HSRT Quantitative Reasoning and Numeracy 2 — Questions and Answers

Question 1: A patient needs 2.5 mg of a drug per kg of body weight. The patient weighs 88 kg. The drug is available as a 50 mg/mL solution. How many mL should be administered?

4.4 mL (Correct answer)
3.5 mL
5.0 mL
2.2 mL

Correct answer: 4.4 mL

Total dose = 2.5 mg/kg × 88 kg = 220 mg. Volume = 220 mg ÷ 50 mg/mL = 4.4 mL.

Weight-based dosing calculation: Total dose = dose (mg/kg) × weight (kg) = 2.5 × 88 = 220 mg. Volume = total dose / concentration = 220 mg / 50 mg/mL = 4.4 mL. This is a fundamental pharmacokinetics numeracy skill used in drug preparation. Errors at any step (incorrect weight, wrong dose, wrong concentration) can result in under- or overdosing. Dimensional analysis (canceling units) is the most reliable method: (2.5 mg/kg) × (88 kg) × (1 mL/50 mg) = 4.4 mL.

Question 2: A clinical trial reports a risk ratio (RR) of 1.45 for myocardial infarction in patients on Drug X vs. placebo. Which numerical statement BEST interprets this finding?

Patients on Drug X have a 45% higher risk of MI relative to patients on placebo (Correct answer)
45% of patients on Drug X will have an MI
Drug X increases the absolute probability of MI by 1.45
Drug X reduces MI risk by 45% compared to placebo

Correct answer: Patients on Drug X have a 45% higher risk of MI relative to patients on placebo

RR = 1.45 means the risk in the exposed group is 1.45 times (45% higher than) the risk in the unexposed group.

The Risk Ratio (relative risk) = Risk in exposed / Risk in unexposed. RR = 1.45 means the exposed group has 1.45 times the risk of the unexposed group — a 45% relative risk increase. This is not an absolute probability — 45% of treated patients will not necessarily have an MI (that depends on baseline risk). RR > 1 indicates increased risk (not reduced), and it does not represent an additive probability. If baseline MI risk is 2%, treated patients have approximately 2% × 1.45 = 2.9% risk — an absolute increase of 0.9%.

Question 3: A nurse needs to infuse 1 liter of normal saline over 8 hours using a standard IV drip set (20 drops/mL). What is the drip rate in drops per minute?

42 drops/min (Correct answer)
25 drops/min
83 drops/min
20 drops/min

Correct answer: 42 drops/min

Total drops = 1000 mL × 20 drops/mL = 20,000 drops. Time = 8 h × 60 min = 480 min. Rate = 20,000 / 480 ≈ 41.7 ≈ 42 drops/min.

IV drip rate calculation: Total volume in mL × drop factor (drops/mL) / total time in minutes. = (1000 mL × 20 drops/mL) / (8 h × 60 min/h) = 20,000 drops / 480 min = 41.67 drops/min ≈ 42 drops/min. This is a fundamental nursing numeracy skill. Errors in drip rate calculation can result in fluid overload or inadequate hydration. Electronic pumps often replace manual drip calculations, but the underlying numeracy remains essential for verification and emergencies.

Question 4: A study shows Disease Y has an incidence of 12 per 100,000 per year in the general population. A clinician sees 2,000 patients per year. How many new cases of Disease Y would be expected in her practice per year?

0.24 cases per year (approximately 1 case every 4 years) (Correct answer)
12 cases per year
2.4 cases per year
0.012 cases per year

Correct answer: 0.24 cases per year (approximately 1 case every 4 years)

Expected cases = (12/100,000) × 2,000 = 0.24 cases per year — approximately one case every 4 years.

Rate scaling: (12 cases / 100,000 people) × 2,000 patients = 24,000/100,000 = 0.24 cases/year. This means the clinician would expect to see approximately 1 new case of Disease Y every 4–5 years. This quantitative reasoning has major implications for clinical practice: rare diseases are genuinely rare in primary care, which explains why a clinician with 20 years of experience may have seen only 5 cases of a disease with incidence of 12/100,000. This also explains why clinical experience alone is insufficient to accurately judge diagnostic probability for rare conditions.

Question 5: A patient's creatinine clearance is 45 mL/min. A drug's recommended dose adjustment states: 'Reduce dose by 50% if CrCl is between 30–59 mL/min.' The standard dose is 400 mg twice daily. What is the adjusted regimen?

200 mg twice daily (Correct answer)
400 mg once daily
200 mg once daily
100 mg twice daily

Correct answer: 200 mg twice daily

50% dose reduction: 400 mg × 0.50 = 200 mg. Frequency (twice daily) is not changed by the instruction. Adjusted dose = 200 mg twice daily.

Renal dose adjustment requires carefully reading whether the adjustment applies to the dose per administration, the frequency, or both. The instruction states 'reduce dose by 50%' — the dose per administration changes (400 mg → 200 mg) but frequency (twice daily) remains. If the instruction were 'reduce frequency by 50%,' it would become 400 mg once daily. Both modifications can achieve total daily dose reduction (200 mg BID = 400 mg/day vs. 400 mg QD = 400 mg/day), but pharmacokinetic profiles differ. Always apply dose adjustment instructions precisely as written.

Question 6: A patient's hemoglobin dropped from 12.4 g/dL to 9.8 g/dL over 2 weeks. The percent decline is approximately:

21% decline (Correct answer)
26% decline
12% decline
79% decline

Correct answer: 21% decline

Percent change = (12.4 - 9.8) / 12.4 × 100 = 2.6 / 12.4 × 100 = 21%.

Percent change calculation: % change = (old value - new value) / old value × 100 = (12.4 - 9.8) / 12.4 × 100 = 2.6 / 12.4 × 100 = 20.97% ≈ 21%. A 21% decline in hemoglobin over 2 weeks is clinically significant and warrants investigation for active bleeding, hemolysis, or bone marrow suppression. This calculation is the basis for monitoring trends in laboratory values and determining whether a change exceeds clinically meaningful thresholds (typically >10% change in chronic conditions, >15–20% indicating acute deterioration).

HSRT Quantitative Reasoning and Numeracy 2

A patient needs 2.5 mg of a drug per kg of body weight.
The patient weighs 88 kg.
The drug is available as a 50 mg/mL solution.
How many mL should be administered?