OAT Quantitative Reasoning 3

Question 1

What is the value of sin(45°) × cos(45°)?

Accepted Answer

1/2

Answer

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?

Accepted Answer

19

Answer

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.

Accepted Answer

x + 3

Answer

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?

Accepted Answer

68

Answer

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?

Accepted Answer

130°

Answer

Third interior angle = 180 − 47 − 83 = 50°; its adjacent exterior angle = 180 − 50 = 130°.

OAT - Optometry Admission Test Practice Test