Coded Inequality Tricks for Bank Exams (Quick Answer)
Coded inequality tricks come down to three moves: first turn every coded symbol (like @, #, %) back into its real sign (<, ≤, =, ≥, >), then join the statements into one chain through the common letters, and finally test each conclusion against the chain, using the either-or rule only when both conclusions fail and talk about the same two letters. If you write the decoded chain once, each conclusion takes about 5 seconds to check.
🔥 Key Exam Takeaway: Never solve a coded question in symbols. Decode first, build the chain, and remember that a chain breaks the moment the signs point in opposite directions (for example A > B < C tells you nothing about A and C).
Coded inequality is a regular part of bank prelims reasoning. It has appeared in IBPS and SBI Clerk, IBPS and SBI PO and IBPS RRB papers, and newer papers often mix it with direct inequalities. Every solved example and practice answer on this page was checked by a brute-force program that tried every possible order of the letters, so you can trust the answers.
What Is Coded Inequality in Reasoning?
In a normal (direct) inequality, the question shows the real signs: A ≥ B > C. In a coded inequality, each sign is hidden behind a symbol, and the meaning of each symbol is given in words. A typical question looks like this:
- 'P @ Q' means 'P is neither greater than nor equal to Q'
- 'P # Q' means 'P is not greater than Q'
- 'P % Q' means 'P is neither smaller than nor greater than Q'
- 'P & Q' means 'P is not smaller than Q'
- 'P © Q' means 'P is neither smaller than nor equal to Q'
The symbols change from paper to paper, so do not memorise symbols. Memorise the phrases. The phrases are always the same five.
Coded Inequality Decoding Table (Phrase to Sign)
| Phrase used in the question | What it rules out | Real sign |
|---|---|---|
| A is greater than B | – | A > B |
| A is neither smaller than nor equal to B | <, = | A > B |
| A is not smaller than B | < | A ≥ B |
| A is either greater than or equal to B | < | A ≥ B |
| A is neither smaller than nor greater than B | <, > | A = B |
| A is not greater than B | > | A ≤ B |
| A is either smaller than or equal to B | > | A ≤ B |
| A is neither greater than nor equal to B | >, = | A < B |
| A is smaller than B | – | A < B |
The elimination trick: there are only three basic relations between two numbers: <, = and >. Whatever the phrase says "not" or "neither … nor" about, cross it out. What is left is the sign.
- "not smaller" → cross out < → left with = and > → ≥
- "neither greater nor equal" → cross out > and = → left with < → <
- "neither smaller nor greater" → cross out < and > → left with = → =
For the rest of this page we use the five codes listed in Section 1:
| Code | Sign |
|---|---|
| @ | < |
| # | ≤ |
| % | = |
| & | ≥ |
| © | > |
Inequality Reasoning Tricks: The Chain Method Step by Step
Step 1: Decode. Rewrite every statement with real signs on your rough sheet. Do this once, not for each conclusion.
Step 2: Join through common letters. If the statements are M < N, N ≤ O and O = P, write them as one line: M < N ≤ O = P. Flip a statement if needed so that the common letter sits in the middle: "T ≤ S" can be written "S ≥ T".
Step 3: Read each conclusion off the chain. Find both letters of the conclusion in the chain and look at every sign between them.
Inequality Rules for Reading a Chain
| Signs between the two letters | Result |
|---|---|
| All signs point the same way and at least one is strict (> or <) | Strict relation (> or <) is definitely true |
| All signs point the same way, none strict, at least one is ≥ or ≤ | ≥ or ≤ is definitely true; > alone and = alone are NOT definite |
| Only '=' signs | '=' is definitely true |
| Signs point in opposite directions (like > and <, or ≥ and ≤) | No definite relation: the chain is broken |
Combining two signs (A ? B ? C → A and C)
| A to B | B to C | A to C |
|---|---|---|
| > | > or ≥ or = | > |
| ≥ | > | > |
| ≥ | ≥ or = | ≥ |
| = | any sign | that same sign |
| < | < or ≤ or = | < |
| ≤ | ≤ or = | ≤ |
| > or ≥ | < or ≤ | No relation |
| < or ≤ | > or ≥ | No relation |
A quick way to remember the strength rule: the strongest sign in the path wins, as long as the path does not change direction. Here > is stronger than ≥, and ≥ is stronger than =.
