Inequality Reasoning Questions for Bank and SSC Exams
Follow the direction of the signs, check their strength, and know when either-or applies.
Inequality reasoning gives you a chain of letters joined by signs such as >, < and =, then asks which conclusions must be true. You do not calculate anything. You only follow the direction of the signs.
There are two forms. Direct inequality uses the signs themselves. Coded inequality replaces each sign with a symbol such as @ or #, so you decode first and then solve the same way.
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The Signs and What They Mean
- A > B
- A is greater than B.
- A < B
- A is less than B.
- A ≥ B
- A is greater than or equal to B. Also written as "A is not less than B".
- A ≤ B
- A is less than or equal to B. Also written as "A is not greater than B".
- A = B
- A is equal to B.
- Either-or
- Two conclusions about the same pair, neither definitely true alone, that together cover every possibility. The answer is then "either I or II follows".
How to Check a Conclusion
- 1
Find the path between the two letters
If the letters are in different statements, join the statements through a common letter.
- 2
Check that every sign points the same way
Between the two letters, all signs must open the same way (all > and ≥ and =, or all < and ≤ and =). If one sign points the other way, there is no definite relation and the conclusion does not follow.
- 3
Decide the strength
If at least one sign on the path is strict (> or <), the result is strict. If all signs are ≥ or =, the result is ≥. If every sign is =, the result is =.
- 4
Compare with the conclusion
The conclusion follows only if it matches the result exactly or is weaker. A ≥ result does not prove a > conclusion.
- 5
Test for either-or
If neither conclusion follows, both are about the same pair, and together they cover all cases (for example > and =, which make ≥), mark "either I or II follows".
Practice question 1
Statement: A > B ≥ C = D < E. Conclusions: I. A > D. II. E > C.
- 1
Conclusion I
Path from A to D: A > B ≥ C = D. All signs point the same way and one is strict, so A > D. I follows.
- 2
Conclusion II
Path from C to E: C = D < E. Both signs point the same way and one is strict, so C < E, which is E > C. II follows.
- 3
Answer
Both I and II follow.
Practice question 2
Statement: P ≥ Q > R, R < S ≤ T. Conclusions: I. P > R. II. Q > S.
- 1
Join the statements
R is common: P ≥ Q > R < S ≤ T.
- 2
Conclusion I
Path P ≥ Q > R. Same direction with one strict sign, so P > R. I follows.
- 3
Conclusion II
Path Q > R < S. The signs point opposite ways, so there is no definite relation between Q and S. II does not follow.
- 4
Answer
Only I follows.
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Practice question 3: The Either-Or Case
Statement: M ≥ N = O ≤ K. Conclusions: I. M > O. II. M = O.
- 1
Find the relation
Path M ≥ N = O. Same direction, no strict sign, so M ≥ O.
- 2
Check each conclusion
M ≥ O does not prove M > O, and it does not prove M = O. Neither follows alone.
- 3
Test for either-or
Both conclusions are about M and O, and > together with = makes exactly ≥. One of them must be true.
- 4
Answer
Either I or II follows.
Practice question 4: Coded Inequality
Here "@" means "greater than", "#" means "not less than", "$" means "equal to", "%" means "not greater than" and "&" means "less than". Statement: J # K, K $ L, L & M. Conclusions: I. J @ L. II. M @ K.
- 1
Decode
@ is >, # is ≥, $ is =, % is ≤, & is <. The statement becomes J ≥ K, K = L, L < M, or J ≥ K = L < M.
- 2
Decode the conclusions
I is J > L. II is M > K.
- 3
Conclusion I
Path J ≥ K = L gives J ≥ L, which does not prove J > L. I does not follow.
- 4
Conclusion II
Path K = L < M gives K < M, which is M > K. II follows.
- 5
Answer
Only II follows.
Common Traps
- check_circleAccepting a strict conclusion from a ≥ result. A ≥ B never proves A > B.
- check_circleMissing a reversed sign in the middle of a long chain. Check every sign on the path, not just the two ends.
- check_circleMarking either-or for different pairs. Either-or needs both conclusions to compare the same two letters.
- check_circleMisreading the coded words. "Not less than" is ≥ and "not greater than" is ≤. Write the decoding table before you solve.
How Bank and SSC Papers Test Inequality
The IBPS PO syllabus lists inequality under reasoning. It is tested in Reasoning Ability in prelims (35 questions, 40 marks) and in Reasoning in mains (40 questions, 60 marks). Questions follow the format above: one or two statements, two conclusions, and a fixed set of answer options such as "only I follows", "either I or II follows" and "both follow".
The SSC CGL reasoning topic list does not name inequality, so treat it mainly as a bank exam topic.
FAQs
What is the difference between direct and coded inequality?expand_more
Direct inequality uses the signs >, <, ≥, ≤ and =. Coded inequality replaces each sign with a symbol and tells you what each symbol means. You decode first, then solve exactly as for direct inequality.
When is the answer "either I or II follows"?expand_more
When neither conclusion follows alone, both compare the same two letters, and together they cover every possibility, such as A > B and A = B when the chain gives A ≥ B.
Is inequality reasoning asked in SSC exams?expand_more
The SSC CGL reasoning topic list does not name inequality. It is a regular topic in bank exams such as IBPS PO, whose syllabus lists it.
Next steps
- Syllogismarrow_forward
- Coding Decodingarrow_forward
- Syllabusarrow_forward
- Number series for bank and SSC examsarrow_forward
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