Mathematical Inequality Questions for Placement 2026 (with Solutions)

Last Updated: March 2026

Introduction to Mathematical Inequality

Mathematical Inequality is a crucial reasoning topic that tests your ability to understand relationships between variables and decode symbolic representations. This topic appears frequently in logical reasoning sections of placement exams, especially in TCS, Infosys, Wipro, and Cognizant assessments. Mastering inequality problems requires understanding of comparison operations and the ability to chain multiple relationships together.

Why This Topic is Important

Inequality questions assess:

Understanding of comparison operators
Logical deduction skills
Ability to chain multiple conditions
Pattern recognition in symbolic relationships
Quick decision-making under time pressure

Companies That Ask Inequality Questions (with Frequency)

Company	Frequency	Difficulty Level
TCS	Very High	Easy to Moderate
Infosys	Very High	Easy to Moderate
Wipro	High	Easy
Cognizant	High	Easy to Moderate
Accenture	Moderate	Easy
Capgemini	Moderate	Moderate
IBM	Moderate	Easy
Tech Mahindra	High	Easy
HCL	Moderate	Easy
LTI Mindtree	Low	Easy

KEY FORMULAS / CONCEPTS

╔══════════════════════════════════════════════════════════════════╗
║               INEQUALITY SYMBOL REFERENCE                        ║
╠══════════════════════════════════════════════════════════════════╣
║                                                                  ║
║  SYMBOL      MEANING                    EXAMPLE                  ║
║  ────────────────────────────────────────────────────────────   ║
║   >          Greater than               A > B means A > B       ║
║   <          Less than                  A < B means A < B       ║
║   ≥          Greater than or equal      A ≥ B means A ≥ B       ║
║   ≤          Less than or equal         A ≤ B means A ≤ B       ║
║   =          Equal to                   A = B means A = B       ║
║                                                                  ║
║  COMMON SYMBOL COMBINATIONS (CODED INEQUALITIES)                 ║
║  ────────────────────────────────────────────────────────────   ║
║   @          Sometimes used for >                                ║
║   #          Sometimes used for <                                ║
║   $          Sometimes used for ≥                                ║
║   %          Sometimes used for ≤                                ║
║   &          Sometimes used for =                                ║
║   *          Sometimes used for ≠ (not equal)                    ║
║                                                                  ║
║  RELATIONSHIP COMBINATIONS                                       ║
║  ────────────────────────────────────────────────────────────   ║
║  If A > B and B > C, then A > C                                  ║
║  If A ≥ B and B ≥ C, then A ≥ C                                  ║
║  If A > B and B ≥ C, then A > C                                  ║
║  If A ≥ B and B > C, then A > C                                  ║
║                                                                  ║
║  NO DEFINITE CONCLUSION CASES                                    ║
║  ────────────────────────────────────────────────────────────   ║
║  If A > B and B < C → No relation between A and C               ║
║  If A ≥ B and B ≤ C → No relation between A and C               ║
║  If A > B and C > B → No relation between A and C               ║
║                                                                  ║
╚══════════════════════════════════════════════════════════════════╝

30 Practice Questions with Step-by-Step Solutions

Question 1

Statements: A > B, B > C, C > D Conclusions: I. A > D II. B > D

Solution: From A > B > C > D, we get A > D and B > D Both conclusions follow. Answer: Both I and II follow

Question 2

Statements: P ≥ Q, Q ≥ R, R = S Conclusions: I. P ≥ S II. P > S

Solution: P ≥ Q ≥ R = S, so P ≥ S But P > S is not necessarily true (P could equal S) Answer: Only I follows

Question 3

Statements: X > Y, Y < Z, Z > W Conclusions: I. X > Z II. Y > W

Solution: X > Y and Y < Z → No relation between X and Z Y < Z and Z > W → No relation between Y and W Answer: Neither follows

Question 4

Statements: M ≤ N, N < O, O ≥ P Conclusions: I. M < O II. N ≥ P

Solution: M ≤ N < O, so M < O ✓ N < O and O ≥ P → No relation between N and P Answer: Only I follows

Question 5

Statements: A = B, B ≥ C, C < D Conclusions: I. A ≥ C II. B < D

Solution: A = B ≥ C, so A ≥ C ✓ B ≥ C and C < D → No relation between B and D Answer: Only I follows

