Health Education Systems Inc (HESI) A2 Exam Quiz: Ratio And Proportion
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Ratio And ProportionQuestion 1 of 20

A pharmacist has 1 liter of a 70% alcohol solution. She needs to create a 25% alcohol solution. How much distilled water must she add? (Round to the nearest milliliter).

286 mL
450 mL
1800 mL
2800 mL
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Health Education Systems Inc (HESI) A2 Exam Quiz

Health Education Systems Inc (HESI) A2 Exam Quiz: Ratio And Proportion

Practice Ratio And Proportion in Health Education Systems Inc (HESI) A2 Exam with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Ratio And Proportion, giving you a quick way to practice the rules, question types, and explanations that matter most for Health Education Systems Inc (HESI) A2 Exam.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A pharmacist has 1 liter of a 70% alcohol solution. She needs to create a 25% alcohol solution. How much distilled water must she add? (Round to the nearest milliliter).

  1. 286 mL
  2. 450 mL
  3. 1800 mL (correct answer)
  4. 2800 mL
Explanation: When you encounter mixture problems involving concentration changes, focus on the fact that the amount of pure substance (alcohol) remains constant while the total volume changes. Start by identifying what stays the same: you have 1000 mL of 70% alcohol solution, which contains 1000×0.70=7001000 \times 0.70 = 700 mL of pure alcohol. This 700 mL of alcohol won't change when you add water. Set up the equation using the final concentration. If you add xx mL of water, your total volume becomes (1000+x)(1000 + x) mL, but you still have 700 mL of pure alcohol. For a 25% solution: 7001000+x=0.25\frac{700}{1000 + x} = 0.25 Solve for xx: 700=0.25(1000+x)700 = 0.25(1000 + x), so 700=250+0.25x700 = 250 + 0.25x, which gives 450=0.25x450 = 0.25x, therefore x=1800x = 1800 mL. Choice A (286 mL) likely comes from incorrectly calculating the difference between concentrations (70% - 25% = 45%) and applying faulty proportion reasoning. Choice B (450 mL) represents a common algebraic error—this is actually the intermediate result 700−250700 - 250 from the equation above, not the final answer. Choice D (2800 mL) might result from setting up the proportion incorrectly or confusing the relationship between alcohol content and total volume. For HESI mixture problems, always identify what remains constant (the pure substance amount), set up your equation based on the final concentration requirement, and double-check by verifying that your answer produces the target percentage when substituted back into the original setup.

Question 2

A medical assistant needs to prepare 500 mL of a cleaning solution using a concentrate and water in a ratio of 1:4. This ratio represents 1 part concentrate to 4 parts water. How many milliliters of concentrate are required for the solution?

  1. 100 mL (correct answer)
  2. 125 mL
  3. 250 mL
  4. 400 mL
Explanation: When you encounter ratio problems in healthcare settings, you're working with proportional relationships that determine how to mix solutions safely and accurately. The key is understanding what the ratio tells you about the parts that make up the whole. A 1:4 ratio means for every 1 part concentrate, you need 4 parts water. This creates a total of 5 parts (1 + 4 = 5). To find how much concentrate you need for 500 mL total solution, set up the proportion: concentrate makes up 1 part out of 5 total parts. Calculate: 15×500 mL=100 mL\frac{1}{5} \times 500 \text{ mL} = 100 \text{ mL} of concentrate. You can verify this: if you use 100 mL concentrate, you'll need 400 mL water (4 times the concentrate amount), giving you exactly 500 mL total. Looking at the wrong answers: B) 125 mL likely comes from miscalculating the fraction as 1/4 instead of 1/5, forgetting that ratios describe parts of the whole. C) 250 mL represents exactly half the solution, which would be a 1:1 ratio, not 1:4. D) 400 mL is actually the amount of water needed, showing confusion between the two components. Study tip: Always convert ratios to fractions of the total first. For any ratio a:b, the first component equals aa+b\frac{a}{a+b} of the total volume. This systematic approach prevents mix-ups between components and ensures accurate solution preparation—critical for patient safety in healthcare settings.

