SCAT Quantitative Comparisons: Geometry 3 — Questions and Answers
Question 1: A parallelogram has base 10 and height 6. A triangle has base 15 and height 8. | Quantity A: Area of the parallelogram | Quantity B: Area of the triangle
- 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
Parallelogram area = 10×6 = 60; triangle area = ½×15×8 = 60, so both are equal.
Question 2: A square has a side length of 5. | Quantity A: The length of a diagonal of the square | Quantity B: 7
- 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
Diagonal = 5√2 ≈ 7.07, which is greater than 7, so Quantity A is greater.
Question 3: An inscribed angle in a circle intercepts an arc of 100°. | Quantity A: The measure of the inscribed angle | Quantity B: 55°
- 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
An inscribed angle equals half its intercepted arc: 100°÷2 = 50°, which is less than 55°, so Quantity B is greater.
Question 4: In a right triangle, one acute angle measures 35°. | Quantity A: The other acute angle | Quantity B: The complement of 35°
- 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 other acute angle = 90° − 35° = 55°, which equals the complement of 35°, so both are equal.
Question 5: A regular hexagon has a perimeter of 36. | Quantity A: The side length of the hexagon | Quantity B: 7
- 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
A regular hexagon has 6 equal sides: 36÷6 = 6, which is less than 7, so Quantity B is greater.
Question 6: A cylinder has radius 3 and height 4. A rectangular prism measures 3 × 4 × 5. | Quantity A: Volume of the cylinder | Quantity B: Volume of the rectangular prism
- 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
Cylinder volume = π×9×4 = 36π ≈ 113.1; prism volume = 3×4×5 = 60, so Quantity A is greater.
Question 7: An exterior angle of a triangle measures 115°. One non-adjacent interior angle of the triangle measures 60°. | Quantity A: The other non-adjacent interior angle | Quantity B: 55°
- 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
An exterior angle equals the sum of the two non-adjacent interior angles: 115° = 60° + x, so x = 55°, making both quantities equal.
SCAT Quantitative Comparisons: Geometry 3
A parallelogram has base 10 and height 6.
A triangle has base 15 and height 8. | Quantity A: Area of the parallelogram | Quantity B: Area of the triangle