GMAT Basics: Simplifying Algebraic Expressions:

by on September 1st, 2011

The GMAT contains a lot of algebra. Don’t feel guilty is you can’t recall the difference between an “integer” and a “whole number” or if your Quant understanding is limited. The GMAT won’t test your knowledge of definitions per se, but a good grasp of the basics of algebra is essential for a good GMAT score and for achieving your MBA.  Let’s start with the basics! An algebraic expression is a mathematical statement which often uses constants and variables. For example: 10x – 14.

PEMDAS is an acronym for the order of operations, which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Always start with what is inside the parentheses then address any exponents to simplify an expression. Next, move left to right, doing all division and multiplication. Finally, again moving from left to right, do any addition or subtraction.  PEMDAS is important to memorize as it will tell you how to simplify expressions correctly.

For example, let’s look at this problem: 4 + 6 / 2 = ?

A GMAT student who didn’t know about PEMDAS, might try to solve from left to right, first adding, then dividing. That would give us a solution of 5. However, we know that division must come before addition! The correct answer is 7.

What about 7 + (2 × 4^2+ 1)? Using PEMDAS, first we will focus on the exponent.

7 + (2 x 16 + 1)

Multiplication comes before addition:

7 + (32 + 1)

And what is inside parentheses comes before what is outside:

7 + (33)

Then we add the final integers to solve:

40 is the answer!

Let’s look at a more challenging expression: –(x – (1 – (4 – 3x)) + 6x). With so many parentheses, where do we start? Begin with the inner-most, and work your way out!

– (x – (1 – (4 – 3x)) + 6x)

- (x – (1 – 4  + 3x) + 6x)

- (x – (-3 + 3x) + 6x)

- (x + 3 – 3x + 6x)

- (4x + 3)

- 4x – 3 is the correct simplification. Let’s look at an example GMAT function.

If f(x) = 3x + 4, what does f(6) = ?

Here, we plug what is inside the parenthesis for x.

f(x) = 3x + 4
f(x) = 3(6) + 4
f(x) = 18 + 4
f(x) = 22

Notice how we multiplied the 3 and the 6 BEFORE we added the 4. Another way the GMAT could present this problem would be to ask:

If f(x) = 3x + 4, what is x when f(x) = 16?

Here, we would plug in 16 for f(x).

f(x) = 3x + 4
16 = 3x + 4
12 = 3x
4 = x

The GMAT can make Functions questions harder by having more than one equation and requiring multiple steps to solve. Let’s see an example.

g(x) = x + 4

w(x) = 5x – 8

What is w(g(2)) = ?

Just like any algebra problem, we start with the innermost parentheses. We will first solve for g(2) by plugging the 2 into the “g” function.

g(x) = x + 4
g(x) = 2 + 4
g(x) = 6

Now we have, w(6) = ? So we will plug the 6 into the “w” function.

w(x) = 5x – 8
w(x) = 5(6) – 8
w(x) = 30 – 8
w(x) = 22

The answer is 22.

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