Question 6

Statements: P < Q, Q ≤ R, R = S Conclusions: I. P < S II. Q = S

Solution: P < Q ≤ R = S, so P < S ✓ Q ≤ R = S, so Q ≤ S, not necessarily Q = S Answer: Only I follows

Question 7

Statements: X ≥ Y, Y > Z, Z ≥ W Conclusions: I. X > W II. Y ≥ W

Solution: X ≥ Y > Z ≥ W, so X > W ✓ Y > Z ≥ W, so Y > W (not Y ≥ W which is weaker) Actually Y > W means Y ≥ W is also true Answer: Both follow

Question 8

Statements: A > B, B = C, C ≥ D Conclusions: I. A > C II. B ≥ D

Solution: A > B = C, so A > C ✓ B = C ≥ D, so B ≥ D ✓ Answer: Both follow

Question 9

Statements: M > N, N ≥ O, O O II. N < P

Solution: M > N ≥ O, so M > O ✓ N ≥ O and O < P → No relation between N and P Answer: Only I follows

Question 10

Statements: P ≤ Q, Q < R, R ≤ S Conclusions: I. P < S II. Q ≤ S

Solution: P ≤ Q < R ≤ S, so P < S ✓ Q < R ≤ S, so Q < S (not Q ≤ S which allows equality) Actually Q < S implies Q ≤ S, so II also follows Answer: Both follow

Question 11

Statements: A ≥ B, C < B, D > C Conclusions: I. A > C II. D < B

Solution: A ≥ B > C, so A > C ✓ D > C and C < B → No relation between D and B Answer: Only I follows

Question 12

Statements: X = Y, Y ≤ Z, Z > W Conclusions: I. X ≤ Z II. Y > W

Solution: X = Y ≤ Z, so X ≤ Z ✓ Y ≤ Z and Z > W → No relation between Y and W Answer: Only I follows

Question 13

Statements: P > Q, R > Q, S > R Conclusions: I. P > R II. S > Q

Solution: P > Q and R > Q → No relation between P and R S > R > Q, so S > Q ✓ Answer: Only II follows

Question 14

Statements: A ≤ B, B = C, C < D Conclusions: I. A < D II. B < D

Solution: A ≤ B = C < D, so A < D ✓ B = C < D, so B < D ✓ Answer: Both follow

Question 15

Statements: M ≥ N, O > N, O O II. P > N

Solution: M ≥ N and O > N → No relation between M and O O N, so P > O > N, thus P > N ✓ Answer: Only II follows

Question 16

Statements: X > Y ≥ Z, Z = W ≤ V Conclusions: I. X > W II. Y ≥ V

Solution: X > Y ≥ Z = W, so X > W ✓ Y ≥ Z = W ≤ V → No relation between Y and V Answer: Only I follows

Question 17

Statements: A = B ≤ C, C > D ≥ E Conclusions: I. A > D II. B ≥ E

Solution: A = B ≤ C and C > D → No definite relation between A and D B ≤ C and D ≥ E, with C > D → No relation between B and E Answer: Neither follows

Question 18

Statements: P < Q = R, R ≥ S > T Conclusions: I. Q > T II. P < R

Solution: Q = R ≥ S > T, so Q > T ✓ P < Q = R, so P < R ✓ Answer: Both follow

Question 19

Statements: M > N ≥ O, O = P ≤ Q Conclusions: I. N > P II. M > Q

Solution: N ≥ O = P, so N ≥ P (not necessarily N > P) M > N ≥ O = P ≤ Q → No relation between M and Q Answer: Neither follows (or only I in some interpretations)

Question 20

Statements: X ≤ Y < Z, Z = A ≥ B Conclusions: I. Y < A II. X < Z

Solution: Y < Z = A, so Y < A ✓ X ≤ Y < Z, so X < Z ✓ Answer: Both follow

Question 21

Statements: C > D = E, E ≥ F > G Conclusions: I. C > F II. D > G

Solution: C > D = E ≥ F, so C > F ✓ D = E ≥ F > G, so D > G ✓ Answer: Both follow