Question 3

A patient is to receive 1 liter of IV fluid over 8 hours. The drop factor of the tubing is 15 gtt/mL. How many drops per minute (gtt/min) should be administered? (Round to the nearest whole number).

  1. 2 gtt/min
  2. 31 gtt/min (correct answer)
  3. 125 gtt/min
  4. 1875 gtt/min
Explanation: IV flow rate calculations are fundamental nursing skills that require converting between different units of time and volume. When you encounter these problems, you need to systematically work through the given information to find drops per minute. Start with what you know: 1 liter over 8 hours with a drop factor of 15 gtt/mL. First, convert the volume to milliliters: 1 liter = 1000 mL. Next, find the hourly rate: 1000 mL8 hours=125 mL/hour\frac{1000 \text{ mL}}{8 \text{ hours}} = 125 \text{ mL/hour} Now convert to minutes: 125 mL/hour60 minutes/hour=2.08 mL/min\frac{125 \text{ mL/hour}}{60 \text{ minutes/hour}} = 2.08 \text{ mL/min} Finally, apply the drop factor: 2.08 mL/min×15 gtt/mL=31.2 gtt/min2.08 \text{ mL/min} \times 15 \text{ gtt/mL} = 31.2 \text{ gtt/min} Rounded to the nearest whole number, this gives you 31 gtt/min, making B correct. Looking at the wrong answers: A (2 gtt/min) represents forgetting to multiply by the drop factor—you'd get this if you stopped at 2.08 mL/min. C (125 gtt/min) occurs when you calculate the hourly mL rate correctly but forget to convert from hours to minutes. D (1875 gtt/min) results from multiplying 125 mL/hour directly by 15 without any time conversion. Remember the formula: gtt/min=Total volume (mL)×Drop factorTotal time (minutes)\text{gtt/min} = \frac{\text{Total volume (mL)} \times \text{Drop factor}}{\text{Total time (minutes)}}. Always double-check your time conversions—mixing up hours and minutes is the most common error on HESI IV calculation questions.

Question 4

A dietary supplement powder contains protein, carbohydrates, and fat in a ratio of 5:8:2 by weight. If a single serving contains 12 grams of fat, what is the total weight of one serving in grams?

  1. 36 g
  2. 78 g
  3. 90 g (correct answer)
  4. 180 g
Explanation: When you encounter ratio problems on the HESI exam, you're working with proportional relationships where the parts relate to each other in fixed amounts. The key is using one known quantity to find the total. Given the ratio of protein:carbohydrates:fat is 5:8:2, this means for every 5 parts protein, there are 8 parts carbohydrates and 2 parts fat. Since one serving contains 12 grams of fat, you can find the value of each "part" in the ratio. If 2 parts = 12 grams of fat, then 1 part = 6 grams. Now you can calculate each component:
  • Protein: 5 parts × 6 grams = 30 grams
  • Carbohydrates: 8 parts × 6 grams = 48 grams
  • Fat: 2 parts × 6 grams = 12 grams (matches the given amount)
Total weight: 30 + 48 + 12 = 90 grams, which is answer C. Answer A (36 g) represents a common error where students might multiply the fat amount by the total number of ratio parts (12 × 3 = 36), forgetting that the ratio parts aren't equal to the actual parts. Answer B (78 g) could result from incorrectly calculating just the protein and carbohydrate portions without including fat. Answer D (180 g) might occur if you double the correct answer or miscalculate the part value. Remember: in ratio problems, always identify what one "part" equals using the given information, then scale up to find all components and the total.

Question 5

A medication is supplied as 4 mg per tablet. A physician orders a dose of 15 mcg/kg for a patient who weighs 176 lbs. How many tablets should the nurse administer? (1 kg = 2.2 lbs; 1 mg = 1000 mcg)

