Algebra

Question 1

Commutative property

Answer 1

Remember that, based on the commutative property, the order of the terms is not important. However, it is standard when writing simplified expressions to write coefficients first, then variables in alphabetical order. Since the GMAT nearly always adheres to this convention in the answer choices, you will recognize correct answers more efficiently if you also develop the habit of writing simplified answers in this standard order.

Question 2

Brackets

Answer 2

“Lock a variable, number, or expression within”

Question 3

Combine like terms/factors

Answer 3

Remember to combine like terms before factoring.

Question 4

Golden rule: What does “x in terms of y” refer to?

Answer 4

“x in terms of y” is an expression that equals x and only contains y (and known numbers).

In other words, “x in terms of y” is the right side of this equation:

x = 15y + 3y

Question 5

The fraction bar tells you to what?

Answer 5

To divide the entire numerator by the entire denominator. Tread carefully and respect PEDMAS

Question 6

Solve using the combination method:

5n + m = 17
2n + m = 11

Answer 6

If “+” shows up in both equations, we can kill “m” by subtracting the second equation from the first.

Question 7

Absolute value equations

Answer 7

Absolute value refers to the positive value of the expression within the absolute value brackets. Equations that involve absolute value generally have two solutions.

Use the following two-step method when solving for a variable expression inside absolute value brackets:

Step 1: isolate the expression within the absolute value brackets.

12 + | w - 4 | = 30
| w - 4 | = 18

Step 2: once you have an equation of the form
| x | = a with a greater than 0, you know that x = positive a. Remove the absolute value brackets and solve for a.

Case 1: x = a (x is positive)
w - 4 = 18
w = 22

Case 2: x = -a (x is negative)
w - 4 = -18
w = -14

Question 8

Solve using the combination method:

5n + m = 17
2n + m = 11

Answer 8

If “+” shows up in both equations, we can kill “m” by subtracting the second equation from the first.

Question 9

Absolute value equations

Answer 9

Absolute value refers to the positive value of the expression within the absolute value brackets. Equations that involve absolute value generally have two solutions.

Use the following two-step method when solving for a variable expression inside absolute value brackets:

Step 1: isolate the expression within the absolute value brackets.

12 + | w - 4 | = 30
| w - 4 | = 18

Step 2: once you have an equation of the form
| x | = a with a greater than 0, you know that x = positive a. Remove the absolute value brackets and solve for a.

Case 1: x = a (x is positive)
w - 4 = 18
w = 22

Case 2: x = -a (x is negative)
w - 4 = -18
w = -14

Question 10

Chapter 4: Fractional bases

Page 56, Manhattan prep

Answer 10

When the base of an exponential expression is a positive proper fraction, and as the exponent increases, the value of the expression DECREASES. The same principal applies to decimals: values decreases as their exponent increases.

Question 11

Fractional Questions: which is greater?

(-3/4)^3 or (-3/4)

Manhattan Prep, Page 65

Answer 11

Raising a proper fraction to a power causes that fraction to move closer to 0 on a number line.

Raising any negative number to an odd power will result in a negative number.

Question 12

Disguised quadratic equations

Page 86, Manhattan Prep

Answer 12

If I have a quadratic expression equal to 0, and I can factor an “x” out of the expression, then x=0 is a solution of the equation!

Question 13

How many ways to solve for a quadratic equation?

Page 86, Manhattan Prep

Answer 13

There are 3 ways primarily to solve for quadratics in the GMAT:

1. Factoring
2. Setting one side of the equation to 0
3. If the other side of the problem is a perfect square, the problem can be solve by taking the square root of both sides of the equation — just remember that if the variable is square, it could be positive or negative. Therefore, when I take the root, make sure to include that the answer could be positive or negative.

Question 14

One solution quadratics

Page 87, Manhattan Prep

Answer 14

Not all quadratics have two solutions. Some have only one. One-solution quadratics are also called PERFECT SQUARES because both roots are the same.

(z+4)(z+4)=0
z= —4

Question 15

Zero in the denominator and the affect on a quadratic equation: undefined

Page 88, Manhattan Prep

Answer 15

It is illegal to set the denominator equal to 0

Question 16

Special quadratic #1

Answer 16

X^2 - y^2 = (x+y)(x-y)

I may need to recognize this product when it is presented in different forms. For example:

a^2 - 1 = (a+1)(a-1)

Question 17

Special quadratic #2

Answer 17

x^2 + 2xy + y^2 = (x+y)(x+y) =
(x+y)^2

I may need to see this in different forms. For example:

(a+b)^2 = a^2 + 2ab + b^2