Mental Reasoning 7- Inequality: Questions and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank, Railways

Mental Reasoning 7- Inequality: Questions and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank, Railways

Inequality reasoning is one of the most common and high-scoring topics in competitive exams like SSC, Bank, Railways, NDA, CDS, BPSC, etc. Let’s cover it from basics to advanced, with all likely types, bilingual explanation, concept, rules, tricks, and examples — so you master every possible pattern.

Mental Reasoning – Inequality

1. Concept (Basic Idea)

Inequality reasoning tests your ability to compare elements (letters/numbers/symbols) based on a given relationship.

You are given statements (relations) and conclusions — you must decide whether the conclusion follows logically from the statement(s).

Example:
Statement: A > B ≥ C = D < E
Conclusion: A > D → True or False?

Hindi:
Inequality में अलग-अलग प्रतीकों (>, <, =, ≥, ≤) के माध्यम से दो या अधिक तत्वों के बीच संबंध दिया जाता है।
आपको निष्कर्ष (conclusion) सही या गलत तय करना होता है।

2. Common Symbols Used

3. Basic Rules of Comparison

When comparing two different elements, always look for a clear, direct relationship through given statements.

Rule 1 – Direct Relation

If A > B and B > C → A > C

Hindi:
अगर A बड़ा है B से और B बड़ा है C से → तो A बड़ा है C से।

Rule 2 – If the direction is opposite, relation can’t be determined

If A > B and B < C → A ? C (indeterminate)

Hindi:
अगर संबंध विपरीत दिशा में है तो कोई निश्चित निष्कर्ष नहीं निकलेगा।

Rule 3 – Equality Chain

If A = B and B = C → A = C

Rule 4 – Mixed Relations

If A > B = C < D → Then A ? D → Can’t be determined

Rule 5 – Inequality Signs Reversal Rule

When you reverse a statement, reverse the symbol too

• If A > B → B < A
• If A ≤ B → B ≥ A

4. Steps to Solve

1.  Write all statements clearly.
2. Combine statements with common elements.
3. Find direct connection between elements in the conclusion.
4. Check for conflict or opposite signs.
5. Determine the correct logical conclusion.

5. Probable / Likely Types of Question

Type 1 – Direct Comparison

Statement: A > B, B > C
Conclusion: A > C → ✅ True

Hindi: A > B और B > C → तो A > C

Type 2 – Opposite Direction (Indeterminate)

Statement: A > B, C > B
Conclusion: A ? C → ❌ Can’t be determined

Hindi: दिशा विपरीत है → निश्चित नहीं कहा जा सकता

Type 3 – Equal + Inequality Mix

Statement: A = B ≥ C
Conclusion: A ≥ C → ✅ True

Type 4 – Multiple Statements

Statement:
A > B = C < D ≥ E
Conclusion: A ? D → ❌ (Cannot be compared directly)

Hindi: जब बीच में प्रतीक बदलते हैं → संबंध अनिश्चित

Type 5 – Combination Chain

Statement: P ≥ Q, Q = R, R > S
Conclusion: P > S → ✅ True

Type 6 – Multiple Conclusions (True / False / Either / Neither)

Sometimes 2 conclusions are given —
You must decide:

• Only I follows
• Only II follows
• Both follow
• Either I or II follows
• Neither follows

Example:
Statement: A > B = C
Conclusions:
(I) A > C
(II) C < A

→ Both same meaning → Either I or II follows

Hindi: जब दोनों निष्कर्ष समान अर्थ रखते हों, “Either” सही होता है।

Type 7 – Symbol Inequality (with artificial codes)

In these, new symbols are introduced with specific meanings.

Example:
If A @ B means A > B
A # B means A = B
A $ B means A < B

Find relation between A and C:
If A @ B $ C → A > B < C → A ? C → ❌ Indeterminate

Hindi:
नए प्रतीक (जैसे @, $, #) के अर्थ दिए जाते हैं → उसी के अनुसार तुलना करें।

Type 8 – Negative Statements (≠)

Statement: A ≠ B, B > C
Conclusion: A > C → ❌ Cannot be determined

Hindi: बराबर न होना का अर्थ केवल “अलग” है, दिशा नहीं बताता।

Type 9 – Coded Inequality (Mixed Logic)

Given:
A + B means A ≥ B
A × B means A = B
A – B means A < B

Then find:
If P + Q × R → P ≥ Q = R → P ≥ R

Answer: True

Type 10 – Reverse Inequality Chain

Statement: A ≥ B ≥ C ≥ D
Conclusion: D ≤ B → ✅ True

6. Golden Rules (Quick Summary Table)

7. Sample Questions (Bilingual with Solution)

Q1.

Statement: A > B ≥ C = D < E
Conclusion: A > D → ✅ True
Explanation: A > B ≥ C = D → A > D

Hindi:
A > B ≥ C = D → A बड़ा है D से → निष्कर्ष सही

Q2.

Statement: P ≥ Q = R < S
Conclusion: P ? S → ❌ Cannot be determined
Hindi: दिशा बदल गई → निष्कर्ष अनिश्चित

Q3.

Statement: A = B > C ≥ D
Conclusion: A > D → ✅ True
Explanation: A = B → B > C ≥ D → A > D

Q4.

Statement: W ≥ X = Y ≤ Z
Conclusion: W ? Z → ❌ Cannot be determined

Q5.

Coded Example:
If A @ B means A > B
A # B means A = B
A $ B means A < B
Find relation between A and C if A @ B $ C
→ A > B < C → Can’t be compared

8. Quick Tricks for Fast Solving

✅ Combine chains of same direction only.
✅ Use comparison elimination: focus only on letters in conclusion.
✅ Ignore middle letters once combined.
✅ If both signs “>” and “<” appear between two elements → no relation possible.
✅ Always reverse symbol when reversing statement.

Hindi:

• समान दिशा में chain बनाएं
• केवल निष्कर्ष के letters पर ध्यान दें
• विपरीत प्रतीक आने पर कोई निश्चित संबंध नहीं

Summary (You Must Remember)

• 5 Main Symbols → >, <, =, ≥, ≤
• Relation exists only when direction same
• If opposite direction → No definite relation
• Always reverse inequality when reversing letters
• Use Either / Neither rule when both conclusions are complementary