OAT Quantitative Reasoning 5 — Questions and Answers
Question 1: Which of the following is equivalent to (2³)⁴ ÷ 2⁶?
- 2²
- 2⁶ (Correct answer)
- 2⁸
- 2⁴
Correct answer: 2⁶
(2³)⁴ = 2¹² and 2¹² ÷ 2⁶ = 2⁶.
Question 2: A car depreciates in value by 15% per year. If it is currently worth $20,000, what will it be worth after 2 years?
- $14,450 (Correct answer)
- $17,000
- $14,000
- $15,200
Correct answer: $14,450
Value = 20,000 × (0.85)² = 20,000 × 0.7225 = $14,450.
Question 3: If vectors u = (3, −1) and v = (2, 4), what is the dot product u · v?
- 10
- 2 (Correct answer)
- 14
- −2
Correct answer: 2
u · v = (3)(2) + (−1)(4) = 6 − 4 = 2.
Question 4: What is the range of the function f(x) = −x² + 4?
- y ≥ 4
- y ≤ 4 (Correct answer)
- all real numbers
- y ≥ −4
Correct answer: y ≤ 4
The parabola opens downward with vertex at (0, 4), so f(x) ≤ 4 for all x.
Question 5: How many distinct arrangements are there of the letters in the word 'LEVEL'?
- 30 (Correct answer)
- 60
- 120
- 24
Correct answer: 30
LEVEL has 5 letters with L repeated 2× and E repeated 2×: 5! / (2! × 2!) = 120/4 = 30.
Question 6: If tan(θ) = 5/12 and θ is in the first quadrant, what is cos(θ)?
- 5/13
- 12/13 (Correct answer)
- 5/12
- 13/12
Correct answer: 12/13
With opposite = 5, adjacent = 12, hypotenuse = 13; cos(θ) = adjacent/hypotenuse = 12/13.
Question 7: A solution is 30% acid. How many liters of pure acid must be added to 20 liters of this solution to make it 50% acid?
- 6 L
- 8 L (Correct answer)
- 10 L
- 12 L
Correct answer: 8 L
(0.30×20 + x) / (20 + x) = 0.50 → 6 + x = 10 + 0.5x → x = 8.
OAT Quantitative Reasoning 5
Which of the following is equivalent to (2³)⁴ ÷ 2⁶?