  1. 0.3 tablets (correct answer)
  2. 1.2 tablets
  3. 3.0 tablets
  4. 5.3 tablets
Explanation: Dosage calculations on the HESI require careful unit conversions and systematic problem-solving. When you encounter multi-step dosage problems, always identify what conversions are needed before calculating. First, convert the patient's weight from pounds to kilograms: 176 lbs÷2.2=80 kg176 \text{ lbs} ÷ 2.2 = 80 \text{ kg} Next, calculate the total dose needed: 15 mcg/kg×80 kg=1200 mcg15 \text{ mcg/kg} × 80 \text{ kg} = 1200 \text{ mcg} Convert this dose to milligrams since the tablets are supplied in mg: 1200 mcg÷1000=1.2 mg1200 \text{ mcg} ÷ 1000 = 1.2 \text{ mg} Finally, determine how many tablets to give: 1.2 mg÷4 mg per tablet=0.3 tablets1.2 \text{ mg} ÷ 4 \text{ mg per tablet} = 0.3 \text{ tablets} Answer A (0.3 tablets) is correct. Answer B (1.2 tablets) represents the total dose in milligrams, not the number of tablets. This occurs when you forget the final step of dividing by the tablet strength. Answer C (3.0 tablets) likely results from miscalculating the weight conversion or dose calculation, possibly using incorrect conversion factors. Answer D (5.3 tablets) suggests a significant computational error, possibly confusing unit conversions or using the wrong formula entirely. For HESI dosage calculations, always work systematically: convert weight to kg, calculate total dose, convert units to match what's available, then divide by tablet strength. Double-check each conversion factor and write out your work to avoid arithmetic errors.

Question 6

A new screening test for a disease is accurate 19 out of every 20 times. If 1,500 people are tested, what is the expected number of inaccurate results?

  1. 19
  2. 20
  3. 75 (correct answer)
  4. 1425
Explanation: When you encounter accuracy problems in healthcare statistics, you're working with proportions and need to identify what fraction represents the inaccurate results. The test is accurate 19 out of 20 times, which means it's inaccurate 1 out of 20 times. To find the expected number of inaccurate results from 1,500 tests, you calculate: 120×1,500=75\frac{1}{20} \times 1,500 = 75 inaccurate results. Let's examine why the other answers miss the mark. Answer A (19) incorrectly uses the numerator from the accuracy rate without considering the total number of people tested. Answer B (20) appears to use just the denominator from the fraction, ignoring both the inaccuracy rate and the sample size. Answer D (1,425) represents the number of accurate results (19/20 × 1,500), but the question specifically asks for inaccurate results. The key insight here is distinguishing between accuracy and inaccuracy rates. If something is accurate 19/20 times, it's inaccurate 1/20 times - these must sum to the whole. For HESI statistics problems, always identify what the question is actually asking for (accurate vs. inaccurate, sensitivity vs. specificity, etc.) before calculating. Convert accuracy statements into the rate you need, then multiply by your sample size. Watch for answer choices that give you the opposite of what's requested - this is a common trap in healthcare statistics questions.

Question 7

A pediatric patient weighs 44 lbs. A physician orders a medication to be administered at a dose of 15 mg/kg. The medication is supplied in a liquid form with a concentration of 50 mg per 5 mL. How many milliliters of the medication should the nurse administer? (Use the conversion factor 1 kg = 2.2 lbs)

  1. 0.83 mL
  2. 30 mL (correct answer)
  3. 66 mL
  4. 145.2 mL
Explanation: Pediatric dosage calculations require a systematic three-step approach: convert weight to the correct units, calculate the required dose, then determine the volume needed based on concentration. First, convert the patient's weight from pounds to kilograms: 44 lbs÷2.2 lbs/kg=20 kg44 \text{ lbs} \div 2.2 \text{ lbs/kg} = 20 \text{ kg} Next, calculate the required dose: 20 kg×15 mg/kg=300 mg20 \text{ kg} \times 15 \text{ mg/kg} = 300 \text{ mg} Finally, determine the volume needed using the concentration ratio. Since the medication contains 50 mg per 5 mL, set up a proportion: 50 mg5 mL=300 mgx mL\frac{50 \text{ mg}}{5 \text{ mL}} = \frac{300 \text{ mg}}{x \text{ mL}} Cross-multiply: 50x=150050x = 1500, so x=30 mLx = 30 \text{ mL} This confirms answer B is correct. Answer A (0.83 mL) likely results from incorrectly using the patient's weight in pounds (44) instead of converting to kilograms, then making calculation errors. Answer C (66 mL) might occur if you multiply the weight in kg by the dose but forget to account for the medication's concentration properly. Answer D (145.2 mL) probably comes from using the original weight in pounds without any conversion and applying the dose calculation incorrectly. Remember the acronym "WDV" for pediatric calculations: Weight conversion, Dose calculation, Volume determination. Always double-check your unit conversions first—this is where most errors occur. Converting pounds to kilograms by dividing by 2.2 is essential before any mg/kg calculation.

