Important concepts for GMAT Mathematics  Part 1
Numbers
Fractions to decimals
Powers of Numbers
Other Numbers
Arithmetic
Order of operations
Fractions
Adding Fractions

Subtracting Fractions

Multiplying Fractions

Dividing Fractions

Dividing Exponents

Multiplying small numbers

ALGEBRA
Simultaneous equations
The first step is to try to eliminate one of the unknowns. Here is an example of solving by substitution.
 Equation 1: 3x + y = 7
 Equation 2: 3x  2y = 10
Using Equation 1 to write y in terms of x gives y = 7  3x. Plugging into equation 2 gives 3x  2(7  3x) = 13. Solving x yields x = 3. Plugging in the expression for y gives y = 2.
One equation with two unknowns
Two unknowns can sometimes be solved in one equation under certain constraints.
 Ex: 9x + 5y = 52, with x and y as positive integers. Here, the only possible solution is x = 3, y = 5.
 Ex: Alex bought x headphones at $9 each and y earphones at $5 each, spending $52 in total. How many earphones did he buy?
We get the same equation 9x + 5y = 52. Be aware of that implicit assumption that x and y are positive integers.
Three Important Algebra Patterns
 Pattern #1: The Difference of Two Squares : A^{2}  B^{2}=(A  B)(A + B)
 Pattern #2: The Squares of a Sum : ( A + B )^{2} = A^{2} + B^{2} + 2AB
 Pattern #3: The Squares of a Difference : ( A  B )^{2} = A^{2}  B^{2} + 2AB
What is the strategy for formula problems with unspecified amounts?
Ex: "The speed of the rocket was increased a certain amount.."
Pick smart (easytoworkwith) numbers! (formula: change/original = %change)
What is the equation for linear sequences?
Sn = k(n) + x
Where k is the constant difference between successive terms.
x is the constant that determines S1 (must be solved for)