Easy NAPLEX Alligation Practice Questions

Concept Explanation

NAPLEX alligation is a mathematical method used to determine the relative amounts of two or more substances of different concentrations needed to prepare a mixture of a desired final concentration. This technique, often referred to as the "alligation grid" or "alligation alternate," simplifies complex pharmacy pharmaceutical calculations by organizing concentrations in a visual layout that subtracts values diagonally to find parts of each ingredient.

To use alligation, you place the higher concentration at the top left, the lower concentration at the bottom left, and the desired concentration in the center. By subtracting the center value from each corner value diagonally, you obtain the "parts" of each ingredient required. For more advanced practice, you can use the AI Question Generator to refine your skills. This method is foundational in compounding, similar to understanding percentage strength or dilution principles.

Solved Examples

1. Problem: How many mL of 50% dextrose and 10% dextrose are needed to prepare 500 mL of 20% dextrose?
   Solution:
   • Place 50% (high) and 10% (low) on the left.
   • Place 20% (desired) in the center.
   • Subtract diagonally: $|20 - 10| = 10$ parts of 50%; $|50 - 20| = 30$ parts of 10%.
   • Total parts: $10 + 30 = 40$ parts.
   • Parts of 50%: $\frac{10}{40} \times 500 \text{ mL} = 125 \text{ mL}$.
   • Parts of 10%: $\frac{30}{40} \times 500 \text{ mL} = 375 \text{ mL}$.
2. Problem: You need to mix 2% ointment and 10% ointment to make 100g of 5% ointment. How much of each is needed?
   Solution:
   • Grid: 10% (top), 2% (bottom), 5% (center).
   • Subtract: $|5 - 2| = 3$ parts of 10%; $|10 - 5| = 5$ parts of 2%.
   • Total parts: $3 + 5 = 8$ parts.
   • 10% ointment: $\frac{3}{8} \times 100 \text{ g} = 37.5 \text{ g}$.
   • 2% ointment: $\frac{5}{8} \times 100 \text{ g} = 62.5 \text{ g}$.
3. Problem: Mix 70% alcohol and 30% alcohol to make 1 liter of 40% alcohol. How much 70% alcohol is required?
   Solution:
   • Grid: 70% (top), 30% (bottom), 40% (center).
   • Subtract: $|40 - 30| = 10$ parts of 70%; $|70 - 40| = 30$ parts of 30%.
   • Total parts: $10 + 30 = 40$ parts.
   • 70% alcohol: $\frac{10}{40} \times 1000 \text{ mL} = 250 \text{ mL}$.

Practice Questions

1. You are asked to prepare 200 mL of a 15% solution using 25% and 10% stock solutions. How many mL of the 25% solution are required?

2. A pharmacist needs to prepare 500g of 3% hydrocortisone cream using 5% and 1% creams. How many grams of 1% cream should be used?

3. How many mL of 80% alcohol and 20% alcohol are needed to prepare 600 mL of 50% alcohol?

4. How many grams of 40% zinc oxide ointment and 10% zinc oxide ointment are needed to make 150g of 20% ointment?

5. A pharmacy technician needs to prepare 1 liter of 20% solution from 50% and 5% stock solutions. How many mL of the 5% solution are required?

6. To prepare 100g of 10% coal tar ointment using 20% and 5% products, how many grams of the 20% product are needed?

7. You have 95% alcohol and 30% alcohol. How many mL of each are required to make 500 mL of 70% alcohol?

8. How many mL of 10% NaCl and 0.9% NaCl are needed to produce 250 mL of 3% NaCl?

Answers & Explanations

1. 66.67 mL: Parts 25% = $15 - 10 = 5$; Parts 10% = $25 - 15 = 10$. Total = 15. $\frac{5}{15} \times 200 = 66.67$.
2. 250g: Parts 5% = $3 - 1 = 2$; Parts 1% = $5 - 3 = 2$. Total = 4. $\frac{2}{4} \times 500 = 250$.
3. 300 mL 80%, 300 mL 20%: Parts 80% = $50 - 20 = 30$; Parts 20% = $80 - 50 = 30$. Equal parts.
4. 50g of 40%, 100g of 10%: Parts 40% = $20 - 10 = 10$; Parts 10% = $40 - 20 = 20$. Total = 30. $\frac{10}{30} \times 150 = 50$.
5. 666.67 mL: Parts 50% = $20 - 5 = 15$; Parts 5% = $50 - 20 = 30$. Total = 45. $\frac{30}{45} \times 1000 = 666.67$.
6. 33.33g: Parts 20% = $10 - 5 = 5$; Parts 5% = $20 - 10 = 10$. Total = 15. $\frac{5}{15} \times 100 = 33.33$.
7. 307.69 mL 95%, 192.31 mL 30%: Parts 95% = $70 - 30 = 40$; Parts 30% = $95 - 70 = 25$. Total = 65. $\frac{40}{65} \times 500 = 307.69$.
8. 53.76 mL 10%, 196.24 mL 0.9%: Parts 10% = $3 - 0.9 = 2.1$; Parts 0.9% = $10 - 3 = 7$. Total = 9.1. $(\frac{2.1}{9.1}) \times 250 = 53.76$.

Quick Quiz

Frequently Asked Questions

Can alligation be used for more than two ingredients?

Yes, alligation can be extended to three or more ingredients, though it requires specific grouping or algebraic methods to solve for the parts of each.

What are the units for alligation?

The units for the concentrations must be the same (e.g., all percentages or all ratios). The final units for volume or weight will match the units you use for the total quantity.

Why is the alligation grid preferred over algebra?

The grid is a visual tool that reduces the likelihood of setup errors, allowing for a quick, standardized approach to solving mixture problems.

Does the order of ingredients on the left side matter?

It does not matter which ingredient is on top as long as you perform the subtraction diagonally to reach the corresponding part value. Typically, placing the higher concentration on top is standard practice.

Is alligation applicable to IV solutions?

Yes, it is commonly used to calculate volumes of different dextrose or saline concentrations needed for parenteral nutrition or specific IV fluids.

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