OAT Quantitative Reasoning 4 — Questions and Answers
Question 1: A cylinder has a radius of 4 cm and a height of 9 cm. What is its volume?
- 36π cm³
- 72π cm³
- 144π cm³ (Correct answer)
- 288π cm³
Correct answer: 144π cm³
V = πr²h = π(4²)(9) = 144π cm³.
Question 2: Solve for x: |2x − 6| = 10
- x = 8 only
- x = −2 only
- x = 8 or x = −2 (Correct answer)
- x = 2 or x = −8
Correct answer: x = 8 or x = −2
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?
- 5
- 7 (Correct answer)
- 8
- 10
Correct answer: 7
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?
- 25 (Correct answer)
- 26
- 31
- √527
Correct answer: 25
c = √(7² + 24²) = √(49 + 576) = √625 = 25.
Question 5: What is the sum of the first 20 positive odd integers?
- 200
- 400 (Correct answer)
- 210
- 380
Correct answer: 400
The sum of the first n odd integers = n²; for n = 20, sum = 400.
Question 6: A store marks up an item by 40%, then offers a 20% discount. What is the net percent change from the original price?
- 12% increase (Correct answer)
- 20% increase
- 8% increase
- 20% decrease
Correct answer: 12% increase
Net factor = 1.40 × 0.80 = 1.12, representing a 12% increase over the original price.
Question 7: Evaluate: ∑(k=1 to 5) of (2k + 1)
- 30
- 35 (Correct answer)
- 40
- 25
Correct answer: 35
Sum = 3 + 5 + 7 + 9 + 11 = 35.
OAT Quantitative Reasoning 4
A cylinder has a radius of 4 cm and a height of 9 cm.
What is its volume?