You can find a lot of information online about the GMAT. I will only write what I thought it was important. Although most of the information required for the math part is basic, I was surprised to notice that time passed and my knowledge about math was fuzzy sometimes and I also need it an update of the English equivalents of the terms used.

Integers = negative or positive numbers. Do not include fractions.
= odd or even.

a=b x q + r (q=quotient r=remainder)
Distinct numbers = cannot be equal
Prime numbers = a positive integer that has exactly 2 different positive divisor (1 and itself). 0 and 1 are not prime numbers
Absolute value of 5 is |5|

Divisibility rules:

• 6 is divisible by 2
• the factors of 20 are 1,2,4,5,10
• 20 is a multiple of 4

Remember:
Most problems at GMAT require more than one step in getting the right answer!
If you are not a native English speaker learn the technical terms!

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For GMAT you do not only need to know English, but you need the basic and correct English.

First, some definitions:

• Noun = a word that is used to name a person, place, thing or idea
• Verb = a word that expresses action
• Adjective = a word that modifies a noun
• Adverb = a word that modifies a verb, adjective or adverb
• Preposition = a word that notes the relation of a noun to an action or a thing
• Phrase = a group of words acting as a single part of a speech. A phrase is missing either a subject or a verb or both
• Prepositional phrase = a group of words beginning with a preposition
• Pronoun = a word that takes the place of a noun
• Clause = a group of words that contains a subject and a verb

Pronoun errors that you meet in the GMAT problems can be identified asking the following questions:

• It is completely clear who or what the pronoun is referring to?
• Does the pronoun agree in number with the noun it is referring to?

Common pronouns:

• Singular: I, me, he, him, she, her, you, it, each, another, one, other, such, mine, yours, his, hers, ours, this, either, neither, each, everyone. Everybody, nobody, no one.
• Plural: we, us, they, them, both, these, those.
• Can be singular or plural: some, any, you, who, which, what, that.

Misplaced modifiers

• When a sentence begins with a participial phrase (a phrase that starts with a verb ending in “ing”), that phrase is supposed to modify the noun or pronoun immediately following it.
• Check that the noun is modified comes directly after the modifying phrase.

Parallel construction

If a sentence contains a list of things, or actions or is broken up into two halves, check to make sure the parts of the sentence are parallel.

Again, if your native language is not English, verify your knowledge tenses:

• Present
• Simple Past
• Present Perfect
• Past Perfect
• Future

Subject-verb agreement

• “The number of …” – singular
• “A number of …” – plural
• Singular pronouns: each, everyone, everybody, nobody

Quantity words

• If two items: between, more, better, less.
• If more than two items: among, most, best, least.

• Countable items: fewer, number, many.
• Non-countable items: less, amount, quantity, much.

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What you need to remember is that GMAT geometry problems always involve more than one step and that when a GMAT problem offers you just a ratio as answer, without any numbers to start from, you need to plug-in any number in the formulas you use.

Some basic tools refer to remembering number replacement and measurements used by GMAT.

• You need to memorize the following approximations: Π = 3, √1 = 1, √2 = 1.4, √3 = 1.7, √4 = 2
• For those used with the metric system memorize this: 12 inches = 1 foot and 3 feet = 1 yard

Also any drawings that have written next: “not drawn to scale” can not be measured.

Going back to the uses that the people which are not native English speaker:

• Line = straight line that extends without end in both directions
• Line segment = part of a line from one point to another
• Right angle = 90
• Perpendicular lines = two lines intersect at right angles
• Parallel lines = two lines in the same plane that do not intersect
• Polygon = closed plane figure formed by three or more line segments called sides
• Vertices = point of intersection of the sides
• Triangle = 3 sides polygon
• Quadrilateral = 4 sides polygon
• Pentagon = 5 sides polygon
• Hexagon = 6 sides polygon
• 180 degrees = sum of the interior angle measures of a triangle
• (n-2) x 180 degrees = sum of the interior angle measures of a polygon with n sides

