### GMAT Algebra in Detail

To tackle GMAT effectively, a root level knowledge of the syllabus is of utmost importance. This knowledge not only helps in defining the boundaries of the test but also for assessing one’s strengths and weaknesses in the areas.

Let’s look at the GMAT-Quant: Algebra syllabus in detail. The questions from Algebra part can be from the following topics:

1.
**Absolute
Values:** Absolute value is the **magnitude
of a real number** without regard to its sign. E.g. |-2| = 2 and |2| = 2.
Here irrespective of the sign the value is always 2. The symbol || is called
the modulus.

2.
**Exponential
Equations:** In exponential
equations, the **variable** is located in the **exponent or power**. E.g. **a ^{x }= a^{y}**

^{ }then x=y (when a is a non zero entity.) In this equation

**a**is called the

**base, x, and y**are called the

**exponents.**The whole equation is called an

**exponential equation.**

Basic laws
of exponents are:

3.
**Exponential
Powers:** Exponential powers
define the number of times the **base** has to be **multiplied by** itself.
E.g. 2^{3 }= 2*2*2. That is the **base** 2 is to be **multiplied**
3 times which is the **exponent. **The basic laws of exponential powers are:

4.
**Roots
and Radicals:** Radical is the **opposite
to the exponent power operation**.

E.g.
Consider,√2. The **square root** is called **Radical**
and the **number 2** is called **Radicant. **To define a cube root, a 3
is placed on the radical and for a fourth root a 4 and so on. Some common operations include:

Memorizing
these squares and radicals will help in beating the time at the exam.

5. **Inequalities:** Inequalities basically defines **how different** two quantities are.

The less than (<), greater than (>), less than or equal (<=), greater than or equal (>=) and not equal to (≠) operators are the general symbols used for comparison between equations and numerical values.

6.
**Linear
Equations**: Linear equations
are the equations in which the **maximum powers** **of a variable is 1.**

E.g.
X+Y+2=0 is a **linear equation** because the **highest power of X/Y in the
equation is ‘1’**. As opposed to **non-linear equations** whose powers are
**not 1**. E.g. X^{-2 }+Y^{-2 }+ 2 = 0.

7.
**Order of
Operations**: When proceeding to
deal with a complex set of operations, there is a need to consider the order by
which the mathematical problem should be approached.

E.g. Consider the
equation, (3+4*6+(5+4)), this can have results like 51 if we proceed from left
to right, or 55 if we proceed from the right to left. But both the results are
wrong and the **correct answer is 36**.

A simple rule is to memorize the order of operations. P – Parentheses E – Exponents M – Multiplication D – Division A – Addition S – Subtraction.

8.
**Quadratic
Equations:** If the **maximum
powers** of variables, in an equation, **is ‘2’** then that equation is
considered as a Quadratic Equation.

E.g. X^{2
}+2XY +Y^{2 }= 0 is said to
be a quadratic equation. Memorizing the factoring methods and the quadratic
root formula can help in winning time in the test.

·
a^{2}–b^{2}=(a+b)(a−b).

·
a^{2}+2ab+b^{2}=(a+b)^{2}.

·
a^{2}–2ab+b^{2}=(a−b)^{2
}.

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