Either-Or Case in Inequality: Rule and Conditions
Mark "Either I or II follows" only when all three conditions hold:
- Neither conclusion is definitely true on its own.
- Both conclusions talk about the same two letters (for example both compare A and C).
- Together they cover every possible case for those two letters.
The pairs that pass condition 3:
| Pair of conclusions | When it is either-or |
|---|---|
| A ≥ B and A < B | Whenever the relation between A and B is not definite (including a broken chain) |
| A ≤ B and A > B | Whenever the relation between A and B is not definite (including a broken chain) |
| A > B and A = B | Only when the chain gives A ≥ B |
| A < B and A = B | Only when the chain gives A ≤ B |
Two common mistakes:
- "A > B, A = B" on a broken chain is NOT either-or. If there is no relation at all, A < B is also possible, so the pair does not cover every case. The answer is "Neither".
- Two conclusions that say the same thing are never either-or. "E < H" and "H > E" are one relation written two ways. If one fails, both fail, so the answer is "Neither".
Coded Inequality Questions with Solutions (IBPS and SBI Pattern)
Codes for all examples: @ = <, # = ≤, % = =, & = ≥, © = >. Answer options in every question: (a) Only I follows, (b) Only II follows, (c) Either I or II follows, (d) Neither follows, (e) Both follow.
Example 1
Statements: M @ N, N # O, O % P Conclusions: I. M @ P II. P & N
- Decode: M < N, N ≤ O, O = P
- Chain: M < N ≤ O = P
- I. M @ P means M < P. From M to P the signs are <, ≤, = (same direction, one strict) → M < P is true.
- II. P & N means P ≥ N. From N to P the signs are ≤, = → N ≤ P, that is P ≥ N → true.
Answer: (e) Both follow.
Example 2
Statements: R © S, S & T, T @ U Conclusions: I. R © T II. U © S
- Decode: R > S, S ≥ T, T < U
- Chain: R > S ≥ T < U
- I. R © T means R > T. Signs from R to T: >, ≥ → R > T is true.
- II. U © S means U > S. Between S and U the signs are ≥ and < → opposite directions → no relation.
Answer: (a) Only I follows.
Example 3 (either-or with > and =)
Statements: A & B, C # B, D © C Conclusions: I. A % C II. A © C
- Decode: A ≥ B, C ≤ B (that is B ≥ C), D > C
- Chain: A ≥ B ≥ C < D
- A to C: ≥, ≥ → A ≥ C. So A = C alone is not definite, and A > C alone is not definite.
- Both conclusions compare A and C, and together "=" and ">" make exactly "≥", which is what the chain gives.
Answer: (c) Either I or II follows.
Example 4 (either-or on a broken chain)
Statements: J © K, L @ K, L # M Conclusions: I. M & K II. K © M
- Decode: J > K, L < K (that is K > L), L ≤ M
- Chain: J > K > L ≤ M
- K to M: > then ≤ → direction changes → no definite relation.
- I says M ≥ K and II says K > M (that is M < K). Same two letters, and ≥ with < covers every case.
Answer: (c) Either I or II follows.
Example 5
Statements: E @ F, F © G, H & G Conclusions: I. E @ G II. H © F
- Decode: E < F, F > G, H ≥ G
- Chain: E < F > G ≤ H
- I. E and G: < then > → broken → not definite.
- II. H and F: F > G ≤ H → broken → not definite.
- The conclusions compare different pairs, so either-or is not allowed.
Answer: (d) Neither follows.
