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 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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