GMAT Formulas

Question 1

What is the formula for change in percent/ change in actual value?

Answer 1

Original + Change = New

** This equation is true for not only the percents but also actual amounts.

** Original percent is always 100%

**Percent change/Change in actual value =Change in Value/Original Value

Percent change/change in actual value= Absolute value of New Value-Old Value/Old value * 100

Question 2

What is the formula for new % or the new value?

Answer 2

New Percent = New Value/Original Value

Question 3

Sum of the interior angles of a polygon

Answer 3

(n-2)*180

Question 4

Area of a triangle

Answer 4

base*height/2

Question 5

Area of a rectangle

Answer 5

length*width

Question 6

Area of a trapezoid

Answer 6

(Base 1 + Base 2)*height/2

Question 7

Area of a parallelogram

Answer 7

base*height

Question 8

Area of Rhombus

Answer 8

Diagonal 1 * Diagonal 2/2

Question 9

Surface area

Answer 9

the sum of all of the faces ** rectangular solid and cube have six faces

Question 10

Volume

Answer 10

length*width*height

Question 11

List 2 key properties in any given triangle?

Answer 11

1) The sum of the three angles of a triangle equals 180. 2) Angles correspond to their opposite sides.

Question 12

What is the triangle inequality law

Answer 12

the sum of any two sides of triangle must be greater than the third side ( Note: the sum of the two sides cannot be equal to the third side, it must be GREATER than the third) AND The third side must be greater than the difference between the lengths of the other two sides.

** If you are given two sides of a triangle, the length of the third side must lie between the difference and the sum of the two given sides.

Question 13

List the common combinations of common right triangle: 3-4-5

Answer 13

3-4-5 (The most popular of all right triangles)

3²+4²=5² = (9+16=25)

Key Multiples: 2* (6-8-10)

                    3\* (9-12-15)

                    4\* (12-16-20)

Question 14

List the common combinations of common right triangle: 5-12-13

Answer 14

Also quite popular on the GMAT 5²+12²=13²= (25+144=169)

Key Multiples: *2(10-24-26)

Question 15

List the common combinations of common right triangle: 8-15-17

Answer 15

Not as frequent on the exam 8²+15²=17² ( 64+225=289)

No common combination

Question 16

What is the ratio of the isosceles triangle

Answer 16

The isosceles right triangle has one 90 angle (Opp hypo) and two 45 angles (opp the two equal legs).

The lengths of the legs of every 45-45-90 triangle have a specific ratio: 45 45 90

                                     leg     leg     hypotenuse

                                      1 :        1 :       √2 

                                      x :       x:     x√2

Question 17

Why is the isosceles triangle (45-45-90) so imp!

Answer 17

Isosceles triangle is very important because it is exactly half of a square. So if you put 2 (45-45-90) triangles together, you get a square. Therefore, if you are given the diagonal of the square, you can use the 45-45-90 ratio to find out the length of a side of the square.

Question 18

What is the ratio of the equilateral triangle

Answer 18

Equilateral triangle is made up of 2, 30-60-90 triangles.

30 60 90

short long hypotenuse

1 : √3: 2

x: x√3: 2x

Question 19

Translate: There are 40% more women than men?

There are 30% more cherries than apples

Answer 19

1.4m=w

c=1.3a

In questions like this, first set up equation that list both variances. ex: a=c. Question says that there are 30% more cherries so how can you balance the equation so both sides are equal if there are 30% more cherries on one side of the equation. You have to multiply apples by 1.3 so you get the equation to balance. Therefore: c=1.3a. So if you multiply apples by 1.3, the equation will equal cherries.

Question 20

Given a square with a side of length 5, what is the length of the diagonal of the square?

Answer 20

d= diagonal of square

d= s√2 , where s is a side of the square

Ans: length of the diagonal of the square 5√2 (5 is s (side))

Question 21

What is the measure of an edge of a cube with a main diagonal of length √60?

Answer 21

diagonal (d) of cube

d = s√3, where s is a side of the cube

Ans: length of a diagonal of the cube is:

d = s√3: √60 = s√3 → s = √60/√3 = √20

Question 22

If the rectangle has a length of 12 and a width of 5, what is the length of the diagonal?

Answer 22

To find the diagonal of a rectangle, you must know EITHER the length and the width OR ONE dimension and the proportion of one of the other.

Ans: 5-12-x is the common right angle. x = 13

Question 23

What is the formula for the “Deluxe” Pythagorean Theorem

Answer 23

d²= x²+y²+z² (x, y, z are the sides of the rectangular solid and d is the main diagonal).

This formula will provide you with main diagonal of a rectangular solid.

Question 24

Define similar triangles?

Answer 24

Triangles are defined as similar if all their corresponding angles are EQUAL and their CORRESPONDING SIDES ARE IN PROPORTION.

Question 25

Describe an observation that can be generalized about similar triangles in terms of its ratio of area?

Answer 25

If two similar triangles have corresponding side lengths in ratio a:b, then their **areas** will be in ratio a² : b². This principle is not limited to only triangles. This principle holds true for **ANY** similar figures: quadrilateral, pentagon etc. For similar solids with corresponding sides in ratio a:b, their **volumes** will be in ratio a³ : b³.