HPAT Numerical Reasoning and Data Analysis 2 — Questions and Answers
Question 1: A hospital's quarterly surgery counts are Q1: 80, Q2: 100, Q3: 120, Q4: 100. What fraction of all surgeries for the year occurred in Q3?
- 1/4
- 3/10 (Correct answer)
- 1/3
- 2/5
Correct answer: 3/10
Total = 80 + 100 + 120 + 100 = 400; Q3 fraction = 120 ÷ 400 = 3/10.
Question 2: A patient's blood glucose (mg/dL) readings: 6am=90, 8am=160, 10am=130, 12pm=105, 2pm=95. Between which time interval did blood glucose decrease the most?
- 6am–8am
- 8am–10am (Correct answer)
- 10am–12pm
- 12pm–2pm
Correct answer: 8am–10am
Glucose fell 30 points from 160 to 130 between 8am and 10am, the largest single-interval drop.
Question 3: A study finds a correlation coefficient of −0.78 between weekly exercise hours and resting heart rate. What does this indicate?
- Strong positive: more exercise raises resting heart rate
- Strong negative: more exercise is associated with lower resting heart rate (Correct answer)
- Weak negative: exercise has minimal effect on heart rate
- No meaningful relationship between exercise and heart rate
Correct answer: Strong negative: more exercise is associated with lower resting heart rate
A coefficient of −0.78 indicates a strong negative relationship: more exercise is associated with a lower resting heart rate.
Question 4: In a study of 500 patients, 155 were exposed to factor Y. Of those exposed, 45 developed condition X. Of the 345 unexposed, 30 developed condition X. What is the approximate risk of developing condition X among those exposed?
- 6%
- 9%
- 29% (Correct answer)
- 45%
Correct answer: 29%
Risk in exposed group = 45 ÷ 155 ≈ 0.29 = 29%.
Question 5: A hospital's infection rate dropped from 4.8% to 3.2% after implementing a new hygiene protocol. What is the absolute reduction in infection rate?
- 0.16%
- 0.016%
- 1.6 percentage points (Correct answer)
- 16 percentage points
Correct answer: 1.6 percentage points
Absolute reduction = 4.8% − 3.2% = 1.6 percentage points.
Question 6: A diagnostic test has 88% sensitivity and 92% specificity. If 200 patients who truly have the disease take the test, approximately how many will receive a false negative result?
- 8
- 16
- 24 (Correct answer)
- 88
Correct answer: 24
False negative rate = 100% − 88% sensitivity = 12%; 200 × 0.12 = 24 patients would falsely test negative.
Question 7: Drug A reduces symptoms in 70% of patients; Drug B in 55%. If 200 patients receive Drug A, how many MORE symptom improvements would be expected compared to the same group receiving Drug B?
- 15
- 20
- 25
- 30 (Correct answer)
Correct answer: 30
Difference = (0.70 − 0.55) × 200 = 0.15 × 200 = 30 additional improvements with Drug A.
HPAT Numerical Reasoning and Data Analysis 2
A hospital's quarterly surgery counts are Q1: 80, Q2: 100, Q3: 120, Q4: 100.
What fraction of all surgeries for the year occurred in Q3?