Example 6 (the "same relation" trap)
Statements: E @ F, F © G, H & G Conclusions: I. E @ H II. H © E
- Chain from Example 5: E < F > G ≤ H. E and H are not related.
- I says E < H. II says H > E. These are the same statement, so if one is not definite the other is not definite either.
Answer: (d) Neither follows (not either-or).
Example 7 (four statements)
Statements: P % Q, Q & R, R © S, T # S Conclusions: I. P © T II. Q % S
- Decode: P = Q, Q ≥ R, R > S, T ≤ S (that is S ≥ T)
- Chain: P = Q ≥ R > S ≥ T
- I. P to T: =, ≥, >, ≥ → one strict sign, same direction → P > T is true.
- II. Q to S: ≥, > → Q > S, so Q = S is false.
Answer: (a) Only I follows.
Example 8 (direct inequality: which expression is true?)
Question: In which expression is 'A > D' definitely true?
(a) A ≥ B > C = D
(b) A > B ≤ C = D
(c) A = B ≥ C ≥ D
(d) A > B = C < D
(a) ≥, >, = → same direction, one strict → A > D. ✔
(b) > then ≤ → broken.
(c) =, ≥, ≥ → only A ≥ D, so A > D is not definite.
(d) =, then < → broken.
Answer: (a).
Example 9 (fill the blank)
Question: Which signs can replace '?' in P ? Q ≥ R > S so that P > S is definitely true?
- With >, ≥ or = the path keeps one direction and already contains a strict '>', so P > S holds.
- With < or ≤ the direction changes, so P and S become unrelated.
Answer: >, ≥ or = (any of the three works; < and ≤ do not).
Common Mistakes in Coded Inequality Questions
| Trap | What students do | What is correct |
|---|---|---|
| Decoding inside each conclusion | Re-read symbol meanings for every conclusion and lose time | Decode all statements once, write the chain, then read conclusions |
| "Not greater" read as "<" | Treat "not greater than" as strictly smaller | "Not greater" leaves < and =, so it is ≤ |
| ≥ chain read as > | A ≥ B ≥ C taken as A > C | Only A ≥ C is definite; A > C alone is not |
| Skipping the direction check | A > B < C taken as A > C | Opposite directions break the chain |
| Either-or on different pairs | I compares A and C, II compares B and D, both fail, mark either-or | Either-or needs the same two letters |
| > and = on a broken chain | Mark either-or | Needs A ≥ B from the chain; otherwise "Neither" |
| Same meaning, two ways | "E < H" and "H > E" marked either-or | They are one statement; answer "Neither" |
Inequality Tricks: Quick Revision Table
| Item | Remember |
|---|---|
| Decode rule | Cross out what "not / neither … nor" mentions from <, =, >; what is left is the sign |
| "Not smaller" | ≥ |
| "Not greater" | ≤ |
| "Neither smaller nor greater" | = |
| "Neither greater nor equal" | < |
| "Neither smaller nor equal" | > |
| Chain strength | Strongest sign wins if direction does not change |
| Broken chain | Any change of direction (> with <, ≥ with ≤) |
| Either-or pairs | ≥ & <, ≤ & > always (if neither is definite); > & = only with ≥; < & = only with ≤ |
| Either-or condition | Both fail + same two letters + together cover all cases |
Coded Inequality Practice Questions with Answers
Use the same codes: @ = <, # = ≤, % = =, & = ≥, © = >. Options: (a) Only I, (b) Only II, (c) Either I or II, (d) Neither, (e) Both.
