Learnist: Simplifying Algebraic Expressions on the GMAT

Algebra is fundamental to GMAT Quant. A great way to get started on your GMAT prep is to refresh your skills in simplifying algebraic expressions!

PEMDAS is an acronym for the order of operations, which are the basic rules which govern the simplification of algebra. Notice how division/subtraction is always done in order from left to right.

Addition and multiplication are both “commutative” which means it doesn’t matter the order in which the operation is performed. This means that A + B = B + A, and A x B = B x A.

The Associative Property for addition and multiplication means that the numbers can be re-grouped in parentheses without a different outcome. For example, 2 + (3 + 7) = (2 + 3) + 7. Like the Commutative law, this is ONLY true for addition and multiplication.

The Distributive law allows us to “distribute” a factor among terms being added or subtracted. That is, a(b + c) = ab + ac. This law, along with the commutative and associative laws, will become second-nature to you the more you practice!

Remember this rule: you can ONLY cancel factors. Try to simplify the numerator and the denominator as much as possible if you’re looking for things to cancel.

Notice that algebraic expressions can be made more complicated with exponents, including negative exponents. Remember your exponent rules! When you have the same base in the numerator and the denominator, you can subtract the exponents.

Watch some video walk-throughs of some GMAT algebra problems involving order of operations and algebraic expressions on the GMAT – Simplifying Algebraic Expressions learnboard.

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Learnist: How the GMAT Tests “Volume”

Volume is the three-dimensional area — the amount of space enclosed by a shape or object. Remember that you need three different values to find volume and surface area (the length, the width and the height) on the GMAT.

Think of any box — a “rectangular solid” is a just a 3-D rectangle. Find the volume by calculating the length x width x height. Find the surface area by calculating 2lw + 2lh + 2wh.

Like the rectangular solid, to find the volume of a cylinder you will calculate the area of the base and multiply it by the height. For a cylinder, the area of the base will always be equal to the area of a circle: pi x r^2. Just multiply it by “h” to find the volume!

Try a couple practice questions on this GMAT – Volume learnboard!

Compound Interest on the GMAT

“Compound interest” occurs when interest earned is added to the principal, which then earns interest. If you’re an investor, compound interest is a very good thing! Usually interest appears on the GMAT in the form of a word problem. Let’s solve one together!

An amount is deposited into an account accruing interest annually at a fixed percentage rate. It is valued at $900 in the third year (after interest has compounded twice), and $1080 in the fourth year (after interest has compounded three times). What is the original amount?

A) 540
B) 600
C) 625
D) 750
E) 800

To calculate the amount earned under compound interest under a certain period of time, you need to know three pieces of information: 1) the initial principle “P”, 2) the rate of interest “R”, and 3) the number of times it compound per year. You will always raise the rate to a power equal to the number of times it compounds.

For example, the amount in an account started with an initial investment of $200 and earning compound interest at a rate of 8% compounded three times a year would be found by the equation:

1 + (8/100)^3 * 200 = Final Amount

Knowing this, we can set up these formulas with the given information from this problem:

(1+(R/100)^2)*P = 900
(1+(R/100)^3)*P = 1080

We can put R/100 so that the R will be the percent and not a decimal. Then we can divide the 2nd equation by the 1st to get:

(1+ R/100)= 1080/900
1 + R/100 = 1.2

Now we can plug in 1.2 for (1 + R/100) into our original equation to find the “original amount”:

1.2^2*P = 900
1.44 * P = 900
P = 900/1.44
P = 625

The answer is (C).