OAT Quantitative Reasoning 2 — Questions and Answers
Question 1: A train travels 240 miles in 3 hours, then 180 miles in 2 hours. What is the average speed for the entire trip?
- 84 mph (Correct answer)
- 90 mph
- 78 mph
- 72 mph
Correct answer: 84 mph
Total distance = 420 miles; total time = 5 hours; average speed = 420/5 = 84 mph.
Question 2: If log₂(x) = 5, what is the value of x?
- 10
- 25
- 32 (Correct answer)
- 64
Correct answer: 32
log₂(x) = 5 means 2⁵ = x, so x = 32.
Question 3: A bag contains 4 red, 5 blue, and 6 green marbles. What is the probability of drawing 2 red marbles in a row without replacement?
- 2/35 (Correct answer)
- 16/225
- 1/15
- 4/45
Correct answer: 2/35
P = (4/15) × (3/14) = 12/210 = 2/35.
Question 4: The sum of three consecutive even integers is 78. What is the largest of the three integers?
- 24
- 26
- 28 (Correct answer)
- 30
Correct answer: 28
Let integers be n, n+2, n+4; 3n + 6 = 78 → n = 24, so the largest is 28.
Question 5: What is the area of a circle inscribed in a square with side length 10?
- 25π (Correct answer)
- 50π
- 100π
- 10π
Correct answer: 25π
The inscribed circle has radius = 5, so area = π(5)² = 25π.
Question 6: If f(x) = 3x² − 2x + 1, what is f(−2)?
- 9
- 17 (Correct answer)
- 13
- −3
Correct answer: 17
f(−2) = 3(4) − 2(−2) + 1 = 12 + 4 + 1 = 17.
Question 7: A rectangle has a perimeter of 56 cm and a length that is 3 times its width. What is the area of the rectangle?
- 147 cm² (Correct answer)
- 196 cm²
- 108 cm²
- 84 cm²
Correct answer: 147 cm²
2(l+w) = 56 → l+w = 28; l = 3w → 4w = 28 → w = 7, l = 21; Area = 7 × 21 = 147 cm².
OAT Quantitative Reasoning 2
A train travels 240 miles in 3 hours, then 180 miles in 2 hours.
What is the average speed for the entire trip?