OAT Quantitative Reasoning 5

Question 1

Which of the following is equivalent to (2³)⁴ ÷ 2⁶?

Accepted Answer

2⁶

Answer

(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?

Accepted Answer

$14,450

Answer

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?

Accepted Answer

2

Answer

u · v = (3)(2) + (−1)(4) = 6 − 4 = 2.

Question 4

What is the range of the function f(x) = −x² + 4?

Accepted Answer

y ≤ 4

Answer

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'?

Accepted Answer

30

Answer

LEVEL has 5 letters with L repeated 2× and E repeated 2×: 5! / (2! × 2!) = 120/4 = 30.

OAT - Optometry Admission Test Practice Test