Inequality Formulas, Concepts, Short Tricks and Tips

Inequalities is a scoring and relatively simple topic in reasoning that frequently appears in major competitive exams like SSC, Banking, RRB, and State-level tests. In this blog, we have provided all the details from Inequality concepts and tricks to formulas and solved questions on Inequalities in reasoning from the 2024–25 exams.

What Is Inequalities in Reasoning?

In reasoning, Inequalities are statements that compare two elements using signs like >, <, ≥, ≤, and =. The task is to deduce the correct relation between two elements based on given statements.

These questions test your logical analysis, statement chaining, and decoding skills. Candidates are expected to apply transitive logic to deduce the answer quickly.

Why Is Inequalities Important in Competitive Exams?

Inequalities often come as one of the first few questions in reasoning sections because they’re fast to solve and easy to score. The questions are usually symbol-based and test your understanding of logical comparison.

ExamNo. of QuestionsDifficulty
SSC CGL / CHSL1–2Easy
IBPS PO / SBI PO3-4Moderate
RRB NTPC / Group D1Easy
State PSC / Police1–2Moderate

Uses of Symbols in Inequalities Questions

There are various types of symbols used in inequalities. The details of the symbols used in inequalities questions are as follows:

SymbolMeaningExample
>Greater thanA > B means A is greater than B
<Less thanA < B means A is less than B
Greater than or equalA ≥ B means A is either greater or equal to B
Less than or equalA ≤ B means A is either less or equal to B
=Equal toA = B means A and B are equal
Not equal toA ≠ B means A and B are not equal

Concepts Used in Inequalities

There are various concepts used in inequalities questions. The details of the concepts used are as follows:

ConceptDetails
Basic Symbols>, <, ≥, ≤, =, ≠
Opposite RelationsA > B → B < A
Transitive LogicIf A > B and B > C → A > C
Either-Or CaseWhen two conclusions are possible but only one is true
Coded InequalitiesSymbols are replaced with @, #, $, etc.
Definite vs IndefiniteOnly statements with complete chain yield a definite answer

What Are the Types of Inequalities Questions in Reasoning?

Inequalities questions appear in different formats across exams. Here’s a breakdown of the most common types:

  • Direct Inequality Statements – Straightforward comparison.
  • Coded Inequality – Symbols like @, # used instead of >, <.
  • Puzzle-Based Inequalities – Logic puzzle with multiple relations.
  • Mixed Concept – Inequality embedded with direction sense or syllogism logic.

Inequalities Formulas

The formulas used to solve inequalities reasoning questions are as follows:

  • If A > B and B > C ⇒ A > C
  • If A ≥ B and B > C ⇒ A > C
  • If A ≥ B and B ≥ C ⇒ A ≥ C
  • If A = B and B = C ⇒ A = C
  • A ≥ B and B ≤ A ⇒ A = B

Use chain-building logic and elimination to arrive at correct conclusions quickly.

Inequalities Tricks for SSC CGL and Other Exams

Here are some proven strategies to solve inequality questions efficiently:

  1. Draw chain diagrams to visualize relations.
  2. Start from individual statements, not conclusions.
  3. Combine statements logically, don’t jump to conclusions.
  4. Reverse symbols when flipping comparisons (A > B ⇒ B < A).
  5. For coded inequalities, decode each symbol first before solving.
  6. Eliminate wrong options using contradiction tests.
  7. Use “either-or” logic only when conclusions are mutually exclusive.

Solved Inequalities Questions from 2024–25 Exams

Memory-based questions from recent exams:

Q1. (SSC CGL 2024 Tier 1 Shift 2 – Memory-Based)
Statements: A > B = C ≥ D
Conclusion: A > D
Answer: True
Explanation: A > B = C ≥ D ⇒ A > D

Q2. (IBPS PO Prelims 2024 – Memory Based)
Statements: P ≥ Q > R, R = S
Conclusion: P > S
Answer: True
Explanation: Q > R = S ⇒ Q > S ⇒ P ≥ Q > S ⇒ P > S

Q3. (Memory Based Test)
Statements: M < N ≤ O, O > P
Conclusion: M < P
Answer: Cannot be determined
Explanation: M < N ≤ O and O > P ⇒ No direct relation between M and P

Inequalities Concepts for Bank Exams

Bank exams like IBPS PO, SBI Clerk often frame coded inequality questions with symbols like:

  • @ → greater than
  • → equal to
  • $ → less than
  • % → greater than or equal to

Example:
If A @ B means A > B, B # C means B = C
Then: What is the relation between A and C?

→ Decode first: A > B = C ⇒ A > C

Common Mistakes to Avoid while Solving Inequality

While solving Inequality reasoning questions, candidates must keep these in mind:

  1. Not reversing the symbol when flipping statements.
  2. Assuming conclusions without full chain logic.
  3. Skipping decoding in coded questions.
  4. Treating “≥” and “>” as the same – they are not.
  5. Failing to check for “either-or” cases properly.

FAQs

Q1. What are the five basic inequality symbols used in reasoning?

Greater than (>), less than (<), equal to (=), greater than or equal to (≥), less than or equal to (≤).

Q2. How to identify the correct conclusion from multiple inequality statements?

Combine the statements logically to form a chain between the target elements.

Q3. What does a coded inequality question mean?

It uses special symbols like @, #, $, % in place of standard inequality signs.

Q4. What is transitive logic in inequalities?

If A > B and B > C, then A > C — this is called transitive property.

Q5. Can inequality questions be puzzle-based?

Yes, sometimes combined with direction, blood relation, or seating logic.


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