# PTCB Practice Math Questions and Answers!

Jun 28th, 2020**PTCB Practice Test Question 1**

**You are required to make 140 grams of medicine with the following formula:**

**Ointment – 8 percent****Zinc oxide – 25 percent****Talc – 4 percent**

**How much talc is required to compound this medicine**?

**2,400mg****3,800mg****5,600mg****6,900mg**

To understand how to answer these kinds of PTCB practice math questions, we must comprehend a few fundamental points.

First, **always notice discrepancies with units**. In this case, we are told to compound 140 grams of medicine, but the answers are listed in milligrams. There are 1,000mg in each gram. This is important, and we will come back to it soon.

Second, students should always **identify the information they need to use** in a question. Many PTCB practice test questions will contain information or details that you do not need to use. Often, this is intentional – *to create distractions*. It also helps examiners fish out candidates who understand the nature of the question and how to find the answer.

We are told to create 140 grams of medicine and asked to find how much talc will be present in this medicine. 4 percent of the formulation is talc; therefore, we need to multiply 4% by 140 grams to establish how much talc is present.

- (4 / 100) x 140 grams =
**5.6 grams**

However, the answers are provided in milligrams – so we need to multiple 5.6 grams by 1,000:

- 5.6 grams x 1,000 = 5,600mg

**There is 5,600mg of talc in the 140 grams of compounded medicine.**

**PTCB Practice Test Question 2**

**If a solution contains a concentration of 120mg/5mL, how many milliliters should be prescribed to the patient if they require 4.5 grams of drug?**

It is important for pharmacy technicians to become comfortable with drug concentrations. You will come across many **PTCB practice math questions** that deal with these kinds of concentration problems.

Initially, it may seem an alien or even difficult language to speak. But by practicing as many PTCB questions as possible, you begin to become ever more fluent in this mathematical language.

Often, you will see terms such as:

**w/w**= weight per 100 grams**w/v**= weight per 100 milliliters**v/v**= volume per 100 milliliters

For example:

**5% w/v concentration**= 5 grams of drug per 100mL of solution

In this case, if we add 1 gram of sodium chloride and make the solution up to 100mL with sterile water, we have created a 1% sodium chloride w/v solution.

**2.5% v/v concentration**= 2.5 mL per 100mL of solution

For example: if you add 50mL of hydrochloric acid to 50mL of water, you have created a total of 100mL volume per volume (v/v) solution. Both are liquids. In this case, the concentration of hydrochloric acid is 50% v/v.

**8% w/w concentration**= 8 grams per 100 grams of medicine. In this case, it does not matter that it may be two liquids. What matters is the weight of the substances itself.

This question does not use these expressions, but it is important for pharmacy technicians to be both familiar and comfortable with them and how to interpret them in any given PTCB math question.

In the question above, we are given a concentration of **120mg/5mL**. In other words, if we have 100mL of the solution, every 5mL teaspoon of that solution will contain 120mg. If the 120mg is a drug, then the patient is receiving that much drug in each teaspoon.

Of course, we can innocently play around with the numbers, too.

- 120mg per 5mL is exactly the same as 24mg per 1mL. We are simply dividing both sides by 5 to determine how many milligrams of drug is in each mL.
- If there are 24mg in 1mL, then there must be 2,400mg in 100mL of solution. 2,400mg is the same as 2.4 grams. Therefore, we can re-write the concentration as
**2.4% w/v solution**.

So, understanding concentrations is important. The numbers are flexible if you know how to use them. It takes practice, but always try to sit down with a pen and paper and practice these kinds of conversions. In a matter of minutes – not hours – you will begin to see real progress.

The question asked us how many milliliters of medicine we need to prescribe to the patient if they require 4.5 grams of drug.

Remember our earlier rule – always identify inconsistent units. In this case, the concentration of drug is 120mg/5mL. However, the patient requires 4.5 grams of drug.

- 4.5 grams is the same as
**4,500mg**(always multiply by 1,000).

So, the patient requires 4,500mg and the concentration of the solution is 120mg/5mL. As we already learned, each 5mL of solution contains 120mg.

Therefore, if we divide 4,500mg by 120mg, we can establish how many doses the patient needs:

- 4,500mg / 120mg =
**37.5 doses**required - 37.5 doses x 5mL = 187.5mL of solution must be dispensed.

In other words, every 5mL of the 187.5mL contains 120mg of drug.

In total, there are **4,500mg of drug within the 187.5mL of medicine**.

**PTCB Practice Test Question 3**

**What is the percentage strength of a 180-gram cream that contains 4,000mg of active ingredient?**

In this case, we are asked to find percentage strength. Percentage strength simply refers to concentrations such as 4% or 5%.

A 4% percentage strength means there are 4 grams of drug in 100 grams of product.

In this case, we have 4,000mg of drug in 180 grams of cream product.

First, we must fix units – as always.

- 4,000mg = 4 grams

Now, we can establish the percentage strength:

- (4 grams / 180 grams) x 100% =
**2.2% percentage strength**

**PTCB Practice Test Question 4**

**Convert 0.8% to a ratio strength.**

A ratio strength looks like 1:250 or 2:5.

In other words:

- 2:5 means
**2 parts of one drug for every 5 parts of another drug**. There are 7 parts in total. If we have 700mL of solution, for example, 2:5 means 200mL of one drug and 500mL of the second drug.

In the question, we are asked to convert 0.8% to a ratio strength.

First, we need to recognize that 0.8% is the same as 0.8 out of 100.

- 0.8% = 0.8 out of 100
- Therefore, if we divide 100 by 0.8, it gives us 125.
- Conclusion: 0.8% is the same as the ratio strength
**1:125**

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