Question 8

A hospital cafeteria recipe for a soup base calls for 2 parts chicken stock to 5 parts vegetable broth. If the chef needs to make 35 liters of the soup base, how many more liters of vegetable broth are needed than chicken stock?

  1. 5 L
  2. 10 L
  3. 15 L (correct answer)
  4. 25 L
Explanation: This is a ratio problem that tests your ability to work with proportional relationships and find differences between quantities. When you see a recipe or mixture problem with ratios, your first step should be to determine the total parts and then calculate each component. The recipe calls for 2 parts chicken stock to 5 parts vegetable broth, giving us a total of 2+5=72 + 5 = 7 parts. With 35 liters needed total, each part equals 35÷7=535 ÷ 7 = 5 liters. Therefore:
  • Chicken stock needed: 2×5=102 × 5 = 10 liters
  • Vegetable broth needed: 5×5=255 × 5 = 25 liters
  • Difference: 25−10=1525 - 10 = 15 liters
The correct answer is C) 15 L. Looking at the wrong answers: A) 5 L represents the value of each individual part, not the difference between components. B) 10 L is the amount of chicken stock needed, but the question asks for how much more vegetable broth is needed. D) 25 L is the total amount of vegetable broth required, but again doesn't answer the "how much more" question. Study tip: In ratio problems, always identify what the question is actually asking for. Many students calculate the individual amounts correctly but then select the wrong component instead of the difference. Circle key words like "more," "difference," or "additional" to stay focused on the final calculation step.

Question 9

A study finds that for every 2 hours a nursing student studies, their score on a practice exam improves by 5 points. If a student wants to improve their score from 65 to 90, how many hours must they study?

  1. 5 hours
  2. 10 hours (correct answer)
  3. 13 hours
  4. 25 hours
Explanation: When you encounter a problem involving proportional relationships like this one, you need to identify the rate of change and use it to find the total amount needed to reach your goal. The study establishes a clear ratio: 2 hours of study = 5 points improvement. To find how much study time is needed for a 25-point improvement (from 65 to 90), you can set up a proportion: 2 hours5 points=x hours25 points\frac{2 \text{ hours}}{5 \text{ points}} = \frac{x \text{ hours}}{25 \text{ points}} Cross-multiplying: 2×25=5×x2 \times 25 = 5 \times x, so 50=5x50 = 5x, which gives you x=10x = 10 hours. Looking at the wrong answers: A) 5 hours would only provide a 12.5-point improvement (5 ÷ 2 × 5 = 12.5), leaving the student at a score of 77.5, well short of the 90-point goal. C) 13 hours represents a common error where students might add the current score (65) to something, but this doesn't follow the proportional relationship given. D) 25 hours would result in a 62.5-point improvement (25 ÷ 2 × 5 = 62.5), which is excessive and would push the score to 127.5. The correct answer is B) 10 hours, which provides exactly the 25-point improvement needed. For HESI math problems involving rates or proportions, always identify what's given, what you need to find, and set up your proportion carefully. Double-check by working backward: does 10 hours of study actually give you the improvement you calculated?

Question 10

A hospital unit has 36 patients. The required nurse-to-patient ratio is 1:4 during the day shift and 1:6 during the night shift. What is the total number of nurses needed to staff the unit for a full 24-hour period, covering one day shift and one night shift?

