CAT Inequalities : Basic Concepts and Notes PDF

An inequality in quantitative aptitude is a mathematical statement that compares two quantities and shows the relationship between them using symbols such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to). It is used to represent a range of values or conditions where one quantity is larger or smaller than the other.

Inequalities in quantitative aptitude are solved by following a set of rules. First, simplify the inequality by combining like terms and performing any necessary operations. Then, isolate the variable on one side of the inequality sign. If you multiply or divide both sides of the inequality by a negative number, the inequality sign must be reversed. Finally, represent the solution on a number line or in interval notation to indicate the range of values that satisfy the inequality.

There are several types of inequalities in quantitative aptitude, including: - Linear inequalities: Inequalities involving linear functions, where the variable has an exponent of 1 and the inequality sign is either <, >, ≤, or ≥. - Quadratic inequalities: Inequalities involving quadratic functions, where the variable has an exponent of 2 and the inequality sign is either <, >, ≤, or ≥. - Absolute value inequalities: Inequalities involving absolute value functions, where the variable is enclosed within absolute value symbols and the inequality sign is either <, >, ≤, or ≥. - Rational inequalities: Inequalities involving rational functions, where the variable is present in the numerator or denominator of a fraction and the inequality sign is either <, >, ≤, or ≥.

Inequalities are useful in quantitative aptitude as they allow us to represent and solve a wide range of real-world problems. They help in determining the possible range of values for a variable, finding conditions for certain events to occur, and making decisions based on given constraints. Inequalities are applicable in various fields such as economics, engineering, finance, and statistics, where analyzing and interpreting numerical data is essential.

When solving inequalities in quantitative aptitude, it is important to avoid the following common mistakes: - Forgetting to reverse the inequality sign when multiplying or dividing both sides by a negative number. - Combining like terms incorrectly or neglecting to simplify the inequality before isolating the variable. - Misinterpreting the solution by flipping the inequality sign or incorrectly representing it on a number line or in interval notation. - Forgetting to consider any given restrictions or conditions mentioned in the problem. - Failing to check the solution by substituting it back into the original inequality to ensure its validity. - Overlooking special cases or exceptions that may arise, such as when dealing with absolute value inequalities or dividing by variables.