Q1. Statements: B & C, C © D, D % E. Conclusions: I. B © E II. E @ C
Q2. Statements: F # G, G @ H, J & H. Conclusions: I. F @ J II. J % G
Q3. Statements: K % L, L & M, N # M. Conclusions: I. K & N II. N % K
Q4. Statements: P © Q, R & Q, R # S. Conclusions: I. S © Q II. S % Q
Q5. Statements: T @ U, U % V, W # V. Conclusions: I. T % W II. W @ U
Q6. Statements: A # B, B © C, D @ C. Conclusions: I. A © D II. D @ B
Q7. Statements: G & H, H % I, I © J, K @ J. Conclusions: I. G © K II. K % I
Q8. Statements: L © M, N & M, O @ N. Conclusions: I. O © L II. L @ N
Q9. Statements: X % Y, Z & Y, Z # V. Conclusions: I. V & X II. X @ V
Q10. Statements: R # S, S % T, U & T, U @ V. Conclusions: I. R @ V II. V © S
Answers and Explanations
Q1. (e) Both follow. Chain: B ≥ C > D = E. B to E has ≥, >, = → B > E true. C to E: >, = → C > E, that is E < C, true.
Q2. (a) Only I follows. Chain: F ≤ G < H ≤ J. F to J has a strict < → F < J true. G to J: <, ≤ → G < J, so J = G is false.
Q3. (a) Only I follows. Chain: K = L ≥ M ≥ N. K to N: =, ≥, ≥ → K ≥ N true. N = K is possible but not definite.
Q4. (c) Either I or II follows. Chain: P > Q ≤ R ≤ S, so Q ≤ R ≤ S gives S ≥ Q. S > Q and S = Q are each possible, and together they make S ≥ Q.
Q5. (d) Neither follows. Chain: T < U = V ≥ W. T and W: < then ≥ → broken, so T = W is not definite. U to W: =, ≥ → U ≥ W, so W < U is not definite (W can equal U).
Q6. (b) Only II follows. Chain: A ≤ B > C > D. A and D: ≤ then > → broken. B to D: >, > → B > D, that is D < B, true.
Q7. (a) Only I follows. Chain: G ≥ H = I > J > K. G to K has strict signs and one direction → G > K true. I to K: >, > → I > K, so K = I is false.
Q8. (d) Neither follows. Chain: L > M ≤ N > O. O and L: broken. L and N: > then ≤ → broken. The conclusions also compare different pairs, so no either-or.
Q9. (a) Only I follows. Chain: X = Y ≤ Z ≤ V. X to V: =, ≤, ≤ → V ≥ X true. X < V is not definite because all three can be equal.
Q10. (e) Both follow. Chain: R ≤ S = T ≤ U < V. R to V has a strict < → R < V true. S to V: =, ≤, < → V > S true.
Coded Inequality FAQs
What is the fastest trick for coded inequality questions?
Decode all statements once into real signs, write one combined chain, then check each conclusion against that chain. This avoids reading the symbol meanings again for every conclusion.
How do I decode 'not greater than' and 'not smaller than'?
"Not greater than" removes ">" and leaves "<" and "=", so it means ≤. "Not smaller than" removes "<" and leaves "=" and ">", so it means ≥.
When is the answer 'either I or II' in inequality?
When neither conclusion is definitely true, both talk about the same two letters, and together they cover every possible case. The usual pairs are ≥ with <, and ≤ with >. The pair > with = works only if the chain gives ≥.
What does a broken chain mean in inequality?
It means the signs between two letters point in opposite directions, like A > B < C. In that case A and C have no definite relation, and any conclusion about them alone is false.
Is coded inequality still asked in bank exams?
Yes. It has appeared in IBPS and SBI Clerk, PO and RRB prelims papers, often as a set of 3–5 questions. Direct inequality is more common in recent papers, but the method on this page solves both.
How many seconds should one inequality question take?
With practice, about 20–30 seconds: around 10 seconds to decode and build the chain, and a few seconds for each conclusion.
Is A ≥ B ≥ C enough to say A > C?
No. A ≥ B ≥ C only proves A ≥ C, because all three letters can be equal. To get A > C you need at least one strict sign (> or <) on the path.
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Practice Next: Bank Reasoning Mock Tests
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- SBI topic-wise inequality tests: SBI PO Inequality Mock Test 01 and SBI Clerk Inequality Mock Test 01.
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