Degrees and angles

• 360 degrees = circle.
• 180 degrees = line

When two parallel lines are cut by a third line, there appear to be eight separate angles, but there are really only two.( If you do not understand that, maybe is time for you to “Google” some more)

Triangles

• One side of a triangle can never be longer than the sum of the lengths of the other two sides of the triangle, or less than their difference
• Equilateral = all sides of equal length (the angles are also equal)
• Isosceles = two sides of the same length
• Right triangle = a right angle (opposite side = hypotenuse, the others = legs)
• Perimeter = the sum of the lengths of the three sides
• Area = (base x altitude)

Pythagorean Theorem = in a right triangle, the square of the hypotenuse equals the sum of the squares of the other sides.

a² + b² = c²

3 – 4 – 5; 6 – 8 – 10; 12 – 5 – 13; 12 – 9 – 15

A right isosceles triangle: 45 – 45- 90 = 1: 1: √2

A 30 – 60 – 90 triangle: 1: √3: 2

Circles

• Circle = a set of points in a plane that are all located the same distance from a fixed point (the center)
• Chord = a line segment that has its endpoints on the circle
• Diameter = a chord that passes through the center of the circle
• Radius = a segment from the center of the circle to a point on the circle (r)
• Length of an arc of the circle = the degree of the arc/360
• Tangent to a circle = a line that has exactly one point (point of tangency) in common with a circle
• Circumference = the distance around the circle. C = 2 Π r
• Area A = Πr²

Rectangles, squares and other four-sided objects

• Parallelogram = a quadrilateral with both pair of opposite sides parallel. Area = base x heights
• Rectangle = Parallelogram with right angles. Area = length x width
• Square = rectangle with all sides equal
• Trapezoid = a quadrilateral with two sides that are parallel. Area = small base x big base x height/2

Solids, volume and surface area

• Rectangular solid = a three dimensional figure formed by six rectangular surfaces.
• Area = sum of the areas of all the faces
• Volume = length x width x height

Cylinder

• Area = 2 Π r² + 2 Π r h
• Volume = Π r² h

Coordinate geometry - Coordinate plane

• X – Axis = horizontal line
• Y – Axis = vertical line
• Point 1 = (x1, y1); point 2 = (x2, y2)

Line in a coordinate plane: y = m x + b

b = y- intercept. m = slope.

m (slope) = (y2-y1) / (x2-x1)

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The math problems at GMAT are basic from 3 areas: Arithmetic, Algebra and Geometry.

Basic arithmetic operations:

• addition (8+8)
• subtraction (8-4)
• multiplication (8×3)
• division (8/2)
• raising to a power
• finding a square root

Fraction: x/y (part/whole) x = numerator, y = denominator.

Decimals are in English indicated by a point.

Ratio: The whole in ratio is sum of all parts. If ratio is a fraction the whole is the sum of the numerator and the denominator.

Average = total sum of the items/total number of the items.

Arithmetic mean = the process of finding an average.

How to find the Median:

1. first order the numbers from least to greatest
2. if n is odd, median is the middle number
3. if n is even, median is the average of the 2 middle numbers

Mode = the number or the numbers that occur most frequently in a list of numbers.

Range = the greatest value in the numerical data minus the least value.

Standard deviation = measures the distance between the arithmetic mean and the set of numbers.

1. first, find the differences between that average and each one of the set of numbers and square each of the differences
2. second, find the average of the squared differences and take the square root of this average

Frequency distribution: if a,b,c = numbers, f = frequency, av = average.

Standard deviation = √ {[(a-av) ² x f + (b-av) ² x f + (c-av) ² x f]/n.}

Exponents – multiplying, dividing, raising a power to a power, distributing.

In a percentage increase or decrease problem, you must put the amount of the increase or decrease over the original amount.
In compound interest problems, the answer will always be a larger number than it would be in a similar simple interest problem.

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