### All GRE Math Resources

## Example Questions

### Example Question #1 : Right Triangles

Quantitative Comparison

Column A

Area

Column B

Perimeter

**Possible Answers:**

Cannot be determined

Column A is greater

Column B is greater

Column A and B are equal

**Correct answer:**

Column A and B are equal

To find the perimeter, add up the sides, here 5 + 12 + 13 = 30. To find the area, multiply the two legs together and divide by 2, here (5 * 12)/2 = 30.

### Example Question #1 : Right Triangles

Given triangle *ACE* where *B* is the midpoint of *AC*, what is the area of triangle *ABD*?

**Possible Answers:**

48

72

24

96

**Correct answer:**

24

If B is a midpoint of AC, then we know AB is 12. Moreover, triangles ACE and ABD share angle DAB and have right angles which makes them similar triangles. Thus, their sides will all be proportional, and BD is 4. ^{1}/_{2}bh gives us ^{1}/_{2 }* 12 * 4, or 24.

### Example Question #46 : Triangles

What is the area of a right triangle with hypotenuse of 13 and base of 12?

**Possible Answers:**

60

30

78

156

25

**Correct answer:**

30

Area = 1/2(base)(height). You could use Pythagorean theorem to find the height or, if you know the special right triangles, recognize the 5-12-13. The area = 1/2(12)(5) = 30.

### Example Question #47 : Triangles

Quantitative Comparison

Quantity A: the area of a right triangle with sides 10, 24, 26

Quantity B: twice the area of a right triangle with sides 5, 12, 13

**Possible Answers:**

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Quantity A is greater.

**Correct answer:**

Quantity A is greater.

Quantity A: area = base * height / 2 = 10 * 24 / 2 = 120

Quantity B: 2 * area = 2 * base * height / 2 = base * height = 5 * 12 = 60

Therefore Quantity A is greater.

### Example Question #48 : Triangles

Quantitative Comparison

Quantity A: The area of a triangle with a height of 6 and a base of 7

Quantity B: Half the area of a trapezoid with a height of 6, a base of 6, and another base of 10

**Possible Answers:**

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

The relationship cannot be determined from the information given.

**Correct answer:**

Quantity B is greater.

Quantity A: Area = 1/2 * *b* * *h* = 1/2 * 6 * 7 = 42/2 = 21

Quantity B: Area = 1/2 * (*b*_{1} + *b*_{2}) * *h* = 1/2 * (6 + 10) * 6 = 48

Half of the area = 48/2 = 24

Quantity B is greater.

### Example Question #49 : Triangles

The radius of the circle is 2. What is the area of the shaded equilateral triangle?

**Possible Answers:**

**Correct answer:**

This is easier to see when the triangle is divided into six parts (blue). Each one contains an angle which is half of 120 degrees and contains a 90 degree angle. This means each triangle is a 30/60/90 triangle with its long side equal to the radius of the circle. Knowing that means that the height of each triangle is and the base is .

Applying and multiplying by 6 gives ).