OAT Quantitative Reasoning and Math 5 — Questions and Answers
Question 1: How many ways can 4 students be arranged in a line?
- 12
- 16
- 24 (Correct answer)
- 48
Correct answer: 24
The number of permutations of 4 students = 4! = 4 × 3 × 2 × 1 = 24.
Question 2: What is the value of (2³)² ÷ 2²?
- 8
- 16 (Correct answer)
- 32
- 64
Correct answer: 16
(2³)² = 2⁶ = 64; then 64 ÷ 2² = 64 ÷ 4 = 16.
Question 3: The ratio of boys to girls in a class is 3:5. If there are 24 boys, how many girls are there?
- 30
- 32
- 40 (Correct answer)
- 35
Correct answer: 40
If 3 parts = 24 boys, then 1 part = 8; girls = 5 × 8 = 40.
Question 4: What is the solution to the system: x + y = 10 and x − y = 4?
- x=3, y=7
- x=7, y=3 (Correct answer)
- x=6, y=4
- x=4, y=6
Correct answer: x=7, y=3
Adding the equations: 2x = 14, so x = 7; substituting: y = 10 − 7 = 3.
Question 5: A sphere has a radius of 3 cm. What is its surface area?
- 12π cm²
- 18π cm²
- 36π cm² (Correct answer)
- 9π cm²
Correct answer: 36π cm²
Surface area of a sphere = 4πr² = 4π(3²) = 36π cm².
Question 6: What is the value of the expression |−8| − |−3| + |2|?
- 7 (Correct answer)
- −7
- 3
- 13
Correct answer: 7
Absolute values: |−8| = 8, |−3| = 3, |2| = 2; result = 8 − 3 + 2 = 7.
Question 7: A data set has a mean of 50 and a standard deviation of 5. What percentage of data falls within one standard deviation of the mean, assuming a normal distribution?
- 50%
- 68% (Correct answer)
- 95%
- 99.7%
Correct answer: 68%
By the empirical rule (68-95-99.7 rule), approximately 68% of data falls within one standard deviation of the mean.
OAT Quantitative Reasoning and Math 5
How many ways can 4 students be arranged in a line?