# GMAT Quantitative Section

##### GMAT Math Topics

GMAT Quantitative (or Math) is 62 minutes section where you will get 31 questions. Like Verbal Section, Quant Section is also Computer-Adaptive. You will get harder or easier question, depending on whether your previous answers was correct or wrong. And once you answer a question, you cannot go back to it.

##### Problem Solving

The Quantitative section of the GMAT uses problem solving and data sufficiency questions to gauge the skill level. Quantitative questions require knowledge of the following concepts.

##### Data Sufficiency

Data Sufficiency problems make up about two-fifths of the quantitative questions on the GMAT. They are not direct questions which ask to give the answer to the question. They ask to determine whether or not you can answer the question with the information given.

##### Substitution Technique for Solving GMAT Math Problems

Substitution is a very useful technique for solving GMAT math problems. It often reduces hard problems to routine simpler ones. In the substitution method, we choose some numbers that have the properties given in the problem and plug them into the answer choices.

##### Basic Principles of Numbers

These concepts form the foundation of more complicated problems, so it is important to know. For example, you could end up with a completely wrong answer if you solve for real numbers when the question asks for integers.

##### Real Numbers

All real numbers correspond to points on the number line and all points on the number line correspond to real numbers. All real numbers except zero are either positive or negative.

##### Properties of Integers

An integer is any number in the set {. . . –3, –2, –1, 0, 1, 2, 3, . . .}. Integers are positive and negative whole numbers.

##### Absolute Value

Absolute Value (or modulus) is the value of a number without regard to its sign. The absolute value of any number is always positive or zero.

##### Divisibility Rules

Divisibility Rules are important to check whether a number is divisible by any other number. This concept is used in many questions.

##### Exponents

As multiplication can be thought of as repeated addition, you can think of exponents as repeated multiplication. This means that 43 is the same as 4 × 4 × 4 or 64. 4means multiplying 4 three times. The result is 64. Here, 4 is the base and superscript 3 is the exponent. If you add a variable into this mix, such as 4b3, the base becomes b and the 4 becomes the coefficient.

##### Roots

Roots are also known as radicalsRoots are sort of the opposite of exponents. So, you square 3 to get 9, the square root of 9 is 3. There are as many roots as there are powers. Most of the time, the GMAT has you work with square roots, but you may also see other roots. If you come upon a cube root or fourth root, you can recognise it by the radical sign, √.

##### Fractions

Fractions, decimals, and percentages are interrelated concepts. They all represent parts of a whole. You can convert from one form to the other to solve several problems. Fractions are really division problems. If you divide the value of a by the value of b, you get the fraction a/b.

##### Decimals

In the decimal system, the position of the period or decimal point determines the place value of the digits. For example, the digits in the number 7,654.321 have the following place values.

##### Percents

Percent is a latin word which means per hundred or number out of 100. A percent can be represented as a fraction with a denominator of 100, or as a decimal.

##### Averages

Problems involving averages are very common on GMAT.

### Ratio

A ratio is the relation between two like numbers or two like values. A ratio may be written as a fraction (3/4), as a division expression (3÷4), or with a colon (3:4), or it can be stated as '3 to 4'. A ratio is simply a fraction. The ratio of the number a to the number b (b ≠ 0) is a/b.

##### Simplifying Algebraic Expressions

Algebra is just a form of arithmetic in which symbols (usually letters) stand for numbers. You use algebra to solve equations and to find the value of a variable. Algebra is based on the operations of arithmetic and on the concept of an unknown quantity, or variable. Letters such as x or n are used to represent unknown quantities. For example, suppose A has 5 more pencils than B, then the number of pencils that A has is B+5.

##### Linear Equations

A linear equation is an algebra equation that contains an unknown variable and no exponent greater than 1. In its simplest form, a linear equation is expressed as ax + b = y, where x is the variable and a and b are constants.

##### Inequalities

An inequality is a statement such as "x is less than y" or "x is greater than or equal to y". In addition to the symbols for add, subtract, multiply, and divide, Mathematics also applies standard symbols to show how the two sides of an equation are related.

