Algebra is my pet hate of the GMAT (along with geometry and a few other things). I will here attempt to describe the little of it I do understand.
In algebra, numbers are often denoted by symbols (such as a, x, or y), this allows the reference to “unknown” numbers, the formulation of equations and the study of how to solve these (for instance, “Find a number x such that 3x + 1 = 10″). Algebraic Expressions are made up of terms; x, y, z and so forth are variable terms, meaning that we don’t really know what they are until we work them out.
Algebra is all about making complicated looking expressions into simpler, smaller ones. There are a few steadfast rules in how to do this.
- Most algebraic expressions consist of something like this “3x+14y = 2, solve for y” this looks confusing at the best of times. How could we find out what they want?
- The first step is to find out exactly what it is they are looking for, in this case it is “y“.
- Once we understand this it is clear that we need to find a way to rewrite this so that it reads “y= something“
- This means moving terms around, the best way to find what “y” is would be isolate it from the terms that are linked to the “x” in the expression.
- We can move terms around on both sides of the equation, but to do that it is important to keep the balance on either side of the “=” sign the same. This means that if we do something, it has to be done equally on both sides.
- Lets move the term “3x” over to be with the term “2“:
3x+14y =2
-3x = -3x
14y = 2 – 3x
- We have taken out “3x” on what side but had to take it out on the other side too. We thus now end up with “14y = 2-3x“, this is better but we need a single “y” and not 14 “y“.
- In any equation, if you want to “break” a term you need to do the opposite operation to what unites it. In this case “14y” is a multiplication (14 x y), we therefore we need to divide the whole thing by “14“
14y/14 = 2-3x/ 14
y = 2-3x/14
- The “x” side is still a little complicated but it doesn’t matter as this gives us a value for the term “y“
Useful Tips for Algebra:
Algebra has a few useful things to remember:
- In working out what the order of operations is for solving Algebraic Equations, you can remember PEMDAS (Please Excuse My Dear Aunt Sally) which actually stands for: Parenthesis, Exponents, Multiply, Divide, Add and Subtract.
Also remember the following rules on positive or negative signs to save time on the GMAT test day:
- Like signs will always give you a positive symbol:
Positive x Positive = Positive
Negative x Negative = Positive
- Unlike signs will always give you a negative symbol:
Negative x Positive = Negative
Positive x Negative = Negative
- On the GMAT, pay a lot of attention to the words used in the question. Out of 5 possible answer, 4 will be traps and only 1 will be correct. The 4 possible answers are designed for the people who don’t read the questions correctly or jump to a conclusion too soon.
- Always do the solutions step by step and write it down. When doing Algebra, a missed positive or negative sign or a small mistakes completely changes the solution and the GMAT is waiting for you with a tempting wrong answer that looks like it might just be right.
