Use our PTCB Math Quiz to practice your pharmacy math skills.

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Question 1 |

**How is 34 written in roman numerals?**

XXXIIII | |

XXLIV | |

XXXIL | |

XXXIV |

Question 1 Explanation:

In the Roman numeral system: C = 100, L = 50, X = 10, V = 5, I = 1. The ones, tens, and hundreds must be treated as separate items.

It is not correct to use four identical symbols to represent a number. So a 4 would not be written as IIII, but instead IV, where it is treated as the difference of the two values: IV = 5 − 1 = 4.

30 = XXX and 4 = IV, so:

34 = XXXIV

It is not correct to use four identical symbols to represent a number. So a 4 would not be written as IIII, but instead IV, where it is treated as the difference of the two values: IV = 5 − 1 = 4.

30 = XXX and 4 = IV, so:

34 = XXXIV

Question 2 |

**Convert this roman numeral to a number: LII**

52 | |

12 | |

102 | |

110 |

Question 2 Explanation:

Recall that C = 100, L = 50, X = 10, V = 5, and I = 1.

L = 50 and II = 2, so:

LII = 52

L = 50 and II = 2, so:

LII = 52

Question 3 |

**A 30 mL dose of nighttime cough suppressant contains 12.5 mg of doxylamine succinate. How many milligrams of doxylamine succinate are in the entire 354 mL bottle?**

240 | |

128.32 | |

375 | |

147.5 |

Question 3 Explanation:

To solve this type of problem you should setup a proportion:

$\dfrac{x}{354 mL} = \dfrac{12.5 mg}{30 mL}$

Then you can cross multiply:

$30(x) = (12.5)(354)$

$30x = 4,425$

Divide both sides by $30$ to solve for $x$:

$x = 147.5$

$\dfrac{x}{354 mL} = \dfrac{12.5 mg}{30 mL}$

Then you can cross multiply:

$30(x) = (12.5)(354)$

$30x = 4,425$

Divide both sides by $30$ to solve for $x$:

$x = 147.5$

Question 4 |

**The pharmacy technician can reconstitute a 100 mL bottle of Amoxycillin in 50 seconds. How many of these bottles can the technician reconstitute in 30 minutes?**

32 | |

36 | |

34 | |

38 |

Question 4 Explanation:

This is another proportion problem. Note that times are given in both seconds and minutes. You need to choose one or the other. We will use seconds, so the first step is to convert 30 minutes to seconds.

There are 60 seconds in a minute:

$30 × 60 = 1800$

Then setup the proportion:

$\dfrac{1~bottle}{50~sec} = \dfrac{x}{1800~sec}$

Then you can cross multiply:

$50(x) = (1)(1800)$

$50x = 1800$

$x = 36$

There are 60 seconds in a minute:

$30 × 60 = 1800$

Then setup the proportion:

$\dfrac{1~bottle}{50~sec} = \dfrac{x}{1800~sec}$

Then you can cross multiply:

$50(x) = (1)(1800)$

$50x = 1800$

$x = 36$

Question 5 |

**The pharmacy recieves a controlled substance order from their wholesaler. There are a total of 435 pills. Of this total, 17% are C2, 19% are C3, 20% are C4, and 44% are C5. How many C3 pills were in the order?**

74 | |

87 | |

19 | |

83 |

Question 5 Explanation:

There are 435 pills, and 19% are C3. To find the number of C3 pills, multiply to total by 0.19:

$435 × 0.19 = 82.65$

This can be rounded to 83.

$435 × 0.19 = 82.65$

This can be rounded to 83.