When you set a quadratic polynomial equal to 0, you get a quadratic equation. Quadratic equation is an equation that can be written in the form ax2 + bx + c = 0, where a, b, and c are constants (real numbers) and a ≠ 0, and x is a variable that you have to solve for.

##### Functions

Functions are relationships between two sets of numbers; each number you put into the formula gives you only one possible answer. An algebraic expression in one variable can be used to define a function of that variable. A function is denoted by a letter such as f or g along with the variable in the expression.

##### Parallel and Intersecting Lines

Geometry starts with the basics - plane geometry, which is the study of lines and shapes in two dimensions. From that foundation, geometry constructs increasingly complex models to more accurately portray the real world. Three-dimensional, or solid geometry is almost as simple as plane geometry, with the added dimension of depth.

##### Angles

When two straight lines meet at a point, they form an angle. The point is called the vertex of the angle, and the lines are called the sides of the angle. The size of an angle depends on how much one side rotates away from the other side. An angle is usually measured in degrees or radians.

##### Triangles

A triangle is a three-sided shape whose three inner angles must sum to 180 degrees. The largest angle will be across from the longest side while the smallest angle will be across from the shortest side of the triangle. If and only if two sides of a triangle are equal, the angles opposite them will be equal as well.

##### Special Right Triangles

In a right triangle, one of the angle is of 90 degrees. The sum of other two angles will be 90 degrees. Two special right triangles are 45-45-90 and 30-60-90.

A quadrilateral is a four sided polygon. The sum of interior angles for all quadrilaterals must be equal to 360 degrees. There are five main types of quadrilaterals each having its own features.

##### Circles

A circle is the set of all points in a plane that are at a fixed distance from a given point. That point is called the center.

##### Polygons

A polygon is a two dimensional shape formed by connecting three or more line segments at vertices. The term originates from the Greek word "poly" which means "many" and "gon" which means "a closed figure".

##### Three-Dimensional Geometry

Three-dimensional geometry, or solid geometry, adds some depth to plane geometrical figures.

##### Coordinate Geometry

Coordinate geometry involves working with points on a graph that is known as the Cartesian coordinate plane. This perfectly flat surface has a system that allows you to identify the position of points by using pairs of numbers.

##### Sets

Group problems regard populations of persons or objects and the way these populations are grouped together into categories. The questions generally ask you to either find the total of a series of groups or determine how many people or objects make up one of the subgroups.

##### Permutation & Combination

The GMAT may test you on the arrangement of groups and sets, so you are likely to see some permutation and combination problems. When you calculate permutations, you figure out the number of ways the elements of a set can be arranged in specific orders. Determining combinations is similar to finding permutations, except that the order of the arrangements doesn’t matter.

##### Statistics

A list of numbers, or numerical data, can be described by various statistical measures. To evaluate data correctly, you need to know the central tendency of numbers and the dispersion of their values.

##### Probability

Probability is the measure of how likely a particular event will occur, but figuring probability is a bit more scientific than telling fortunes and reading tarot cards. You express probability as a percentage, fraction, or decimal.

##### Time & Speed Problems

The distance that an object travels is equal to the product of the average speed at which it travels and the time it takes to travel that distance. Rate is another word used in place of speed.

##### Work Problems

Work problems ask you to find out how much work gets done in a certain amount of time. You use this formula for doing algebra work problems: Production = Rate of Work × Time.

##### Mixture Problems

In mixture problems, substances with different characteristics are combined, and it is necessary to determine the characteristics of the resulting mixture. The question involves mixing of two substances with different concentrations resulting in a net mixture of definite concentration.

##### Interest Problems

Interest can be computed in two ways. With simple annual interest, the interest is computed on the principal only and is given by: Interest = Principle x Interest Rate x Time.

##### Discount

If a price is discounted by n percent, then the price becomes (100-n) percent of the original price.

##### Profit

Gross profit is equal to revenues minus expenses, or selling price minus cost. ##### Sets and Venn Diagrams

A set is simply a collection of objects or elements. For example, A is set of 5 numerical members as represented below.