### All GRE Math Resources

## Example Questions

### Example Question #21 : Geometry

The formula to find the radius of the largest circle that can fit in an equilateral triangle is , where is the length of any one side of the triange.

What is the largest diameter of a circle that can fit inside an equilateral triangle with a perimeter of cm?

**Possible Answers:**

cm

cm

cm

cm

**Correct answer:**

cm

The diameter is

To solve for the largest diameter multiply each side by 2.

The resulting formula for diamenter is

.

Substitute in 5 for S and solve. Diameter = = 2.89 cm

### Example Question #21 : Plane Geometry

Quantity A: The diameter of a circle with area of

Quantity B: The diameter of a circle with circumference of

Which of the following is true?

**Possible Answers:**

The relationship of the quantities cannot be determined.

Quantity B is larger.

Quantity A is larger.

Both quantities are equal.

**Correct answer:**

Quantity B is larger.

Consider each quantity separately.

**Quantity A**

Recall that the area of a circle is defined as:

We know that the area is . Therefore,

Divide both sides by :

Therefore, . Since , we know:

**Quantity B**

This is very easy. Recall that:

Therefore, if , . Therefore, Quantity B is larger.

### Example Question #22 : Plane Geometry

Quantity A: The diameter of a circle with area of

Quantity B: The diameter of a circle with circumference of

Which of the following is true?

**Possible Answers:**

Quantity B is larger.

The relationship between the quantities cannot be determined.

The two quantities are equal.

Quantity A is larger.

**Correct answer:**

Quantity B is larger.

Consider each quantity separately.

**Quantity A**

Recall that the area of a circle is defined as:

We know that the area is . Therefore,

Divide both sides by :

Therefore, . Since , we know:

**Quantity B**

This is very easy. Recall that:

Therefore, if , .

Now, since your calculator will not have a square root button on it, we need to estimate for Quantity A. We know that is . Therefore, . This means that . Therefore, Quantity B is larger.

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