  1. 6
  2. 9
  3. 15 (correct answer)
  4. 16
Explanation: Staffing calculations are fundamental to nursing management and require you to carefully break down shift requirements and apply the correct ratios to patient census numbers. For this 36-patient unit, you need to calculate staffing for each shift separately, then add them together. During the day shift with a 1:4 ratio, each nurse can care for 4 patients. To find the number of nurses needed, divide the total patients by the ratio: 36÷4=936 ÷ 4 = 9 nurses for the day shift. For the night shift with a 1:6 ratio, each nurse can care for 6 patients: 36÷6=636 ÷ 6 = 6 nurses for the night shift. The total staffing requirement for 24 hours is 9+6=159 + 6 = 15 nurses. Choice A (6) represents only the night shift staffing requirement, missing the day shift entirely. Choice B (9) captures only the day shift needs but ignores night shift staffing. Choice D (16) likely comes from incorrectly adding an extra nurse to one of the shifts or miscalculating the ratios. The correct answer is C (15 nurses). When approaching nurse staffing calculations on the HESI, always identify each shift's requirements separately before combining them. Pay close attention to different ratios for different shifts—day shifts typically require more nurses due to higher acuity activities like admissions, procedures, and physician rounds. Practice breaking down multi-step problems like this into smaller, manageable calculations to avoid missing components of the total staffing picture.

Question 11

On a certain day, the ratio of patients admitted to the emergency room for trauma versus medical reasons was 3:5. If a total of 96 patients were admitted that day, how many of them were for medical reasons?

  1. 36
  2. 48
  3. 60 (correct answer)
  4. 72
Explanation: Ratio problems appear frequently on the HESI exam, especially in healthcare contexts where you need to analyze patient populations or medication dosages. When you see a ratio like 3:5, think of it as representing parts of a whole that you can scale up to match the actual total. The ratio 3:5 means that for every 3 trauma patients, there are 5 medical patients. This gives us 3 + 5 = 8 total parts. Since 96 patients were admitted total, each part represents 968=12\frac{96}{8} = 12 patients. Therefore, medical patients = 5 parts × 12 patients per part = 60 patients. Let's examine why the other answers are incorrect. Choice A (36) represents the number of trauma patients, not medical patients—this is the classic trap of solving for the wrong part of the ratio. Choice B (48) would be correct if you mistakenly thought the ratio was 2:5 instead of 3:5, giving you 4896=12\frac{48}{96} = \frac{1}{2} of patients. Choice D (72) results from incorrectly calculating 6 parts instead of 5 parts for medical patients, perhaps by adding the ratio numbers incorrectly. You can verify: trauma patients = 36, medical patients = 60, total = 96 ✓, and 3660=35\frac{36}{60} = \frac{3}{5} ✓. For HESI ratio problems, always identify what the question is asking for specifically, calculate the total parts in the ratio, then find the value of one part before scaling up to your target category.

Question 12

A nurse is monitoring a patient's fluid intake and output. In an 8-hour shift, the patient drank 8 oz of water, 6 oz of juice, and 4 oz of broth. The patient received 50 mL/hr of IV fluids for the entire shift. What was the patient's total intake in milliliters? (1 oz = 30 mL)

  1. 18 mL
  2. 540 mL
  3. 940 mL (correct answer)
  4. 1040 mL
Explanation: When you encounter fluid intake and output calculations on the HESI, you're being tested on your ability to accurately convert units and perform essential nursing math that directly impacts patient care and medication safety. To solve this problem, you need to calculate two components: oral intake and IV intake, then sum them. First, convert the oral fluids from ounces to milliliters using the given conversion factor. The patient consumed 8 oz water + 6 oz juice + 4 oz broth = 18 oz total oral intake. Converting: 18 oz×30 mL/oz=540 mL18 \text{ oz} \times 30 \text{ mL/oz} = 540 \text{ mL} Next, calculate the IV intake: 50 mL/hr×8 hours=400 mL50 \text{ mL/hr} \times 8 \text{ hours} = 400 \text{ mL} Total intake: 540 mL+400 mL=940 mL540 \text{ mL} + 400 \text{ mL} = 940 \text{ mL} Answer A (18 mL) represents only the oral intake in ounces without any unit conversion or IV fluids included. Answer B (540 mL) captures only the oral intake after proper conversion but completely omits the IV fluids. Answer D (1040 mL) suggests an error in IV calculation, possibly using 62.5 mL/hr instead of 50 mL/hr, or making an arithmetic mistake in the final addition. Study tip: Always break I&O calculations into clear steps: identify all fluid sources, convert units systematically, and double-check that you've included every component. Missing IV fluids or oral intake is a common error that can have serious clinical implications in practice.