Question 22

Statements: P ≤ Q < R, S > R = T Conclusions: I. P < T II. S > Q

Solution: P ≤ Q < R = T, so P < T ✓ S > R > Q, so S > Q ✓ Answer: Both follow

Question 23

Statements: A ≥ B > C, C = D ≤ E Conclusions: I. B > D II. A > E

Solution: B > C = D, so B > D ✓ A ≥ B > C = D ≤ E → No relation between A and E Answer: Only I follows

Question 24

Statements: M < N = O, O ≥ P > Q Conclusions: I. N > Q II. M < O

Solution: N = O ≥ P > Q, so N > Q ✓ M < N = O, so M < O ✓ Answer: Both follow

Question 25

Statements: X > Y = Z ≥ W, W < V = U Conclusions: I. Z W

Solution: Z ≥ W and W < V = U → No relation between Z and U X > Y = Z ≥ W, so X > W ✓ Answer: Only II follows

Question 26

Statements: A = B ≥ C, C > D = E Conclusions: I. A > E II. B ≥ D

Solution: A = B ≥ C > D = E, so A > E ✓ B ≥ C > D, so B > D (implies B ≥ D) ✓ Answer: Both follow

Question 27

Statements: P ≥ Q > R, R = S ≤ T S II. P > T

Solution: Q > R = S, so Q > S ✓ P ≥ Q > R = S ≤ T → No relation between P and T Answer: Only I follows

Question 28

Statements: M = N ≤ O, O > P ≥ Q Conclusions: I. N > P II. M ≤ O

Solution: N ≤ O and O > P → No relation between N and P M = N ≤ O, so M ≤ O ✓ Answer: Only II follows

Question 29

Statements: X < Y ≤ Z, Z > W = V Conclusions: I. Y ≤ W II. X < Z

Solution: Y ≤ Z and Z > W → No relation between Y and W X < Y ≤ Z, so X < Z ✓ Answer: Only II follows

Question 30

Statements: C ≥ D = E, E < F = G Conclusions: I. C > G II. D < F

Solution: C ≥ D = E < F = G → No relation between C and G D = E < F, so D < F ✓ Answer: Only II follows

SHORTCUTS & TRICKS

Trick 1: Chain Rule

Always look for chains: A > B > C → A > C (direct relationship)

Trick 2: Break in Chain = No Conclusion

If the chain breaks (like A > B and C > B), no definite conclusion between A and C

Trick 3: Equal Signs Pass Through

If A = B and B > C, then A > C. Equality is transitive.

Trick 4: ≥ and ≤ Relationships

A ≥ B ≥ C implies A ≥ C, could be A > C or A = C

Trick 5: Opposite Directions = No Conclusion

If one goes up (>) and other goes down (<), typically no conclusion

Trick 6: Priority Order

and < are stronger than ≥ and ≤. If you get A > B, that's better than A ≥ B.

Trick 7: Quick Elimination

If one conclusion clearly doesn't follow, check if the other might save time.

Common Mistakes to Avoid

Assuming Transitivity Blindly: Not all relationships are transitive. A > B and C > B doesn't mean A > C.
Confusing ≥ with >: A ≥ B means A > B OR A = B. Don't assume strictly greater.
Missing Hidden Chains: Sometimes you need to combine multiple statements to see the chain.
Equal Sign Direction: A = B means both A ≥ B and B ≥ A are true.
Overlooking Contradictions: Check if conclusions contradict each other - they can't both be false if they cover all cases.
Rushing Through: Take 10-15 seconds to write down the chain visually.
Symbol Confusion: In coded inequalities, always decode first before analyzing.

5 Frequently Asked Questions

Q1: How do I approach coded inequalities quickly? A: First decode all symbols to standard inequalities, then solve normally. Practice common symbol mappings.

Q2: What if both conclusions seem to follow but one is stronger? A: Check if the stronger conclusion necessarily follows. If A ≥ B follows, A > B might not.

Q3: How can I practice inequality problems effectively? A: Start with basic chains, then move to complex 4-5 statement problems. Time yourself.

Q4: Are there any calculator tricks for inequalities? A: No calculators needed! These are pure logical reasoning. Practice mental chaining.

Q5: How much time should I spend per inequality question? A: Aim for 30-45 seconds. If stuck, mark and move on.

Practice these 30 questions to master Mathematical Inequalities for your placement exams!