose of 30 mg/kg of body weight daily in divided doses every 6 to 12 hrs. Th e dry powder is dissolved by adding water for injection, in an amount to yield the desired concentration as indicated in the following table (for a 1-g vial).
    Approximate
    Concentration (mg/mL) Volume (mL)
    200 4.2
    250 3.2
    400 1.8

Reconstituting at the lowest possible concentration, what volume (in mL) would be withdrawn to obtain a day’s dose for a 50-lb child?

(A) 3.40 mL
(B) 22.73 mL
(C) 2.50 mL
(D) 2.27 mL

Answer 12

(A) 3.40 mL

Question 13

13. The atropine sulfate is available only in the form of 1/150 gr tablets. How many atropine sulfate tablets would you use to compound the following prescription?

atropine sulfate 1/200 gr
codeine phosphate ¼ gr
aspirin 5 gr
d.t.d. #24 capsules
Sig: 1 capsule p.r.n.

(A) 3 tablets
(B) 6 tablets
(C) 12 tablets
(D) 18 tablets

Answer 13

(D) 18 tablets

Question 14

14. In 25.0 mL of a solution for injection, there are
    4.00 mg of the drug. If the dose to be administered
    to a patient is 200microgram, what quantity (in mL) of this solution should be used?

(A) 1.25 mL
(B) 125.00 mL
(C) 12.00 mL
(D) None of the above

Answer 14

14. The answer is A [see I.A.2; II].
    Dimensional analysis is oft en useful for calculating
    doses. Considering that 4 mg of the drug is present in
    each 25 mL of solution, we can easily calculate the number
    of milliliters to be used to give a dose of 0.200 mg
    (200 g). Always include units in your calculations.
    25ml/4mg x 0.200mg = 1.25ml

Question 15

15. How many milligrams of papaverine will the patient receive each day?

Rx papaverine hcl 1.0 g
aqua 30.0 mL
syrup tolu, q.s. a.d. 90.0 mL
Sig: 1 teaspoon t.i.d.

(A) 56.0 mg
(B) 5.6 mg
(C) 166.0 mg
(D) 2.5 mg

Answer 15

(C) 166.0 mg

Question 16

16. Considering the following formula, how many grams of sodium bromide should be used in fi lling this prescription?
    Rx sodium bromide 1.2 g
    syrup tolu 2.0 mL
    syrup wild cherry, q.s. a.d. 5.0 mL
    d.t.d. #24

(A) 1.2 g
(B) 1200.0 g
(C) 28.8 g
(D) 220.0 g

Answer 16

(C) 28.8 g

Question 17

17. How many milliliters of a 7.5% stock solution of
    KMnO4 should be used to obtain the KMnO needed?
    KMnO4, q.s.
    Distilled water, a.d. 1000 mL
    Sig: 2 teaspoons diluted to 500 mL yield a 1:5000
    solution

(A) 267.0 mL
(B) 133.0 mL
(C) 26.7 mL
(D) 13.3 mL

Answer 17

17. Th e answer is B [see V.A; VI].
    First, determine the mass of drug in the fi nal diluted
    solution.
    _ 5010 0p apratr ts
    x g
    _500 g ; x 0.1 g
    Now, if 0.1 g of drug is present in 500 mL of 1:5000
    solution, 2 teaspoons (10 mL) of the prescription contains
    the same amount of drug (0.1 g) before dilution.
    From this, the amount of drug in 1000 mL (the total
    volume) of the prescription can be determined:
    0.1 g
    _10 mL
    x g
    _1000 m L ; x 10 g

Finally, to obtain the correct amount of drug to formulate
the prescription (10 g), we are to use a 7.5%
stock solution. Recalling the defi nition of percentage
strength w/v
1070.5 m g L 10 g 133.3 mL or 133 mL

Question 18

18. Th e formula for Ringer’s solution follows. How much sodium chloride is needed to make 120 mL?

Rx sodium chloride 8.60 g
potassium chloride 0.30 g
calcium chloride 0.33 g
water for injection, q.s. a.d. 1000 mL

(A) 120.00 g
(B) 1.03 g
(C) 0.12 g
(D) 103.00 g

Answer 18

(B) 1.03 g

Question 19

19. How many grams of talc should be added to 1 lb of a powder containing 20 g of zinc undecylenate per 100 g to reduce the concentration of zinc undecylenate to 3%?