Question 6 |

**Of all the prescriptions received at the pharmacy last Tuesday, 892 were refills. The remainder were new prescriptions, with 168 from patient drop-offs, 183 coming in electronically, and 69 coming in by phone. What percentage of the total prescriptions received were new drop-offs?**

14% | |

52.5% | |

12.8% | |

16.8% |

Question 6 Explanation:

First calculate the total prescriptions received:

$892 + 168 + 183 + 69 = 1,312$

Then take the number of new drop-off prescriptions (168) and divide it by the total number:

$168 ÷ 1,312 = 0.128$

To convert a decimal to a percentage, multiply by 100:

$0.128 × 100 = 12.8\%$

$892 + 168 + 183 + 69 = 1,312$

Then take the number of new drop-off prescriptions (168) and divide it by the total number:

$168 ÷ 1,312 = 0.128$

To convert a decimal to a percentage, multiply by 100:

$0.128 × 100 = 12.8\%$

Question 7 |

**A patient comes to the pharmacy counter with a prescription for Amoxicillin 250mg/5mL and the directions indicate 1¼ tsp po bid x 10d. What is the total quantity needed for dispensing?**

125 mL | |

150 mL | |

187.5 mL | |

200 mL |

Question 7 Explanation:

Recall that 1 teaspoon equals 5 mL. So 1¼ teaspoons equals 6.25 mL. Since it is twice a day (bid) for 10 days you must calculate:

$6.25 × 2 × 10 = 125 mL$

$6.25 × 2 × 10 = 125 mL$

Question 8 |

**What volume of a drug for injection 100mg/45mL should be used for 250mg?**

45 mL | |

100 mL | |

112.5 mL | |

250 mL |

Question 8 Explanation:

First calculate how many milligrams are in 1 milliliter:

$100 ÷ 45 = 0.45$

Since 250 mg is needed, multiply:

$0.45 × 250 = 112.5$

$100 ÷ 45 = 0.45$

Since 250 mg is needed, multiply:

$0.45 × 250 = 112.5$

Question 9 |

**The pharmacist is preparing 200 mL of a famotidine suspension containing 75 mg/5 mL. How many 20 mg tablets of famotidine will be needed?**

3,000 | |

40 | |

150 | |

400 |

Question 10 |

**You need 800 mL of 10% dextrose solution. How much of your 50% and 5% dextrose solution will you need to mix?**

Mix 89 mL of the 50% and 711 mL of the 5%. | |

Mix 122 mL of the 50% and 678 mL of the 5%. | |

Mix 111 mL of the 50% and 889 mL of the 5%. | |

Mix 100 mL of the 50% and 700 mL of the 5%. |

Question 10 Explanation:

This is an alligation problem, so you should setjup a tic-tac-toe table. The highest concentration goes in the upper left corner and the lowest concentration in the lower left corner.
The desired concentration goes in the middle:

Subtract diagonally across the middle, making sure you subtract the smaller number from the larger number. Add the word 'parts' next to the result:

Now the number of parts needed for each concentration is lined up across the table:

So you need 5 parts of the 50% and 40 parts of the 5%, for a total of 45 parts.

Amount of 50% needed will be: $\dfrac{5}{45} × 800 = 89$

Amount of 5% needed will be $\dfrac{40}{45} × 800 = 711$

Subtract diagonally across the middle, making sure you subtract the smaller number from the larger number. Add the word 'parts' next to the result:

Now the number of parts needed for each concentration is lined up across the table:

So you need 5 parts of the 50% and 40 parts of the 5%, for a total of 45 parts.

Amount of 50% needed will be: $\dfrac{5}{45} × 800 = 89$

Amount of 5% needed will be $\dfrac{40}{45} × 800 = 711$

Question 11 |

**How is 59 written in roman numerals?**

CIX | |

LVIII | |

LIX | |

ILX |

Question 12 |

**Convert this roman numeral to a number: CXXVI**

76 | |

116 | |

91 | |

126 |

Question 13 |

**Which of the following quantities will fill a 16 ounce container the most without causing any overflow?**

600 mL | |

465 mL | |

485 mL | |

400 mL |

Question 13 Explanation:

Recall that 1 oz = 30 mL. So 16 oz = 480 mL. Of these answers choices 485 mL is the closest to 480 mL, but that would cause overflow. The next lowest answer is correct, 465 mL.

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