Inequalities Tips and Tricks for Government Exams

Introduction

In such types of questions of Inequality, a group of elements is given with a certain coded relationship denoted by <, >, =, ≤, ≥ and ≠.

To understand the symbols, let us discuss the meaning of the given symbols:

• ‘X > Y’; Here, the symbol ‘>‘ means ‘greater than’, hence the relation shows that X is greater than Z.
• ‘X < Y’; Here, the symbol ‘<‘ means ‘smaller than’, hence the relation shows that X is smaller than Z;
• ‘X = Y’; Here, the symbol ‘=’ means ‘equal to’, hence the relation shows that X is equal to Z;
• ‘X ≤ Y’; Here, the symbol ‘≤’ means ‘either smaller than or equal’, hence the relation shows that X is smaller than or equal to Z;
• ‘X ≥ Y’; Here, the symbol ‘≥’ means ‘either greater than or equal’, hence the relation shows that X is greater than or equal to Z;
• ‘X ≠ Y’; Here, the symbol ‘≠’ means ‘not equal’, hence the relation shows that X is not equal to Y.

Tips

• If in a question, K < M < L is given, then K < M, M < L and K < L are considered to be true.
• If in a question, K > M ≥ L is given, then K > L is considered to be true and K ≥ L is not true.
• If in a question, K ≥ L = M is given, in that case, either K > M or K = M is true.
• If in a question, K < M > L is given, then no relation can be found between K and L because of opposite symbols.

Types

1. Single statement Inequality: 

• In this type of question, the relation between the elements is given in a single series by coded relationship symbols i.e. <, >, =, ≤, ≥ and ≠. 

2. Multiple statements Inequality:

• In this type of question, the relation between the elements is given in two or more different series. To get the exact relation, we have to arrange it by matching the similar elements in a single series.

3. Not equal types Inequality:

• In this type of question, the ‘≠’ (not equal) relation are given between the elements. The not equal symbol is meant to show a comparison between the two quantities which are unequal hence, among the two quantities one will be either greater or smaller than the other quantity. To get the exact relation, we have to consider the both possibilities i.e. either ‘>’ or ‘<‘. 

4. Filler Inequality:

• In this type of question, the relation between the elements is not given and in the place of coded symbols (which represented by <, >, =, ≤, ≥ and ≠) blank or space was/were given. You have to find out the proper coded symbol/s to fill the blank or space according to a certain conditions which generally mentioned with the questions. 

5. Conditional Inequality:

• It is an inequality which is true for some variables or for a particular condition but not true for all values of variables.  And the solution of inequality consists of only real numbers as the term ” Less than or Greater than” are not defined for establish a certain relation. 

Solved Examples