(A) 3026.7 g
(B) 2572.7 g
(C) 17.0 g
(D) 257.0 g

Answer 19

(B) 2572.7 g

Question 20

20. How many milliliters of a 0.9% aqueous solution can be made from 20.0 g of sodium chloride?

(A) 2222 mL
(B) 100 mL
(C) 222 mL
(D) 122 mL

Answer 20

(A) 2222 mL

Question 21

21. Th e blood of a reckless driver contains 0.1% alcohol. Express the concentration of alcohol in parts per million.

(A) 100 ppm
(B) 1000 ppm
(C) 1 ppm
(D) 250 ppm

Answer 21

(B) 1000 ppm

Question 22

22. Syrup is an 85% w/v solution of sucrose in water. It has a density of 1.313 g/mL. How many milliliters of water should be used to make 125 mL of syrup?
    (A) 106.25 mL
    (B) 164.10 mL
    (C) 57.90 mL
    (D) 25.00 mL

Answer 22

Th e answer is C [see I.A; V.A.1].
Using the density, the weight of 125 mL of syrup can
be calculated:
125 mL 1.313 g/mL 164.125 g
Using proportion and the sucrose concentration in
w/v, the weight of sucrose in 125 mL of syrup can be
calculated:
100 mL
_125 mL
85 g
_x g ; x 106.25 g
Finally, the weight of water in 125 mL of syrup can be
calculated:
164.125 g 106.25 g 57.875 g
which has a volume of 57.90 mL.

Question 23

23. How many grams of benzethonium chloride should be used in preparing 5 gal of a 0.025% w/v solution?

(A) 189.25 g
(B) 18.90 g
(C) 4.73 g
(D) 35.00 g

Answer 23

(C) 4.73 g

Question 24

24. How many grams of menthol should be used to prepare this prescription?
    Rx menthol 0.8%
    alcohol, q.s. a.d. 60.0 mL

(A) 0.48 g
(B) 0.80 g
(C) 4.80 g
(D) 1.48 g

Answer 24

(A) 0.48 g

Question 25

25. How many milliliters of a 1:1500 solution can be made by dissolving 4.8 g of cetylpyridinium chloride in water?

(A) 7200.0 mL
(B) 7.2 mL
(C) 48.0 mL
(D) 4.8 mL

Answer 25

(A) 7200.0 mL

The answer is A [see I; V].
The problem is easily solved by proportion. Th e question to be answered is if 1 g of drug is present in 1500 mL of a solution, what volume can be made with 4.8 g of drug?
1 g
_4.8 g
1500 mL
_x mL ; x 7200.0 mL
(the volume of 1 to 1500 solution that can be prepared
from 4.8 g of drug)

Question 26

26. The manufacturer specifies that one Domeboro tablet dissolved in 1 pint of water makes a modified Burow’s solution approximately equivalent to a 1:40 dilution. How many tablets should be used in preparing ½ gal of a 1:10 dilution?
    (A) 16 tablets
    (B) 189 tablets
    (C) 12 tablets
    (D) 45 tablets

Answer 26

(A) 16 tablets

Question 27

27. How many milliosmoles of calcium chloride
    (CaCl2∙2H2O mol wt 147) are represented in
    147 mL of a 10% w/v calcium chloride solution?

(A) 100 mOsmol
(B) 200 mOsmol
(C) 300 mOsmol
(D) 3 mOsmol

Answer 27

27. The answer is C [see VII.B].
    Recalling the expression for ideal osmolar concentration:
    mOsmol/L
    100 g/L
    _147 g/mo l 3 1000
    mOsmol/L 0.147 L
    300 mOsmol

Question 28

28. How many grams of boric acid should be used in compounding the following prescription?

Phenacaine HCl 1.0% (NaCl eq = 0.17)
Chlorobutanol 0.5% (NaCl eq = 0.18)
Boric acid, q.s. (NaCl eq = 0.52)
Purified H2O, a.d. 30 mL
Make isotonic solution
Sig: 1 drop in each eye

(A) 0.37 g
(B) 0.74 g
(C) 0.27 g
(D) 0.47 g

Answer 28

(A) 0.37 g

Question 29

29. A pharmacist prepares 1 gal of KCl solution by mixing 565 g of KCl (valence 1) in an appropriate vehicle. How many milliequivalents of K are in 15 mL of this solution? (atomic weights: K 39; Cl 35.5)

(A) 7.5 mEq
(B) 10.0 mEq
(C) 20.0 mEq
(D) 30.0 mEq
(E) 40.0 mEq

Answer 29

(D) 30.0 mEq

Question 30

30. A vancomycin solution containing 1000 mg of
    vancomycin hydrochloride diluted to 250 mL with
    D5W is to be infused at a constant rate with an
    infusion pump in 2 hrs. What is the rate of drug
    administration?

(A) 2.08 mg/min
(B) 8.33 mg/min
(C) 4.17 mg/min
(D) 16.70 mg/min
(E) 5.21 mg/min

Answer 30

(B) 8.33 mg/min