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Basic Symbol Inequality

Basic Symbol Inequality problems present mathematical inequalities using coded symbols (e.g., @ means >, # means <, $ means =). You must decode the symbols, understand the relationship between variables, and determine which conclusions logically follow from the given statement. These problems test your ability to interpret symbolic representations and apply basic inequality rules.

10Worksheets
200+Practice Questions
BeginnerDifficulty
1-2 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Basic Symbol Inequality

Basic Symbol Inequality problems present mathematical inequalities using coded symbols (e.g., @ means >, # means <, $ means =). You must decode the symbols, understand the relationship between variables, and determine which conclusions logically follow from the given statement. These problems test your ability to interpret symbolic representations and apply basic inequality rules.

Prerequisites

Understanding of inequality symbols (>, <, =, ≥, ≤, ≠) Knowledge of transitive property Basic logical reasoning Ability to decode symbol mappings
Why This Matters: Basic Symbol Inequality is the foundation of coded inequality problems. You can expect 2-3 questions in SSC CGL, 2-3 in Banking PO, and 2-3 in Railways RRB exams.

How to Solve Basic Symbol Inequality Problems

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Step 1: Note the symbol mapping provided (e.g., @ = >, # = <, $ = =)

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Step 2: Replace each coded symbol with its actual mathematical meaning

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Step 3: Write the decoded inequality statement clearly

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Step 4: Analyze the relationship between variables using the inequality chain

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Step 5: Evaluate each conclusion independently against the decoded statement

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Step 6: Apply transitive property: if A > B and B > C, then A > C

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Step 7: Determine which conclusions must be true based on the given information

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Step 8: Select the appropriate answer (I only, II only, Both, Neither, or Either-Or)

Pro Strategy: Always decode the entire statement first before evaluating conclusions. Use the transitive property carefully - it only works when the inequality signs point in the same direction (e.g., A > B > C gives A > C; A < B < C gives A < C). When signs are opposite (e.g., A > B < C), no direct relationship exists between the outer variables.

Example Problem

Example: If @ means >, # means <, and $ means =, decode the statement: A @ B # C. Which conclusion follows? Solution: Step 1: Symbol mapping: @ = >, # = <, $ = = Step 2: Decode: A @ B # C becomes A > B < C Step 3: Relationship: A is greater than B, and B is less than C Step 4: No direct relationship can be established between A and C (A could be greater than, less than, or equal to C) Step 5: Conclusion 'A > C' may or may not be true → does not follow Step 6: Conclusion 'B < C' is directly given → follows Answer: Only the conclusion stating B < C follows

Pro Tips & Tricks

  • Memorize common symbol mappings: @, #, $, %, ^, & are frequently used
  • Decode the entire statement before looking at conclusions
  • For transitive relationship, all intermediate signs must point the same direction
  • When signs are opposite (>< or <>), no definite conclusion exists between outer terms
  • A single statement can have multiple valid conclusions
  • Use the 'chain method': write variables in order with their relationships

Shortcut Methods to Solve Faster

A > B and B > C → A > C (transitive)
A < B and B < C → A < C (transitive)
A > B and B < C → no definite relation between A and C
A = B and B = C → A = C
A ≥ B and B ≥ C → A ≥ C
A ≤ B and B ≤ C → A ≤ C
A > B and B = C → A > C
A < B and B = C → A < C

Common Mistakes to Avoid

Applying transitivity incorrectly when signs point in opposite directions
Forgetting to decode all symbols before analysis
Assuming a conclusion is false when it could be true (possibility vs certainty)
Confusing '≥' with '>' (greater than or equal vs strictly greater)
Missing that 'A ≠ B' means A is either greater than OR less than B

Exam Importance

Basic Symbol Inequality is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
2-3 questions
CAT
1-2 questions
INSURANCE
2-3 questions

Ready to Master Basic Symbol Inequality?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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