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Coded Inequality Tricks: Direct Chains, Coded Symbols and Either-Or Cases

Read the path between two letters • Opposite signs break the chain • Combining statements • Decoding symbols • Either-or: same pair, together complete

Banking SSC 📅 Last updated: 2026-10-23

An inequality question gives a chain of letters joined by the signs >, <, ≥, ≤ and =, then asks whether some conclusions about two of the letters are certainly true. The whole method rests on one idea: find the path in the chain from one letter to the other, and read the signs along that path.

  • If every sign on the path points the same way, a relation follows.
  • If the path has at least one strict sign (> or <), the result is strict.
  • If every sign on the path allows equality (≥, ≤ or =), the result is ≥ or ≤.
  • If any two signs on the path point in opposite directions, no relation follows.

The equals sign does not change the direction, so you can step across it freely.

Worked example 1: one conclusion follows

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

For I, the path A > B ≥ C = D points one way and contains a strict sign, so A > D follows. For II, the path from B to E is B ≥ C = D < E, and the signs ≥ and < point in opposite directions, so no relation is fixed. To see this, take A = 9, B = 4, C = 4, D = 4 and E = 6. Every sign holds, yet E − B = 2, so B is below E here. Only I follows.

One counterexample is enough to reject a conclusion. If you can find any set of values that satisfies the chain but breaks the conclusion, the conclusion does not follow.

Worked example 2: no relation between the ends

Statement: J < K > L. Conclusions: I. J > L, II. J < L.

K is larger than both J and L, but nothing says how J and L compare. With J = 1, K = 5 and L = 3, J − L = −2, so J is smaller.

With J = 4, K = 5 and L = 2 instead, J − L = 2, so J is larger. Both cases satisfy the statement. Since the two conclusions are strict, they do not cover the case J = L either. Neither follows.

Either-or is the step most candidates get wrong. Mark "either I or II follows" only when all three conditions hold:

  1. Neither conclusion is certain on its own.
  2. Both conclusions are about the same two letters.
  3. Together they cover every possibility the chain allows.

The usual pairs are > with = (when the chain gives ≥), < with = (when the chain gives ≤), and > with ≤ or < with ≥ (when the chain gives no relation at all).

Worked example 3: an either-or pair

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

The path from P to R is P ≥ Q = R, so P ≥ R. With P = Q = R = 5 and S = 1 the statement holds and P − R = 0, so P > R is not certain.

With P = 7, Q = R = 5 and S = 1, P − R = 2, so P = R is not certain either. Yet one of the two must be true, because P ≥ R means P is greater than or equal to R. Either I or II follows.

When the question gives separate statements, join them into one chain through their common letters before reading any path.

Worked example 4: two statements

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

The combined chain is M ≥ N > O = P ≤ Q. For I, the path M ≥ N > O = P gives M > P. For II, the path from N to Q is N > O = P ≤ Q, which has opposite signs. With M = 5, N = 4, O = P = 2 and Q = 3, Q − N = −1, so II fails. Only I follows.

In a coded question each sign is replaced by a symbol, and the code changes from paper to paper. Decode first, writing the real signs above the symbols, and only then apply the path method.

Worked example 5: decoding first

Code: @ means >, $ means ≥, & means =. Statements: A @ B, B $ C, C & D. Conclusion: A @ D.

Decoded, the statements are A > B, B ≥ C and C = D, which combine to A > B ≥ C = D. The path from A to D has a strict sign and one direction, so A > D, and the coded conclusion A @ D follows.

  • ✘ Marking either-or for two conclusions about different pairs of letters.
  • ✘ Marking either-or when one of the two conclusions is already certain.
  • ✘ Reading ≥ followed by > as ≥. One strict sign makes the result strict.
  • ✘ Applying the path method before decoding every symbol.

Relations of a different kind appear in syllogism questions, and the full list of reasoning topics is in the study hub.

Q1. Statement: X > Y ≥ Z = W. Conclusions: I. X > W II. Y < W easy

✅ Answer: (a) Only I follows

💡 Explanation: The path from X to W is X > Y ≥ Z = W, which gives X > W, so I follows. The same path gives Y ≥ W, so Y < W is false and II does not follow.

Q2. Statement: F ≤ G = H < I. Conclusions: I. F < H II. F = H medium

✅ Answer: (c) Either I or II follows

💡 Explanation: The path from F to H gives F ≤ H. Neither F < H nor F = H is certain alone, but both use the same pair and together they cover F ≤ H, so either I or II follows.

Q3. Statement: R > S < T ≥ U. Conclusions: I. R > T II. U < S medium

✅ Answer: (d) Neither I nor II follows

💡 Explanation: Between R and T the signs > and < point in opposite directions, so no relation can be fixed. Between S and U the signs < and ≥ also oppose each other. Neither conclusion follows.

Q4. Statements: K ≥ L, L > M, M = N. Conclusions: I. K = N II. K > N medium

✅ Answer: (b) Only II follows

💡 Explanation: Joining the statements gives K ≥ L > M = N. One strict sign on the path makes the whole result strict, so K > N. II follows and I is false.

Q5. In a code, P % Q means P < Q, P & Q means P ≤ Q, P $ Q means P = Q and P # Q means P > Q. Statements: M % N, N & O, O $ P. Conclusions: I. P # M II. O # N hard

✅ Answer: (a) Only I follows

💡 Explanation: Decoded, the statements read M < N ≤ O = P. Then P > M, so I follows. Between N and O the relation is only N ≤ O, so O > N is not certain and II does not follow.

Q6. Statements: B ≤ C, C = D, D ≤ E. Conclusions: I. E > B II. E = B hard

✅ Answer: (c) Either I or II follows

💡 Explanation: Joining the statements gives B ≤ C = D ≤ E, so E ≥ B. Each conclusion alone is uncertain, but they share the pair and together make E ≥ B, so either I or II follows.

Is there a 'both follow' option in these questions?

Many bank papers give five options, including 'Both I and II follow'. The method is the same: test each conclusion on its own first. Both follow only when each is certain separately, which is never possible for an either-or pair.

Why does one strict sign make the whole result strict?

If A ≥ B and B > C, then A is at least B, and B is strictly more than C, so A must be strictly more than C. Equality would need every sign on the path to allow equality, and one strict sign rules that out.

All problems and solutions on this page are original. No outside facts are relied on; every numeric answer is recomputed by software before publishing.

How this page was prepared. Drafted with AI assistance (Claude (Anthropic AI model)) from the sources listed above. 6 calculations on this page were recomputed by software and matched. Automated checks also covered structure, internal links and duplicate text. Software checks cannot confirm facts. Reviewed by praveenkumar on 2026-10-23 against the sources listed above.

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