SCAT - School and College Ability Quantitative Comparisons: Geometry Questions and Answers

Question 1

Compare the quantities in Column A and Column B.

**Column A:** The area of a square with a side length of 6.

**Column B:** The area of a rectangle with a length of 9 and a width of 4.

Accepted Answer

The two quantities are equal.

Answer

To find the area of the square in Column A, you multiply the side length by itself: 6 * 6 = 36. To find the area of the rectangle in Column B, you multiply the length by the width: 9 * 4 = 36. Since both quantities equal 36, the two quantities are equal.

Question 2

Compare the quantities in Column A and Column B.

**Column A:** The circumference of a circle with a radius of 5.

**Column B:** The perimeter of a square with a side length of 8.

Accepted Answer

Quantity B is greater.

Answer

The formula for the circumference of a circle is 2πr. For Column A, the circumference is 2 * π * 5 = 10π. Using the approximation π ≈ 3.14, Quantity A is approximately 10 * 3.14 = 31.4. The formula for the perimeter of a square is 4s. For Column B, the perimeter is 4 * 8 = 32. Since 32 is greater than 31.4, Quantity B is greater.

Question 3

An isosceles triangle ABC has side AB equal to side AC. The measure of angle B is 50 degrees. Compare the quantities in Column A and Column B.

**Column A:** The measure of angle A.

**Column B:** 60 degrees.

Accepted Answer

Quantity A is greater.

Answer

In an isosceles triangle, the angles opposite the equal sides are also equal. Since side AB = side AC, angle C must equal angle B, which is 50 degrees. The sum of the angles in any triangle is 180 degrees. Therefore, angle A = 180 - (angle B + angle C) = 180 - (50 + 50) = 180 - 100 = 80 degrees. Since 80 degrees (Quantity A) is greater than 60 degrees (Quantity B), Quantity A is greater.

Question 4

Compare the quantities in Column A and Column B.

**Column A:** The volume of a cube with an edge length of 4 cm.

**Column B:** The volume of a rectangular prism with a length of 5 cm, a width of 4 cm, and a height of 3 cm.

Accepted Answer

Quantity A is greater.

Answer

The volume of a cube is calculated as edge³. For Column A, the volume is 4 * 4 * 4 = 64 cm³. The volume of a rectangular prism is length * width * height. For Column B, the volume is 5 * 4 * 3 = 60 cm³. Since 64 is greater than 60, Quantity A is greater.

Question 5

A triangle has two sides with lengths 7 and 10. Compare the quantities in Column A and Column B.

**Column A:** The length of the third side.

**Column B:** 12.

Accepted Answer

The relationship cannot be determined from the information given.

Answer

According to the Triangle Inequality Theorem, the length of the third side must be greater than the difference of the other two sides and less than their sum. So, the third side (x) must be within the range: 10 - 7 < x < 10 + 7, which simplifies to 3 < x < 17. Since the third side could be a value less than 12 (e.g., 5) or a value greater than 12 (e.g., 15), the relationship cannot be determined from the given information.

(SCAT) School and College Ability Test Practice Test

(SCAT) School and College Ability Test Practice Test

SCAT - School and College Ability Quantitative Comparisons: Geometry Questions and Answers