SCAT Quantitative Comparisons: Geometry 2 — Questions and Answers
Question 1: A rectangle has length 8 and width 5. A square has a perimeter of 24. | Quantity A: Area of the rectangle | Quantity B: Area of the square
- Quantity A is greater (Correct answer)
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given
Correct answer: Quantity A is greater
The rectangle has area 8×5=40; the square has side 24÷4=6 and area 36, so Quantity A is greater.
Question 2: Triangle ABC has two angles measuring 55° and 75°. | Quantity A: The third angle of the triangle | Quantity B: 50°
- Quantity A is greater
- Quantity B is greater
- The two quantities are equal (Correct answer)
- The relationship cannot be determined from the information given
Correct answer: The two quantities are equal
The third angle = 180 − 55 − 75 = 50°, so both quantities are equal.
Question 3: Circle P has a radius of 6. | Quantity A: Area of circle P (in square units) | Quantity B: 4 times the circumference of circle P
- Quantity A is greater
- Quantity B is greater (Correct answer)
- The two quantities are equal
- The relationship cannot be determined from the information given
Correct answer: Quantity B is greater
Area = 36π ≈ 113.1; 4 × circumference = 4 × 12π = 48π ≈ 150.8, so Quantity B is greater.
Question 4: A cube has a side length of 4. | Quantity A: Volume of the cube | Quantity B: Total surface area of the cube
- Quantity A is greater
- Quantity B is greater (Correct answer)
- The two quantities are equal
- The relationship cannot be determined from the information given
Correct answer: Quantity B is greater
Volume = 4³ = 64; surface area = 6 × 4² = 96, so Quantity B is greater.
Question 5: A right triangle has legs of length 9 and 40. | Quantity A: The hypotenuse of the triangle | Quantity B: 42
- Quantity A is greater
- Quantity B is greater (Correct answer)
- The two quantities are equal
- The relationship cannot be determined from the information given
Correct answer: Quantity B is greater
Hypotenuse = √(81 + 1600) = √1681 = 41, which is less than 42, so Quantity B is greater.
Question 6: Point A is at (1, 2) and point B is at (4, 6) in the coordinate plane. | Quantity A: The distance from A to B | Quantity B: 5
- Quantity A is greater
- Quantity B is greater
- The two quantities are equal (Correct answer)
- The relationship cannot be determined from the information given
Correct answer: The two quantities are equal
Distance = √((4−1)² + (6−2)²) = √(9+16) = √25 = 5, so the quantities are equal.
Question 7: Two lines intersect forming vertical angles. One angle measures (3x + 10)° and its vertical angle measures (5x − 20)°. | Quantity A: x | Quantity B: 16
- Quantity A is greater
- Quantity B is greater (Correct answer)
- The two quantities are equal
- The relationship cannot be determined from the information given
Correct answer: Quantity B is greater
Vertical angles are equal: 3x + 10 = 5x − 20, giving x = 15, which is less than 16, so Quantity B is greater.
SCAT Quantitative Comparisons: Geometry 2
A rectangle has length 8 and width 5.
A square has a perimeter of 24. | Quantity A: Area of the rectangle | Quantity B: Area of the square