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PTCB Math Practice
PTCB Test Prep

**Pharmacy calculations are one of the toughest parts of the PTCB exam. PTCB concentration calculations can alone be challenging enough. After all, it can be difficult to conceptualize what is going on.**

Here, we break concentration calculations down to the most fundamental level – reviewing three different kinds of question that could appear on the day of your PTCB exam.

We learn how to **understand what these questions are asking**, how you can solve these problems in multiple formats, and – most importantly of all – understanding what is going on. You should not enter the PTCB exam unless you understand the math concepts. **Memorizing formulae is not enough**.

Examiners often include answers that reflect the most common kinds of mistake. Unless you understand these PTCB practice questions in detail, you may get caught out – and that’s not a risk worth taking.

Let’s get started then – with one of the most common kinds of concentration calculation asked on the PTCB test.

**Note: before reviewing each explained answer, try to attempt each of these questions yourself first!**

**How many milligrams of magnesium acetate is needed to prepare 400mL of a 0.05% w/v solution?**

The question asks us to find a quantity of magnesium acetate to add to 400mL of solution. The end concentration of this solution must be 0.05% w/v.

First, note that 0.05% w/v = 0.05 grams per 100mL of solution.

It is always important to ensure that units are consistent. Therefore, we must convert 0.05 grams to milligrams – which is 50 milligrams.

In other words, there must be 50mg *in each 100mL* of the final 400mL solution.

If there is 50mg in 100mL, then the target 400mL must contain 200mg of magnesium acetate.

Another way to solve this PTCB pharmacy calculation problem is to use the following formula at the lower end of this graphic:

**How many mL of a 1:200 w/v stock solution is used to make 3L of a 1:3000 w/v solution?**

To solve this question, the best approach is to convert ratios to percentage form:

- 1:200 = (1/200) x 100 =
**0.5% w/v** - 1:3000 = (1/3000) x 100 =
**0.033% w/v**

The target volume is 3-liters, which is the same as **3,000mL** (remember: the question is asking us to find the value in milliliters).

Now that we have three of four variables resolved, we can plug these values into the following equation (where C refers to concentration and V refers to volume).

**C1 x V1 = C2 x V2**

0.033% x 3,000mL = 0.5% x V2

0.033% x 3,000mL / 0.5% = V2

99 / 0.5% = V2

V2 = 198mL

Therefore, when we add 198mL of a 1:200w/v stock solution to 3-liters, it produces a final concentration of 1:3,000 w/v solution.

**When 200mL of a 1:400v/v solution is diluted to 800mL, what is the ratio strength v/v?**

This question asks us to find the ratio strength (in volume/volume) when 200mL of a 1:400v/v solution is diluted to 800mL. This is one of the more difficult kinds of PTCB concentration calculations but let’s review it step-by-step, so you can learn exactly what is going on.

First, as always, the starting point must be to convert the ratio into a percentage. It makes life much easier.

- (1/400) x 100 = 0.25%

As above, we now have three variables to plug into the concentration-volume equation, namely:

- Initial 200mL volume (
**V1**) - Initial concentration of 0.25% (
**C1**) - Final volume of 800mL (
**V2**)

Therefore, we must find **C2**.

**C1 x V1 = C2 x V2**

0.25% x 200mL = C2 x 800mL

(0.25% x 200mL) / 800mL = C2

C2 = **0.0625%**

However, recall that the question asked us to find the ratio strength in v/v. Therefore, we must convert this percentage to a ratio.

Note that all percentages are, by definition, over 100. The same is true of 0.0625%, which is the same as 0.0625 / 100.

0.0625/100 is an inconvenient number, therefore, to create a more convenient fraction, we should multiply both the numerator and denominator by 100.

(0.0625 / 100) x 100 = 6.25/10,000

Now, we must reduce this fraction to its **simplest form** to give us the optimum ratio. We achieve this by dividing both the numerator and denominator by 6.25:

(6.25/10,000) / 6.25 = 1/1,600

- 6.25 divides
**neatly**into 6.25 to give us 1 (the ideal ratio format).

- 10,000 / 6.25 gives us 1,600.

Therefore, the final ratio concentration in its most reduced form is **1:1,600v/v**.

**That concludes our review of PTCB concentration calculations. We hope you found this guide useful. Be sure to check back to our PTCB Test Prep blog soon for more exclusive content to help you master the pharmacy technician exam.**

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