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Inequality (Coded Inequality) Questions with Solutions

Coded Inequality questions give you a chain of order relationships between letters and ask which conclusions definitely follow — the logic is close to Syllogism, but with ordering instead of set membership. Here’s the approach, four fully worked examples covering the patterns that trip people up most, and a few to try yourself.

The approach, quickly

  • Some questions use coded symbols (like @, #, $) in place of >, <, =, ≥, ≤ — always check the legend given at the start of the question before solving anything.
  • A chain like A > B ≥ C only gives a definite conclusion about the endpoints (A and C) if every link points the SAME direction. A > B ≥ C combines to A > C; a chain that reverses direction partway (like A > B < C) gives no definite relationship between A and C at all.
  • When a strict relation (>) is proven between two letters, the non-strict version (≥) is also considered to follow, since "greater than" always implies "greater than or equal to". The reverse isn’t true: proving only ≥ does not let you conclude the strict >.
  • When you suspect no definite relationship can be proven, try to find two different valid number assignments that satisfy all the statements but give opposite results for the conclusion — if you can, neither conclusion follows. If you can even make the two letters exactly equal in a valid assignment, that rules out both "greater than" and "less than" as safe conclusions.

Worked examples

1. Statements: A > B, B > C, C > D. Conclusions: I. A > D. II. B > D. Which of the conclusions logically follow?

Solution

  1. The whole chain points the same direction: A > B > C > D.
  2. Combining consistently: A > D (skipping through B and C), and B > D (skipping C). Both are forced by the chain.

Answer: Both conclusions follow

2. Statements: P ≥ Q, Q = R, R > S. Conclusions: I. P > S. II. P ≥ S. Which of the conclusions follow?

Solution

  1. Since Q = R, the chain becomes P ≥ R > S. Even in the boundary case where P equals R exactly, R > S still makes P > S strictly — so P > S is forced in every valid case.
  2. Since P > S is proven, the weaker P ≥ S is also always true (> always implies ≥). Both conclusions follow, with I being the exact relationship.

Answer: Both conclusions follow

3. Statements: X < Y, Y < Z, Z = W. Conclusions: I. X < W. II. X < Z. Which of the conclusions follow?

Solution

  1. X < Y < Z combines directly to X < Z — Conclusion II is forced.
  2. Since Z = W, substituting gives X < Z = W, so X < W too — Conclusion I is forced as well.

Answer: Both conclusions follow

4. Statements: A > B, C > B, C > D. Conclusions: I. A > D. II. D > A. Which of the conclusions follow?

Solution

  1. A and C both relate to B, but neither relates directly to D through a single consistent chain — A connects to B, and D connects to C, with no link bridging A and D together.
  2. Try a valid number assignment: B = 1, C = 10, A = 3, D = 3 satisfies every statement (3 > 1, 10 > 1, 10 > 3) but gives A = D exactly — ruling out both "A > D" and "D > A" as safe conclusions.

Answer: Neither conclusion follows

Try these yourself

Check whether the chain points one consistent direction, then check against the answer.

1. Statements: M > N, N ≥ O, O > P. Conclusions: I. M > P. II. N > P. Which of the conclusions follow?

Answer: Both conclusions follow

2. Statements: P = Q, Q < R, R = S. Conclusions: I. P < S. II. P < R. Which of the conclusions follow?

Answer: Both conclusions follow

3. Statements: X > Y, Z > Y, Z > W. Conclusions: I. X > W. II. W > X. Which of the conclusions follow?

Answer: Neither conclusion follows (Y is the shared reference point — there is no direct chain between X and W)

Where this comes up

Inequality is a regular topic in the Reasoning/General Intelligence section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — and is especially common in banking exams.

Practice more Inequality questions

This page covers the approach and a handful of worked examples. Pariksha Saathi has full topic-wise practice sets for Inequality (and every other Reasoning/Quant/English topic) with instant scoring and explanations — free, no account required.

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