Coded inequality
Inequality reasoning questions — free, machine-verified practice
Inequality reasoning questions give you a chain of comparison symbols, such as P ≥ Q > R, and ask which of the given conclusions must follow. Solve one by decoding every symbol, joining the statements into a single unbroken chain between the two letters being compared, and accepting a conclusion only when it holds in every possible case, never merely in a likely one.
Coded inequality is one of the highest-yield topics in banking prelims: a set of four or five questions is common in IBPS and SBI papers, the method is fully mechanical, and a prepared candidate can finish the set in under three minutes. That combination — high frequency, low time cost — is why it is usually the first section experienced aspirants attempt.
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Every question below was generated by the same engine that mints the Deduce daily puzzle, and machine-proven to have exactly one correct answer before it reached this page. The walkthrough is the engine's own, step for step.
Question 1
Which of the following conclusions is DEFINITELY true from the given expression?
Code: % = >, @ = >=, * = <, $ = <=, # = =
Expression: F % E, E % C, C % A
- E = C
- A = C
- A > F
- C > E
- F > A
Show the worked solution
- First decode each symbol: % means >, @ means >=, * means <, $ means <=, # means =.
- So the expression reads: F > E, E > C, C > A.
- Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
- From the closure, F > A is the only option that must hold — the others are either false or can't be concluded.
Question 2
Which of the following conclusions is DEFINITELY true from the given expression?
Code: * = >, # = >=, @ = <, $ = <=, % = =
Expression: F # C, C % B, B # A, C * A
- C = A
- B > C
- F < A
- B > A
- F < B
Show the worked solution
- First decode each symbol: * means >, # means >=, @ means <, $ means <=, % means =.
- So the expression reads: F >= C, C = B, B >= A, C > A.
- Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
- From the closure, B > A is the only option that must hold — the others are either false or can't be concluded.
Question 3
Which of the following conclusions is DEFINITELY true from the given expression?
Code: % = >, $ = >=, @ = <, * = <=, # = =
Expression: B $ D, D $ E, E $ C, D % C
- D = C
- E < C
- B > C
- D > E
- B < D
Show the worked solution
- First decode each symbol: % means >, $ means >=, @ means <, * means <=, # means =.
- So the expression reads: B >= D, D >= E, E >= C, D > C.
- Run the chain: "≥" combines to "≥", but a strict ">" anywhere on the path makes the result strict ">" (e.g. A ≥ B > C ⇒ A > C). "=" links both directions.
- From the closure, B > C is the only option that must hold — the others are either false or can't be concluded.
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How to solve inequality reasoning questions, step by step
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Decode every symbol before you read the conclusions
Coded questions replace >, ≥, = and < with symbols like @, #, $. Rewrite the whole statement in ordinary signs first. Reading conclusions while still translating is where most avoidable errors happen.
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Join the statements into one continuous chain
To judge a conclusion about A and D, you need an unbroken path from A to D. If the letters sit in two separate statements with no shared letter linking them, no relationship can be derived at all.
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Check that every link points the same way
A chain proves something only when all its arrows face one direction. A > B > C gives A > C. A > B < C gives nothing — B is smaller than both ends, which tells you nothing about how A and C compare.
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Take the weakest link as the result
Mixing strict and non-strict signs weakens the conclusion. A > B ≥ C still yields A > C, because one strict link is enough. But A ≥ B ≥ C yields only A ≥ C — you cannot upgrade it to A > C.
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Test the two conclusions together for an either–or case
When both conclusions concern the same pair, both are individually false, and between them they cover every remaining possibility, the answer is “either I or II follows”. The classic trigger is a given A ≥ B with conclusions A > B and A = B.
What each combination proves
What each combination proves
| Chain | What follows |
|---|
| A > B > C | A > C |
|---|
| A > B ≥ C | A > C — one strict link is enough |
|---|
| A ≥ B ≥ C | A ≥ C only — never A > C |
|---|
| A > B < C | Nothing. B is below both; A and C are unrelated |
|---|
| A = B ≥ C | A ≥ C |
|---|
| A ≥ B, conclusions A > B and A = B | Either I or II follows — together they are exhaustive |
|---|
Common mistakes
Reading a conclusion as true because it looks likely
“Must follow” means true in every arrangement the statements permit. If you can construct one case where the conclusion fails, it does not follow — however plausible it seems.
Turning ≥ into > somewhere along the chain
A ≥ B ≥ C leaves A = B = C entirely possible, so A > C is false. Underline each ≥ as you translate; the weakest link caps the whole chain.
Missing the either–or pair
Candidates mark “neither follows” and move on. Before doing that, check whether the two conclusions describe the same pair and together exhaust the possibilities — if so, the answer is either–or.
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FAQ
How do you solve inequality reasoning questions quickly?
Decode every coded symbol into >, ≥, = or < first, then join the statements into one unbroken chain between the two letters being compared. Read the result off the chain: all arrows the same way proves a relation, one strict link makes it strict, and a break in direction proves nothing. Check the either–or case last.
What does “either I or II follows” mean in an inequality question?
It means neither conclusion is individually guaranteed, but between them they cover every possibility left open, so one of them must be true. It is triggered when both conclusions concern the same pair of letters — most often a given A ≥ B with conclusions A > B and A = B.
Why does A > B < C give no conclusion?
Both statements say B is the smaller element, so B sits below A and below C. That fixes nothing about how A and C compare to each other: A could be larger, smaller or equal. A chain proves a relation only when every link points the same direction.
Are coded and uncoded inequality questions solved differently?
No. A coded question adds one translation step at the start; after you rewrite the symbols as ordinary signs, the reasoning is identical. Aspirants who lose marks on coded sets usually do so in the translation, not the logic, so write the decoded chain out rather than holding it in your head.
How many inequality questions appear in bank exams?
In IBPS and SBI prelims, coded inequality typically appears as a set of four to five questions in the reasoning section. Because the method is mechanical and needs no diagram, it is one of the fastest sets available, and most toppers attempt it early to bank marks before the longer puzzles.
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