Geometry

Practice Questions

GMAT Quantitative Reasoning › Geometry

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1

A tetrahedron is a solid with four triangular faces.

Give the volume of a tetrahedron.

Statement 1: The tetrahedron has four equilateral faces.

Statement 2: The surface area of the tetrahedron is $120 \sqrt{3}$ .

2

$\bigtriangleup ABC$ is a right triangle. Evaluate .

Statement 1: and

Statement 2: $\bigtriangleup ABC$ is not a 30-60-90 triangle.

3

The radius of Circle A is equal to the sidelength of Square B. A sector of Circle A has the same area as Square B. Which of the following is the degree measure of this sector?

4

Let and be real numbers.

What is the product of and its complex conjugate?

Statement 1: $a^{2}+b^{2}= 71$

Statement 2: $a^{2}-b^{2}= 39$

5

Let be a positive integer.

True or false: $i^{N} = 1$

Statement 1: is a prime number.

Statement 2: is a two-digit number ending in a 7.

6

Sector

The circle in the above diagram has center . Give the ratio of the area of the white sector to that of the shaded sector.

Statement 1:

Statement 2: $m \angle ACB = 30 ^{\circ }$

7

What is the measure of $\angle 1$ ?

Statement 1: $\angle 1$ is an exterior angle of an equilateral triangle.

Statement 2: $\angle 1$ is an interior angle of a regular hexagon.

8

What is the height of the right triangle?

The area of the right triangle is .
The base of the right triangle measures .

9

Tetra_1

In the above diagram, a tetrahedron - a triangular pyramid - with vertices is shown inside a cube. Give the volume of the tetrahedron.

Statement 1: The perimeter of Square is 16.

Statement 2: The area of $\bigtriangleup EGH$ is 8.

10

What is the circumference of Circle ?

1.) The diameter of the circle is .

2.) The area of the circle is $25\pi$ .

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