OAT Quantitative Reasoning 3 — Questions and Answers
Question 1: What is the value of sin(45°) × cos(45°)?
- 1
- 1/2 (Correct answer)
- √2
- √2/4
Correct answer: 1/2
sin(45°) = cos(45°) = √2/2; their product = (√2/2)² = 1/2.
Question 2: A sequence is defined by aₙ = 2aₙ₋₁ − 3, with a₁ = 5. What is a₄?
- 13
- 19 (Correct answer)
- 23
- 29
Correct answer: 19
a₂ = 2(5)−3 = 7; a₃ = 2(7)−3 = 11; a₄ = 2(11)−3 = 19.
Question 3: Simplify: (x² − 9) / (x − 3) for x ≠ 3.
- x − 3
- x + 3 (Correct answer)
- x² + 3
- x − 9
Correct answer: x + 3
x² − 9 = (x−3)(x+3); dividing by (x−3) gives x + 3.
Question 4: If 5% of a number is 17, what is 20% of the same number?
- 68 (Correct answer)
- 85
- 34
- 51
Correct answer: 68
5% of n = 17 → n = 340; 20% of 340 = 68.
Question 5: Two angles of a triangle measure 47° and 83°. What is the measure of the exterior angle adjacent to the third interior angle?
- 50°
- 130° (Correct answer)
- 140°
- 150°
Correct answer: 130°
Third interior angle = 180 − 47 − 83 = 50°; its adjacent exterior angle = 180 − 50 = 130°.
Question 6: What is the slope of a line perpendicular to y = (3/4)x − 2?
- 3/4
- −3/4
- 4/3
- −4/3 (Correct answer)
Correct answer: −4/3
The slope of the given line is 3/4; the perpendicular slope is its negative reciprocal: −4/3.
Question 7: A data set has values: 8, 12, 15, 15, 18, 22. What is the median?
- 15 (Correct answer)
- 15.5
- 14.5
- 16
Correct answer: 15
With 6 sorted values, median = average of 3rd and 4th values = (15 + 15)/2 = 15.
OAT Quantitative Reasoning 3
What is the value of sin(45°) × cos(45°)?