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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GMAT Data Sufficiency Problem of the Day!

Check out this mean and consecutive numbers question from GMAT Prep!

What is the average (arithmetic mean) of 11 consecutive integers?

1) the average of the first nine integer equals 7
2) the average of the last nune integer equals 9.

To start, recognize that this is a “value” DS question, so we need to know the exact average in order to have sufficiency.

Average = sum of terms/ # of terms

Avg = (a + b + c + d + e + f + g + h + i + j + k) / 11

We know the 11 numbers are consecutive, so we need to know at least one of the numbers and its placement to find the set.

STATEMENT 1.

7 = (a + b + c + d + e + f + g + h + i) / 9

63 = a + b + c + d + e + f + g + h + i

What 9 consecutive numbers sum to 63?

Let’s call the middle number x. We can re-write the sequence as:

63 = (x – 4)+(x – 3)+(x – 2)+(x – 1)+(x)+(x + 1)+(x + 2)+(x + 3)+(x + 4)

63 = 9x

7 = x = middle number of the first 9 terms. We can find the other numbers now since we know they are consecutive integers.

The set is 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

SUFF.

STATEMENT 2.

The same logic applies. We can determine the set. The answer is (D).

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!