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Coded Inequality

Coded Inequality problems present inequality statements using symbols (like @, #, $, %, &) instead of mathematical symbols. You are given a mapping (e.g., @ means >, # means <, $ means =) and must decode the statements to determine which conclusions follow logically.

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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 Coded Inequality

Coded Inequality problems present inequality statements using symbols (like @, #, $, %, &) instead of mathematical symbols. You are given a mapping (e.g., @ means >, # means <, $ means =) and must decode the statements to determine which conclusions follow logically.

Prerequisites

Understanding of inequality symbols (>, <, ≥, ≤, =) Symbol decoding skills Transitive property application Logical deduction
Why This Matters: Coded Inequality problems appear in 2-3 questions in SSC CGL and Banking PO exams. They test decoding skills and transitive reasoning.

How to Solve Coded 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 in the statement 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 by applying transitive property

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Step 6: Determine which conclusions must be true based on the decoded statement

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Step 7: Select the appropriate answer

Pro Strategy: Always decode the entire statement first before evaluating conclusions. Create a mapping table for quick reference. Apply transitive property only when all signs point in the same direction. When signs are opposite, no definite conclusion exists between the outer variables.

Example Problem

Example: If @ means >, # means <, $ means =. Decode: A @ B # C. Which conclusion follows? Solution: Step 1: @ = >, # = <, $ = = Step 2: A @ B becomes A > B, B # C becomes B < C Step 3: Decoded statement: A > B < C Step 4: Signs are opposite ( > then < ) → no direct relation between A and 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 B < C follows

Pro Tips & Tricks

  • Write the symbol mapping at the top of your workspace
  • Decode from left to right, replacing each symbol with its meaning
  • For chains with 3 or more variables, check direction consistency
  • If the chain has consistent direction, transitivity applies
  • If the chain changes direction (e.g., > then <), outer variables have no definite relation
  • The '=' symbol preserves direction and can be included in transitive chains

Shortcut Methods to Solve Faster

If all decoded symbols are > or ≥, the chain is descending
If all decoded symbols are < or ≤, the chain is ascending
Mixed > and < in the same chain → no transitive conclusion
A = B and B = C → A = C
A > B and B = C → A > C

Common Mistakes to Avoid

Forgetting to decode all symbols before analysis
Applying transitivity when signs point in opposite directions
Confusing the direction of coded symbols
Assuming a conclusion is false when it could be true

Exam Importance

Coded 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
GMAT
1-2 questions
INSURANCE
2-3 questions

Ready to Master Coded 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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