PCAT Quantitative Reasoning 5 — Questions and Answers
Question 1: A drug has a half-life of 6 hours. What fraction of the original dose remains after 24 hours?
- 1/8
- 1/16 (Correct answer)
- 1/32
- 1/64
Correct answer: 1/16
24 hours = 4 half-lives; (1/2)⁴ = 1/16 of the dose remains.
Question 2: Solve for y: 3y/4 − 5 = 7
- 12
- 14
- 16 (Correct answer)
- 18
Correct answer: 16
3y/4 = 12 → 3y = 48 → y = 16.
Question 3: If f(x) = 3x² − 2x + 1, what is f(−2)?
- 9
- 13
- 17 (Correct answer)
- 21
Correct answer: 17
f(−2) = 3(4) − 2(−2) + 1 = 12 + 4 + 1 = 17.
Question 4: Two pipes can fill a tank in 4 and 6 hours respectively. How long will it take to fill the tank together?
- 2.0 hours
- 2.4 hours (Correct answer)
- 3.0 hours
- 3.6 hours
Correct answer: 2.4 hours
Combined rate = 1/4 + 1/6 = 5/12 tanks/hr; time = 12/5 = 2.4 hours.
Question 5: What is the slope of the line passing through (2, −3) and (8, 9)?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
Slope = (9 − (−3)) / (8 − 2) = 12/6 = 2.
Question 6: Convert 0.000325 to scientific notation.
- 3.25 × 10⁻²
- 3.25 × 10⁻³
- 3.25 × 10⁻⁴ (Correct answer)
- 3.25 × 10⁻⁵
Correct answer: 3.25 × 10⁻⁴
0.000325 = 3.25 × 10⁻⁴ because the decimal moves 4 places to the right.
Question 7: A pharmacy technician earns $18.50/hour and works 37.5 hours per week. What are the gross weekly earnings?
- $656.25
- $693.75 (Correct answer)
- $712.50
- $740.00
Correct answer: $693.75
$18.50 × 37.5 = $693.75.
PCAT Quantitative Reasoning 5
A drug has a half-life of 6 hours.
What fraction of the original dose remains after 24 hours?