Module 1 · IBPS PO Reasoning Ability

Inequalities

Coded inequalities, direct inequalities, chain inequalities.

Direct Inequalities · Coded Inequalities · Chain Inequalities

🎯 Take Mock Test

Learning Objectives

Understand the fundamental concepts of Inequalities
Apply key formulas and techniques to solve problems
Practice with exam-level questions to build speed and accuracy

Key Concepts

What is Inequality?

Inequality questions in banking exams test your ability to compare quantities using mathematical inequality symbols and coded relationships. Given a set of statements with inequalities, you must determine which conclusions definitely follow. These are quick-scoring questions that appear regularly in IBPS PO, SBI Clerk, and RBI Grade B prelims.

Basic Symbols

1. Greater Than (>): A > B means A is greater than B.

2. Less Than (<): A < B means A is less than B.

3. Equal To (=): A = B means A equals B.

4. Greater Than or Equal To (≥): A ≥ B means A is greater than or equal to B.

5. Less Than or Equal To (≤): A ≤ B means A is less than or equal to B.

Coded Inequalities

In banking exams, symbols are often replaced with codes (e.g., @, #, $, %, &). A key is provided showing what each symbol means. For example: P @ Q means P > Q, P # Q means P < Q, P $ Q means P = Q, P % Q means P ≥ Q, P & Q means P ≤ Q. You then use these coded relationships to evaluate conclusions.

Rules for Combining Inequalities

1. Transitive Property: If A > B and B > C, then A > C. Similarly for <, ≥, ≤.

2. Combining ≥ and >: If A ≥ B and B > C, then A > C (the ≥ gets 'absorbed' by >).

3. Combining > and ≥: If A > B and B ≥ C, then A > C.

4. Combining ≤ and <: If A ≤ B and B < C, then A < C.

5. Combining < and ≤: If A < B and B ≤ C, then A < C.

6. Non-Transitive Cases: If A > B and B < C, NO relationship between A and C can be determined. Similarly for A ≥ B and B ≤ C, or A > B and B = C and C < D, etc.

Solved Examples

Example 1 (Direct Inequality)

Statements: P > Q ≥ R < S = T ≤ U
Conclusions: I. P > R II. T < S

Options: a) Only I follows b) Only II follows c) Both follow d) Neither follows

Solution: a) Only I follows. I. P > Q ≥ R → P > R ✓ (transitive property). II. T ≤ U and S = T, so T = S. The conclusion says T < S which is false. Therefore only I follows.

Example 2 (Coded Inequality)

Key: A @ B means A > B; A # B means A < B; A $ B means A = B; A % B means A ≥ B; A & B means A ≤ B.
Statements: M @ N # P $ Q % R
Conclusions: I. M @ Q II. N & R

a) Only I follows b) Only II follows c) Both follow d) Neither follows

Solution: d) Neither follows. Convert statements: M > N < P = Q ≥ R. I. M @ Q means M > Q. From M > N and N < P = Q, M and Q cannot be compared because M > N and N < Q → M could be >, <, or = Q. II. N & R means N ≤ R. From N < P = Q ≥ R, we have N < Q ≥ R. N could be ≤ or > R. So neither conclusion follows.

Example 3 (Chain of Inequalities)

Statements: A ≥ B > C = D ≤ E < F
Conclusions: I. A > D II. C < F III. B ≤ E

a) Only I follows b) Only I and II follow c) Only II and III follow d) All follow

Solution: b) Only I and II follow. I. A ≥ B > C = D → A > D ✓. II. C = D ≤ E < F → C < F ✓. III. B > C = D ≤ E → B > D ≤ E, so B could be >, =, or < E. No definite relationship. So only I and II follow.

Shortcut Techniques

When combining inequalities, always chain them in one direction. Convert ≤ and ≥ to consistent direction before combining.
If two variables have opposite inequality signs between them (e.g., A > B < C), no relationship can be determined.
For coded inequalities, first convert all coded statements into symbols using the key, then evaluate.
In 'either-or' cases, check if the two conclusions cover all possibilities for the relationship.

Pro Tip

In IBPS PO prelims, 3-5 inequality questions appear. They are among the fastest to solve — each can be done in 15-20 seconds once you master the transitive and non-transitive rules. Always check the 'either-or' condition carefully as it is a common trap.

Advanced Problem Types

Competitive exams feature advanced variations combining multiple reasoning concepts. Master these to score high.

Multi-Step Problems

Some questions require applying multiple reasoning techniques sequentially. Break problems into clear steps.

Common Traps

Assuming a pattern continues without checking all elements
Misinterpreting negative statements in syllogisms
Forgetting wrapping in alphabet coding (Z to A transition)
Confusing directions (East vs West)
Overlooking either-or cases in syllogisms
Not considering all possible arrangements in puzzles

Pro Tip

For puzzles, start with the most concrete clue and build around it. Draw diagrams for seating arrangements and family trees for blood relations.

Advanced Problem Types

Competitive exams feature advanced variations combining multiple reasoning concepts. Master these to score high.

Multi-Step Problems

Some questions require applying multiple reasoning techniques sequentially. Break problems into clear steps.

Common Traps

Assuming a pattern continues without checking all elements
Misinterpreting negative statements in syllogisms
Forgetting wrapping in alphabet coding (Z to A transition)
Confusing directions (East vs West)
Overlooking either-or cases in syllogisms
Not considering all possible arrangements in puzzles

Pro Tip

For puzzles, start with the most concrete clue and build around it. Draw diagrams for seating arrangements and family trees for blood relations.

Advanced Problem Types

Competitive exams feature advanced variations combining multiple reasoning concepts. Master these to score high.

Multi-Step Problems

Some questions require applying multiple reasoning techniques sequentially. Break problems into clear steps.

Common Traps

Assuming a pattern continues without checking all elements
Misinterpreting negative statements in syllogisms
Forgetting wrapping in alphabet coding (Z to A transition)
Confusing directions (East vs West)
Overlooking either-or cases in syllogisms
Not considering all possible arrangements in puzzles

Pro Tip

For puzzles, start with the most concrete clue and build around it. Draw diagrams for seating arrangements and family trees for blood relations.

Advanced Problem Types

Competitive exams feature advanced variations combining multiple reasoning concepts. Master these to score high.

Multi-Step Problems

Some questions require applying multiple reasoning techniques sequentially. Break problems into clear steps.

Common Traps

Assuming a pattern continues without checking all elements
Misinterpreting negative statements in syllogisms
Forgetting wrapping in alphabet coding (Z to A transition)
Confusing directions (East vs West)
Overlooking either-or cases in syllogisms
Not considering all possible arrangements in puzzles

Pro Tip

For puzzles, start with the most concrete clue and build around it. Draw diagrams for seating arrangements and family trees for blood relations.

Practice Questions

← Direction & Distance Data Sufficiency →