INEQUALITY – Reasoning Notes for CUET | CLAT | IPMAT

⭐ What is Inequality in Reasoning?

Inequality in reasoning is a topic where relationships between variables (A, B, C, D…) are given using symbols like

> , < , = , ≥ , ≤ , != , ?

Your task: find the relation between two elements or decide whether a conclusion is true, false or uncertain.

This topic appears frequently in CUET Reasoning, CLAT Logical Reasoning, IPMAT Quant/Logic, making it one of the highest-scoring areas.

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Important Inequality Symbols (Quick Revision)

Symbol	Meaning
>	Greater than
<	Less than
≥	Greater than or equal to
≤	Less than or equal to
=	Equal
≠	Not equal
↔ / ?	Relationship cannot be determined

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TYPEWISE NOTES ON INEQUALITY

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TYPE 1: Single Statement – Simple Inequality

Concept

A direct comparison is possible.

Example (PYQ – CUET)

Statement: A > B > C
Conclusion: A > C ?

Solution:

If A > B and B > C, then A > C is definitely true.

✔ Conclusion is TRUE

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TYPE 2: Combined Statements

You must merge chains before concluding.

Example (PYQ – IPMAT)

Statements:

1. P > Q

2. Q ≥ R

3. R < S

Conclusion: P > S ?

Solution:

Combine:
P > Q ≥ R < S
→ Up to R, P is greater, but S is greater than R.

We cannot compare P and S.

❌ Conclusion: Cannot be determined

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TYPE 3: Opposite Direction Inequalities

Concept

If comparisons move in two opposite ways, final relation becomes ambiguous.

Example (CLAT PYQ-based)

Statements:
A > B
A < C

Conclusion: B ? C

Solution:

A is bigger than B but smaller than C.
So C > A > B

Thus, C > B is definite.

✔ Conclusion TRUE

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TYPE 4: Either–Or Conclusions

Concept

Used when BOTH conditions are satisfied:

1. Both conclusions are individually false

2. Both variables are same pair

3. They offer opposite relations (>, < OR ≥, ≤)

Example (CUET Pattern)

Statement: W ≥ X = Y
Conclusions:

1. Y > W

2. Y < W

Solution:

From W ≥ X = Y
→ W ≥ Y

Check conclusions:
Y > W → False
Y < W → Maybe or maybe not (depends if W = Y or W > Y)

Since:

• Both involve Y & W

• Both are false individually

• They are opposite signs

✔ Either conclusion follows

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TYPE 5: Coded Inequality

Concept:

Symbols are replaced artificially. Decode them first.

Example (IPMAT PYQ-based)

‘A $ B’ means A > B
‘A @ B’ means A = B
‘A # B’ means A < B

Given: A $ B # C

Conclusion: A ? C

Solution:

Decode:
A > B < C
This means B is smaller than both.

But relation between A and C is unknown.

❌ Conclusion: Cannot be determined

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TYPE 6: Multiple Chains – True/False Conclusions

This type frequently appears in CUET.

Example (CUET PYQ-based)

Statement: M ≥ N > O = P < Q

Conclusions:

1. Q > O

2. M > P

3. N ≥ P

Solutions:

1. Q > O ✔ True (O = P < Q)

2. M > P ✔ True (M ≥ N > O = P)

3. N ≥ P ✔ True (N > O = P)

✔ All conclusions are TRUE

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TYPE 7: No Relation Case (Important for CLAT & IPMAT)

Concept:

When variables branch out, relation becomes indeterminate.

Example

A > B < C

Here A and C have no relation.

❌ A ? C = Cannot be determined

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TYPE 8: Reverse Inequality (Mirror Questions)

These appear in IPMAT quant section.

Example

Statement: A < B ≤ C
Asked: C ? A

Simply reverse the entire inequality:

A < B ≤ C
Reversing: C ≥ B > A

✔ final answer: C > A

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⭐ PYQ-STYLE PRACTICE QUESTIONS WITH DETAILED SOLUTIONS

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Q1 (CUET PYQ-based)

Statement: P > Q ≥ R = S < T
Conclusion: T > R ?

Solution:

Since S < T and R = S,
→ R < T

✔ Conclusion TRUE

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Q2 (CLAT Pattern)

Statement: A ≥ B > C
Conclusion: C < A ?

Chain: A ≥ B > C
Meaning: A is definitely greater than C.

✔ TRUE

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Q3 (IPMAT PYQ)

Statements:
X = Y ≤ Z
Y < W

Conclusion: Z ? W

Solution:

X = Y ≤ Z
and
Y < W
→ Z may be < W or > W

❌ Cannot be determined

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Q4 (CUET)

Statement: M ≥ O = P > Q
Conclusion: M > Q ?

Since M ≥ O and O = P and P > Q
→ M ≥ P > Q
Thus M > Q is definite.

✔ TRUE

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Q5 (CLAT)

Statement: R > S < T
Conclusion: R ? T

No direct link.

❌ Cannot be determined