PCAT Quantitative Reasoning 4 — Questions and Answers
Question 1: If 20% of a number is 35, what is 45% of the same number?
- 63.75
- 70.25
- 78.75 (Correct answer)
- 87.50
Correct answer: 78.75
The number is 35/0.20 = 175; 45% of 175 = 0.45 × 175 = 78.75.
Question 2: A pharmacist dispenses tablets at a rate of 12 tablets per minute. How many tablets are dispensed in 2.5 hours?
- 1,440
- 1,680
- 1,800 (Correct answer)
- 2,160
Correct answer: 1,800
2.5 hours = 150 minutes; 12 × 150 = 1,800 tablets.
Question 3: Simplify: √(48) − √(12)
- 2√3 (Correct answer)
- 4√3
- 6√3
- 8√3
Correct answer: 2√3
√48 = 4√3 and √12 = 2√3; 4√3 − 2√3 = 2√3.
Question 4: If the area of a circle is 100π cm², what is its circumference?
- 10π cm
- 20π cm (Correct answer)
- 25π cm
- 50π cm
Correct answer: 20π cm
A = πr² = 100π → r = 10; C = 2πr = 20π cm.
Question 5: A student scored 78, 85, 90, and 73 on four exams. What score is needed on the fifth exam to achieve an average of 84?
- 90
- 94 (Correct answer)
- 96
- 98
Correct answer: 94
Total needed = 84 × 5 = 420; current total = 326; needed = 420 − 326 = 94.
Question 6: Which expression equals (a + b)² − (a − b)²?
- 2ab
- 4ab (Correct answer)
- 2a²
- 4b²
Correct answer: 4ab
(a+b)² = a²+2ab+b² and (a−b)² = a²−2ab+b²; the difference is 4ab.
Question 7: A 2 L IV bag drips at 80 mL/hour. How many hours will the bag last?
- 20 hours
- 22 hours
- 25 hours (Correct answer)
- 30 hours
Correct answer: 25 hours
2,000 mL ÷ 80 mL/hr = 25 hours.
PCAT Quantitative Reasoning 4
If 20% of a number is 35, what is 45% of the same number?