PCAT Quantitative Reasoning 3 — Questions and Answers
Question 1: A right triangle has legs of length 7 and 24. What is the length of the hypotenuse?
- 23
- 25 (Correct answer)
- 26
- 31
Correct answer: 25
Hypotenuse = √(7² + 24²) = √(49 + 576) = √625 = 25.
Question 2: Which of the following is equivalent to (x²y³)⁴ / (x³y²)?
- x⁵y¹⁰ (Correct answer)
- x⁸y¹²/x³y²
- x⁵y¹⁰
- x⁸y¹⁰ / y²
Correct answer: x⁵y¹⁰
(x²y³)⁴ = x⁸y¹²; dividing by x³y² gives x⁵y¹⁰.
Question 3: What is the probability of rolling an even number on a standard six-sided die twice in a row?
- 1/6
- 1/4 (Correct answer)
- 1/3
- 1/2
Correct answer: 1/4
P(even) = 3/6 = 1/2 each roll; combined probability = (1/2)(1/2) = 1/4.
Question 4: If 5x − 3 = 2x + 12, what is x?
- 3
- 4
- 5 (Correct answer)
- 6
Correct answer: 5
5x − 2x = 12 + 3 → 3x = 15 → x = 5.
Question 5: A solution contains 45 mg of drug per 15 mL. What volume contains 120 mg?
- 30 mL
- 40 mL (Correct answer)
- 45 mL
- 60 mL
Correct answer: 40 mL
Concentration = 45/15 = 3 mg/mL; 120 mg ÷ 3 mg/mL = 40 mL.
Question 6: What is the median of the data set: {3, 7, 9, 15, 21, 25, 30}?
- 9
- 12
- 15 (Correct answer)
- 21
Correct answer: 15
The data set has 7 values; the middle (4th) value in order is 15.
Question 7: How many ways can a committee of 3 be chosen from 8 people?
- 24
- 56 (Correct answer)
- 112
- 336
Correct answer: 56
C(8,3) = 8! / (3! × 5!) = 56.
PCAT Quantitative Reasoning 3
A right triangle has legs of length 7 and 24.
What is the length of the hypotenuse?