# Quant Ability

In compound interest, where the interest for each period is added to the principal before interest is calculated for the next period. With this method the principal grows as the interest is added to it. This method is used in investments such as savings account and bonds.

Problems based on ages are generally asked in most of the competitive examinations. To solve these problems, the knowledge of linear equations is essential.

A boat is said to go downstream if it is moving along the direction of the stream. The net speed of the boat in this case is called downstream speed. A boat is said to go upstream if it is moving in the direction opposite to the direction of the stream. The net speed of the boat in this case is called upstream speed.

Pipes are connected to a tank or cistern and are used to fill or empty the tank. Inlet is a pipe connected with a tank or a cistern or a reservoir, that fills it. Outlet is a pipe connected with a tank or a cistern or a reservoir, emptying it.

Number Systems forms the base for Quantitative Ability and clearing of concepts is important for CAT and other management exams. A measurement carried out, of any quantity, leads to a meaningful value called the Number. This value may be positive or negative depending on the direction of the measurement and can be represented on the number line.

### Factors of a Number

Representing a number as prime factors helps in analysing problems.

A divisibility rule is a method to determine whether a given integer is divisible by a fixed divisor without performing the division. You can do this by examining the digits of the integer.

Suppose there are two numbers, a and b. If a number a divides another number b exactly, then a is factor of b and b is called multiple of a.

The terms percent means for every hundred. Percentage is a way of expressing a number as a fraction of 100. It is denoted by using the percent sign, %. For example, when a person made a profit of 20 percent, it means that the person gained Rs. 20 for every hundred rupees invested in the business. Scoring 60 percent marks means out of every 100 marks the candidate scored 60 marks.

Business transactions have now-a-days become common feature of life. When a person deals in the purchase and sale of any item, he either gains or loses some amount. The aim of any business is to earn profit.

The lending and borrowing of money involves the concept of simple interest and compound interest. If you borrow money for certain period of time, you have to return the borrowed sum of money (Principal) with some extra money. This extra money is called Interest.

The terms "Time" and "Distance" are related to the speed of a moving object. The questions on speed, time and distance are based on one general formula: Distance = Speed × Time

In daily life, there are situations where we need to complete a particular job in a reasonable time. We have to complete the project earlier or later depending upon the needs. Accordingly, the men on duty have to be increased or decreased. The time and the men engaged for a project are inversely proportional to each other. The more the number of men involved, the lesser is the time required to finish a job.

Average is defined as the ratio of sum of the quantities to the number of quantities. Average or mean is said to be a measure of central tendency.

Mixtures are formed when two or more quantities of different values are mixed together. Alligation is a practical method of solving arithmetic problems related to mixtures of ingredients.

Ratio is a relation between two quantities or numbers. It is a relation that one quantity bears to another with respect to magnitude. A ratio of a and b is denoted by a:b and is read as a is to b. In a ratio, the first part (a) is called antecedent and second part (b) is called consequent.

A function p(x) of the form p(x) = a0 + a1x + a2x2 + ... + anxn where a0, a1, a2, ..., an are real numbers, an ≠ 0 and n is a non-negative integer is called a polynomial in x.

A Linear Equation is an equation whose graph is a straight line. Each term has a degree of atmost 1. Each term can have degree 0 (constant term) or degree 1. A linear equation in one variable is an equation that involves only one variable x. Geeral form of linear equation can be written as ax + b = 0. There are no higher or lower order terms such as x2, x3 or x1/2.

Linear Equation can have degree of at most 1 and has only one solution. Quadratic Equation can have degree of at most 2 and has two solutions.

A Progression is a sequence of numbers which have some kinf of relation. This relation determines what kind of a progression is. Generally, there are two types of progressions:

1. Arithmetic Progression (AP)
2. Geometric Progression (GP)

A function is a rule which indicates an operation to perform. A function is a relation between input and output. For example, there is a system, which finds the square of the given input. That means the output is a square of the given input.

Binomial Expression: An algebraic expression consisting of two terms with a positive or negative sign between them. Example: (x+y)

### Laws of Indices

am x an = a(m+n)

am / an = a(m-n)

(am)n = a(mn)

a(-m) = 1/(am)

a0 = 1

a1 = a

A comparison relationship between two algebraic expressions or quantities is known as an Inequalities.

Logarithm is the exponent or power to which a stated number called the base is raised to yield a specific number. For example, in the expression 102 = 100, the logarithm of 100 to the base 10 is 2.

Combination & Permutation deals with arrangement of thing. If the order doesn't matter, then it is called Combination. If the order does matter, then it is a Permutation.

Probability is the likelihood or chance of an event occurring.

Geometry is branch of mathematics concerned with shapes, sizes and properties of figures. Geometry includes knowledge of angles, lines, triangles, quadrilaterals, circles and polygons.

A triangle is a polygon of three sides. Sum of the angles of a triangle is 180 degrees. Triangles are classified in two general ways: by their sides and by their angles.

Two figures are said to be similar, if they have the same shape but not necessarily the same size. If the angles of one triangle are equal to the angles of another triangle, then the triangles are said to be Equiangular. Equiangular triangles have the same shape but may have different sizes. Therefore, equiangular triangles are also called Similar Triangles.

A quadrilateral is a polygon with four sides (edges) and four vertices (corners). The word quadrilateral is made of the words quad (meaning four) and lateral (meaning sides). So, quadrilateral is simply a four sided figure.

A square has four equal sides and four equal angles (90 degree angles or right angles). A rectangle is a quadrilateral with 4 right angles. It is similar to square except that its sides are not equal.

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides are parallel and equal in length. The diagonals bisect each other.

A circle is a locus of all points which are equidistant from a point. If O is a fixed point in a given plane, the set of points in the plane which are at equal distances from O will form a circle.

Mensuration is the branch of Mathematics which deals with the study of geometric shapes, their area, volume and different parameters in geometric objects.

Vedic Mathematics is a system of mathematics consisting of a list of 16 basic sutras, or aphorisms. They were presented by a Hindu scholar and mathematician, Bharati Krishna Tirthaji Maharaja, during the early part of the 20th century.