OAT Quantitative Reasoning and Math 5

Question 1

How many ways can 4 students be arranged in a line?

Accepted Answer

24

Answer

The number of permutations of 4 students = 4! = 4 × 3 × 2 × 1 = 24.

Question 2

What is the value of (2³)² ÷ 2²?

Accepted Answer

16

Answer

(2³)² = 2⁶ = 64; then 64 ÷ 2² = 64 ÷ 4 = 16.

Question 3

The ratio of boys to girls in a class is 3:5. If there are 24 boys, how many girls are there?

Accepted Answer

40

Answer

If 3 parts = 24 boys, then 1 part = 8; girls = 5 × 8 = 40.

Question 4

What is the solution to the system: x + y = 10 and x − y = 4?

Accepted Answer

x=7, y=3

Answer

Adding the equations: 2x = 14, so x = 7; substituting: y = 10 − 7 = 3.

Question 5

A sphere has a radius of 3 cm. What is its surface area?

Accepted Answer

36π cm²

Answer

Surface area of a sphere = 4πr² = 4π(3²) = 36π cm².

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