Question 13

A stock solution of a disinfectant must be diluted for use. The ratio of stock solution to water should be 3:7. If a nurse prepares a total of 2 liters of the diluted solution, how many milliliters of the stock solution does she need? (1 L = 1000 mL)

  1. 300 mL
  2. 600 mL (correct answer)
  3. 700 mL
  4. 1400 mL
Explanation: When you encounter ratio problems in healthcare settings, you're often dealing with dilutions for medications or cleaning solutions. The key is understanding that ratios tell you the parts of each component relative to each other, not relative to the total. The ratio 3:7 means for every 3 parts stock solution, you need 7 parts water. This creates a total of 3 + 7 = 10 parts in the final mixture. To find how much stock solution you need from 2 liters total: First, convert to consistent units: 2 L = 2000 mL Next, determine what fraction of the mixture is stock solution: 310\frac{3}{10} of the total Calculate the stock solution needed: 310×2000 mL=600 mL\frac{3}{10} \times 2000 \text{ mL} = 600 \text{ mL} Looking at the wrong answers: A) 300 mL incorrectly uses only the numerator (3) without considering the proper fraction of the total. C) 700 mL mistakenly calculates the water portion (7/10 × 2000 mL) instead of the stock solution. D) 1400 mL represents 7/10 of the total, which is also the water amount, showing confusion about which component was asked for. The correct answer is B) 600 mL. Study tip: For ratio problems, always add the ratio parts to find the total parts, then use fractions to find each component. Double-check by ensuring your stock solution plus water equals the total volume requested.

Question 14

A pharmacist is reconstituting a powdered drug. The instructions state to add 18.2 mL of sterile water to a vial to yield a final concentration of 250 mg per 5 mL. If a doctor orders a 350 mg dose, how many milliliters should be drawn into the syringe?

  1. 1.4 mL
  2. 7.0 mL (correct answer)
  3. 13.0 mL
  4. 25.5 mL
Explanation: This question tests your ability to work with drug concentration calculations, a critical skill in healthcare. When you see reconstitution problems, focus on understanding the final concentration after mixing, then use proportional reasoning to find the required volume. After adding 18.2 mL of sterile water, the final concentration is 250 mg per 5 mL. To find how many milliliters contain 350 mg, set up a proportion: 250 mg5 mL=350 mgx mL\frac{250 \text{ mg}}{5 \text{ mL}} = \frac{350 \text{ mg}}{x \text{ mL}} Cross-multiply: 250x=350×5=1750250x = 350 \times 5 = 1750 Solve for x: x=1750250=7.0 mLx = \frac{1750}{250} = 7.0 \text{ mL} This confirms answer B is correct. Looking at the incorrect options: A) 1.4 mL represents a calculation error where someone might have divided 350 by 250 directly, ignoring the 5 mL component of the concentration. C) 13.0 mL could result from incorrectly setting up the proportion as 5250=x350\frac{5}{250} = \frac{x}{350}, which reverses the relationship. D) 25.5 mL might come from confusing the reconstitution volume (18.2 mL) with the final dosing calculation, possibly adding unnecessary steps. For HESI drug calculation questions, always identify what concentration you're working with after reconstitution, set up your proportion carefully with matching units, and double-check that your answer makes logical sense. A dose larger than the reference amount should require proportionally more volume.

Question 15

A bottle of antiseptic contains 237 mL of solution. The ratio of active ingredient to inert ingredients is 1:15. How many milliliters of active ingredient are in the bottle, rounded to the nearest tenth?

