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# PTCB Math – Clark’s Rule and Young’s Rule!

Jun 21st, 2020

### PTCB Math Practice

It is estimated that 6-10 questions on math appear on the PTCB exam.

Math is often one of the most challenging topics for students. Unlike other parts of the test which can be memorized, math is something that needs to be worked out – step-by-step – until you have figured out the correct answer.

Most PTCB students fear the math part of the exam – and for good reason, too.

At PTCB Test Prep, we recommend students not to “memorize” a method, but to understand what is happening with each question. The more you understand, the easier it becomes to work things out. It also gives you the opportunity to identify any potential errors in your methods.

But this takes practice – lots of it.

### Clark’s Rule and Young’s Rule

Here, we review PTCB math questions that concern Clark’s rule and Young’s rule.

The math is straightforward. You simply need to learn the formulae and apply it correctly. That is what we focus on here and, at the end of this guide, we have put together some assessment questions for you to practice.

It is not enough just to read math and hope that you have that topic covered. Instead, you need to apply and practice each method.

Both Clark’s rule and Young’s rule are used to determine pediatric doses (aged 2-17 years) based on the average adult dose. Children do not have the same extent of drug metabolism as adults. Lower doses are needed for children who are also smaller and weigh less than adults.

Clark’s rule and Young’s rule are used to correct for this and to ensure children receive a safe dose to treat their condition.

### Clark’s Rule

The formula for Clark’s rule is as follows:

Adult dose x [weight of child (lbs) / 150 ] = Child’s dose

In words – we must multiply the standard adult dose by the child’s weight in pounds (lbs) divided by 150.

It is important to remember that the child’s weight must be in pounds. The question may offer the weight in kilograms, in which case you must convert kilograms to pounds (to convert kg to lbs, we multiply by 2.2).

Here is a sample question:

#### Q. Using Clark’s rule, what is the dose for a 12-year old girl who weighs 31.7kg if the average adult dose is 500mg?

In this case, we simply plug the values into the equation – but first, we must convert 31.7 kilograms to pounds.

31.7kg x 2.2 = 70 pounds (lbs)

Now, we can complete the equation:

• Child’s dose = 500mg x (70lbs / 150)
• Child’s dose = 500mg x (0.47)
• Child’s dose = 235mg

Let’s take a look at one more sample question using Clark’s rule:

Q. The average adult dose for a drug is 250mg. Using Clark’s rule, what dose should be given to an 8-year old child who weighs 57lbs?

This time, we are given pounds and so do not need to perform any conversions.

Now, we can complete the equation:

• Child’s dose = 250mg x (57lbs / 150)
• Child’s dose = 250mg x (0.38)
• Child’s dose = 95mg

And that is how we use Clark’s rule. The method is simple – you merely need to remember the equation and the need, if necessary, to perform any conversions.

### Young’s Rule

Young’s rule also gets tested on the PTCB exam.

The difference between the two rules is that Clark’s rule uses weight as the basis of the calculation whereas Young’s rule uses age. This is easy to remember, too – as “Young” refers to age itself.

The formula for Young’s rule is:

Child’s dose = Adult Dose x [Age / (Age + 12)]

Let’s now put this equation into practice.

Q. The pediatric dose for a 9-year old child who weighs 63lbs needs to be determined. You learn that the adult dose for the same drug is 200mg. Using Young’s rule, what dose should the child be given?

We can now plug these values into the equation:

• Child’s dose = 200mg x [9 / (9 + 12)]
• Child’s dose = 200mg x [9 / 21]
• Child’s dose = 200mg x 0.43
• Child’s dose = 86mg

One important factor to remember is – do not use information in a question just because it is in the question. In this case, the weight of the child is given. But when asked to use Young’s rule, the child’s weight is not needed. You may also fall into the trap of using Clark’s rule instead.

You must avoid both temptations and stick to the facts at hand.

One more recommendation is to avoid performing multiple steps at once. In the answer above, note how we only perform 1 step – even if it seems easy or obvious. In a pressurized exam setting, it becomes easy to overlook important details. And in math, these details matter. It is far better to be careful and work through each step – one at a time – to prevent any avoidable and needless errors.

### Self-Assessment PTCB Questions

Now that we have covered both Clark’s rule and Young’s rule, it’s time for you to put this theory into practice. Take a few moments to learn both equations as best you can.

Once you feel that both equations are firmly cemented to memory, take out a pen and paper, and begin to work on the following five PTCB practice test questions.

Answers to each question are provided at the end of this PTCB study guide.

Question 1

Write down the both equations for Young’s rule and Clark’s rule.

Question 2

Using Clark’s rule, what is the dose for a 11-year old boy who weighs 35.2kg if the average adult dose is 400mg?

Question 3

A 7-year old pediatric patient is admitted to hospital. You are tasked with determining what dose of the medicine he should be prescribed. If the adult dose is 100mg and the child weighs 40kg, what dose – using Young’s rule – should the child be administered?

Question 4

A 42-year old adult, weighing 164lbs, is administered 500mg of a drug. A patient called Sam, who is six times younger than the adult, also requires the same medicine. What dose should Sam be administered?

Question 5

A 10-year old boy needs to be prescribed an antibacterial drug. He weighs 32kg and stands at 1.4 meters tall. The adult dose for the same medicine is 75mg. The boy ends up being prescribed 35mg. Which formula – Clark’s rule or Young’s rule – was used to arrive at this specific dose?

### Conclusion

This completes our guide to Clark’s rule and Young’s rule.

There are six take-home messages to extract from this study guide:

• Memorizing the specific formula for both rules.
• Knowing that weight is used for Clark’s rule and age for Young’s rule.
• That both rules are used to calculate pediatric doses based on adult doses.
• Perform conversions where necessary – kilograms to pounds, for example.
• To reduce error, do not perform more than one math step at a time.
• Do not use information in a question just because it is present. It may be irrelevant to the question/answer and put there to distract you.

If you have worked through our sample PTCB practice test questions, here is the answer sheet for all five problems:

• Answer 1: See above for both equations.
• Answer 2: 206mg
• Answer 3: 37mg
• Answer 4: 184mg
• Answer 5: Clark’s rule was used to arrive at 35.25mg or rounded down to 35mg. Young’s rule arrives at the lower figure of 33.75mg.

Whilst we could offer explained answers, it would be far more edifying for the student to re-try any questions they happened to get wrong. Learning from mistakes is an important part of excelling at math.

If you would like access to hundreds more PTCB math questions, register to one of our three online courses today where you can receive instant access. In the meantime, check back to our blog soon for more great content to help you master the 2020 PTCB exam.

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### Elaine Walker

Elaine joined PTCB Test Prep in 2017, currently serving as the lead product development manager overseeing both course development and quality improvement. Mrs. Walker is a graduate of California State University and has worked as a pharmacy technician for over twenty years – with particular interests in pediatric pharmacy, extemporaneous compounding, and hospital pharmacy. Over the past 8-years, she has helped prepare thousands of students for the PTCB examination.