What I discovered using the 2005 edition of “Cracking the GMAT” (The Princeton Review) was that algebra problems can be solved without using algebra, but an easier method: plugging in.

Basically you just replace with number the unknown data represented with letters. Sounds stupid, but it works and you gain time.

Plugging in a number in the question:

1. Pick one or more numbers to replace the letters in the problem (question)
2. Using your numbers, find an answer to the problem
3. Plug your numbers into the answer choices to see which choice equals the answer you found in step 2

Plugging in a number in the answers:

1. Always start with answer C. Plug that number into the problem and check if it gives you a solution.
2. If choice C is too small, choose the next larger number
3. If choice C is too big choose the next smaller number

If the question contains “must be”, “could be” or “cannot be”, the problems can be solved by plugging in but you may need to plug more than one number.
You must have at least as many distinct equations as you have variables for the equation to be solvable.

ax² + bx + c = 0

x = [-b +/- √ (b²-4ac)] / 2a

Also, simultaneous equation can be solved an addition or subtraction of one equation from the other. This way you can eliminate one of the unknowns.

GMAT’ “most wanted”:

• (x + y) ² = x² + 2xy + y²
• (x + y)(x – y) = x² – y²

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The arithmetic for GMAT is simple, as is practically everything about GMAT.
Attention: Simple does not mean easy! It is not easy because you have the TIME constraint and your own pride.
We all make the mistake of paying less attention to something because is easy. I am not saying to you have to pay more attention to the problems. The GMAT problems are not THE PROBLEM. TIME is THE PROBLEM.
Remember the formulas and practice with them until they become a reflex. But pay attention to your own ego, that will whisper in your year “I can do this problem too”. When you feel that is taking you too much time, and this means ONE MINUTE, click a random answer and move on!

Now, arithmetic:

1.Rate x Time problems: The only formula you need is rate x time = distance         r x t = d

2. Work problems: ALWAYS think of how much of the job can be done in one hour.

3. Mix problems:

Interest = principal x interest rate x time.
Discount = if a price is discounted by n percent, the price becomes 100-n percent of the original price.|
Profit = revenues minus expenses = selling price minus cost.

4. Functions:

The strange character * or # is part of a fix unit not a formula. What you replace with numbers are letters like x or y.
Domain = the set of all allowable inputs for a function.
Sequence = a function defined only for input values that are the positive integers and possibly 0.

5. Probability.

An event is a particular set of outcomes.
Numerator = the number of possibilities that match what you want.
Denominator = the total number of possibilities.

Six-sided die:

1. one side, one time 1/6
2. two sides, one time 2/6
3. one side, both times 1/6 x 1/6 = 1/36
4. one side or another chosen first 1/6 + 1/6 = 2/6 = 1/3
5. the odds that one side does not happen 5/6
6. the odds that at least one side will happen 1- 5/6 = 1/6

6. Permutations and Combination.

Different source, order does not matters:

• When a problem ask you to choose a number of items to fill specific spots and each spot is filled from a different source, all you multiply the number of choices for each of the spots.

Single source, order matters:

• When a problem asks you to choose from the same source to fill specific spots, you multiply the number of choices for each of the spots. Attention: the number of choices keeps getting smaller. n! = n(n-1)(n-2) … x3x2x1

Single source, order matters but only for a selection:                An/k = n!/(n-k)!

Single source, order does not matters:       C n/k = n!/k!(n-k)!

7. Sets

Set = collection of numbers (elements) or other objects.
T = {1, 2 , 3, 4, 5}                   S = {1, 2, 3}.
|S| = 3 (number of elements).
S = subset of T

Union S U T = {1, 2 , 3, 4, 5}.
Intersection S ∩ T = {1, 2, 3}.
Disjoint or mutually exclusive = no elements in common.

Venn diagrams = google! :)
|S U T| = |S| + |T| – |S ∩ T|
If S and T are disjoint then |S U T| = |S| + |T| since |S ∩ T| = 0.

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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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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 1,4,5,10
• 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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On data sufficiency GMAT problems all the drawings are useless in solving the problem. Also remember TIME is of the essence. If you written down more than three rows of formulas for any GMAT problem … STOP … click on any answer and move on. The closer you think you are to the answer, the more time you loose!

If a question asks “what is x?” it means: can a single value for x be found?

For data sufficiency GMAT problems, when see the word “percent” think part/whole

For a data sufficiency statement to be sufficient there must be as many equations as there are variables.

• A single equation with two variables cannot be solved
• Two distinct equations with the same two variables can be solved, using simultaneous equations

Just because there is only one variable does not mean an equation has just one solution.

• An equation with a variable raised to an even power may have more than one solution
• An equation with a variable raised to an odd power will have only one solution

Data sufficiency yes or no: if a statement answers the question in the affirmative or in the negative, it is sufficient.

The answer can be no!!!

Never assume!!!

Just because one statement seems to agree with the other does not mean they are necessarily saying the same thing. !!!

When you look at Statement 2 always cover up Statement 1 and think like you never saw it. !!!

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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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