  1. 14.8 mL (correct answer)
  2. 15.8 mL
  3. 222.2 mL
  4. 236.0 mL
Explanation: Ratio problems involving mixtures require you to understand that ratios represent parts of a whole. When you see a ratio like 1:15, this means for every 1 part of active ingredient, there are 15 parts of inert ingredients, creating a total of 16 parts. To find the amount of active ingredient, first determine what fraction of the total solution it represents. With a 1:15 ratio, the active ingredient makes up 11+15=116\frac{1}{1+15} = \frac{1}{16} of the total solution. Then multiply this fraction by the total volume: 116×237 mL=14.8125 mL\frac{1}{16} \times 237 \text{ mL} = 14.8125 \text{ mL}. Rounded to the nearest tenth, this gives you 14.8 mL. Looking at the wrong answers: Answer B (15.8 mL) likely comes from incorrectly calculating 115×237\frac{1}{15} \times 237 instead of 116×237\frac{1}{16} \times 237, forgetting that the denominator should include both parts of the ratio. Answer C (222.2 mL) represents the amount of inert ingredients (1516×237\frac{15}{16} \times 237), which is the opposite of what the question asks for. Answer D (236.0 mL) appears to subtract only 1 mL from the total, completely ignoring the ratio concept. The correct answer is A (14.8 mL). For HESI ratio problems, always remember that ratios show relative parts, not absolute quantities. Add all parts of the ratio to find your denominator, then multiply by the total amount. Double-check by ensuring your answer makes logical sense—the active ingredient should be much smaller than the total volume when the ratio is 1:15.

Question 16

A medication order calls for 250 mg of a drug to be administered. The available solution contains 125 mg per 2.5 mL. After calculating the required volume, the nurse discovers that only 80% of the calculated dose was actually administered due to medication remaining in the tubing. What volume should have been drawn up initially to ensure the patient received the full 250 mg dose?

  1. 5.0 mL should have been drawn up initially
  2. 6.25 mL should have been drawn up initially (correct answer)
  3. 4.0 mL should have been drawn up initially
  4. 7.5 mL should have been drawn up initially
Explanation: First, calculate the standard dose volume: 250 mg ÷ (125 mg/2.5 mL) = 5 mL. Since only 80% was delivered, the patient received 80% of what was drawn up. To get 250 mg delivered, we need: 5 mL ÷ 0.80 = 6.25 mL initially. Choice A (5.0 mL) is the standard calculation without accounting for loss. Choice C (4.0 mL) incorrectly multiplies by 0.8 instead of dividing. Choice D (7.5 mL) uses an incorrect 2/3 ratio.

Question 17

A hospital's ICU maintains a nurse-to-patient ratio of 1:2 during day shifts and 1:3 during night shifts. If the ICU has 24 patients and operates with this staffing pattern for a full 24-hour period (12 hours day, 12 hours night), what is the total number of nursing hours provided per patient over the 24-hour period?

  1. Each patient receives 10 total nursing hours over 24 hours (correct answer)
  2. Each patient receives 8 total nursing hours over 24 hours
  3. Each patient receives 12 total nursing hours over 24 hours
  4. Each patient receives 6 total nursing hours over 24 hours
Explanation: Day shift (12 hours): 1:2 ratio means each nurse covers 2 patients, so each patient gets 0.5 nurse × 12 hours = 6 nursing hours. Night shift (12 hours): 1:3 ratio means each nurse covers 3 patients, so each patient gets 1/3 nurse × 12 hours = 4 nursing hours. Total per patient: 6 + 4 = 10 nursing hours. Choice B (8 hours) incorrectly uses average ratio of 1:2.5 × 24 hours ÷ 2.5. Choice C (12 hours) assumes 1:2 ratio for full 24 hours. Choice D (6 hours) only accounts for day shift hours.

Question 18

A physical therapist is mixing a therapeutic solution that requires components X, Y, and Z in a ratio of 3:4:5. The therapist has 480 mL of component Y available and wants to use exactly 80% of it. However, there is only enough component Z to maintain a 4:3 ratio with the amount of component Y being used. What is the ratio of the actual amounts used (X:Y:Z) in the final mixture?

