SCAT Quantitative Comparisons: Geometry 2

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

Accepted Answer

Quantity A is greater

Answer

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°

Accepted Answer

The two quantities are equal

Answer

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

Accepted Answer

Quantity B is greater

Answer

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

Accepted Answer

Quantity B is greater

Answer

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

Accepted Answer

Quantity B is greater

Answer

Hypotenuse = √(81 + 1600) = √1681 = 41, which is less than 42, so Quantity B is greater.

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