OAT Quantitative Reasoning 4

Question 1

A cylinder has a radius of 4 cm and a height of 9 cm. What is its volume?

Accepted Answer

144π cm³

Answer

V = πr²h = π(4²)(9) = 144π cm³.

Question 2

Solve for x: |2x − 6| = 10

Accepted Answer

x = 8 or x = −2

Answer

2x − 6 = 10 → x = 8, or 2x − 6 = −10 → x = −2.

Question 3

In a class of 30 students, 18 play soccer and 14 play basketball. If 5 play neither sport, how many play both?

Accepted Answer

7

Answer

Students playing at least one sport = 25; by inclusion-exclusion: 18 + 14 − both = 25 → both = 7.

Question 4

If a right triangle has legs of length 7 and 24, what is the length of the hypotenuse?

Accepted Answer

25

Answer

c = √(7² + 24²) = √(49 + 576) = √625 = 25.

Question 5

What is the sum of the first 20 positive odd integers?

Accepted Answer

400

Answer

The sum of the first n odd integers = n²; for n = 20, sum = 400.

OAT - Optometry Admission Test Practice Test