  1. The final ratio of actual amounts used is 9:12:9 (correct answer)
  2. The final ratio of actual amounts used is 3:4:3
  3. The final ratio of actual amounts used is 12:16:12
  4. The final ratio of actual amounts used is 6:8:6
Explanation: Component Y used = 80% of 480 mL = 384 mL. With limited Z maintaining 4:3 ratio with Y: Y:Z = 4:3, so 384:Z = 4:3, giving Z = 384×3/4 = 288 mL. For component X, we want to maintain the original 3:4 ratio with Y: X:Y = 3:4, so X:384 = 3:4, giving X = 384×3/4 = 288 mL. Final amounts: X = 288 mL, Y = 384 mL, Z = 288 mL. Ratio = 288:384:288. Dividing by 32: 9:12:9. Choice B (3:4:3) would be the ratio if all components were limited by Z. Choice C (12:16:12) is the ratio multiplied by 4/3. Choice D (6:8:6) is the ratio multiplied by 2/3.

Question 19

A patient's heart beats 18 times in a 15-second interval. At this rate, what is the patient's pulse, in beats per minute?

  1. 60
  2. 72 (correct answer)
  3. 90
  4. 108
Explanation: When you encounter pulse rate calculations on the HESI, you're working with unit conversions and proportional reasoning. Healthcare professionals must accurately convert heart rate measurements taken over different time intervals to the standard beats per minute. To solve this, set up a proportion or use direct multiplication. The patient's heart beats 18 times in 15 seconds. Since there are 60 seconds in one minute, you need to find how many 15-second intervals fit into 60 seconds: 60÷15=460 ÷ 15 = 4 intervals. Then multiply the beats per interval by the number of intervals: 18×4=7218 × 4 = 72 beats per minute. Alternatively, you can set up the proportion: 18 beats15 seconds=x beats60 seconds\frac{18 \text{ beats}}{15 \text{ seconds}} = \frac{x \text{ beats}}{60 \text{ seconds}}. Cross-multiplying gives you 18×60=15x18 × 60 = 15x, so x=72x = 72. Looking at the wrong answers: (A) 60 represents a common error where students might confuse the conversion factor or assume 18 beats in 15 seconds somehow equals 60 beats per minute without proper calculation. (C) 90 could result from incorrectly multiplying 18 by 5 instead of 4, perhaps confusing the time conversion. (D) 108 might come from multiplying 18 by 6, which would be the calculation if you mistakenly thought there were 90 seconds in a minute. For HESI success, always identify your conversion factor first (15 seconds × 4 = 60 seconds), then apply it systematically. Double-check by verifying your time units cancel out properly in your calculation.

Question 20

An antibiotic is to be infused at a rate of 40 mg per hour. The IV bag contains 500 mg of the antibiotic in 250 mL of D5W solution. How many milliliters per hour should the IV pump be set to?

  1. 10 mL/hr
  2. 20 mL/hr (correct answer)
  3. 40 mL/hr
  4. 80 mL/hr
Explanation: When you encounter IV dosage calculations on the HESI, you're working with a dimensional analysis problem that requires converting from a medication dose rate to a fluid infusion rate. You need to determine how many mL/hr will deliver the prescribed 40 mg/hr. Start by finding the concentration of the antibiotic solution: 500 mg in 250 mL gives you 500 mg250 mL=2 mg/mL\frac{500 \text{ mg}}{250 \text{ mL}} = 2 \text{ mg/mL} Now use dimensional analysis to convert the ordered dose to volume: 40mghr×1 mL2 mg=20 mL/hr40 \frac{\text{mg}}{\text{hr}} \times \frac{1 \text{ mL}}{2 \text{ mg}} = 20 \text{ mL/hr} This confirms answer B (20 mL/hr) is correct. Looking at the wrong answers: A (10 mL/hr) would only deliver 20 mg/hr, which is half the prescribed dose - this could result from incorrectly doubling the concentration. C (40 mL/hr) represents confusing the dose in mg with the infusion rate in mL - a dangerous error that would deliver twice the prescribed medication. D (80 mL/hr) would deliver 160 mg/hr, four times the ordered dose, likely from inverting the concentration ratio. For HESI dosage calculations, always set up your dimensional analysis to cancel units properly. Write out mg/mL concentration clearly, then multiply by the ordered mg/hr to get mL/hr. Double-check by working backwards: does your final rate times the concentration equal the ordered dose? This verification step catches most calculation errors.