Inequalities for IBPS PO

Inequality questions should take you under 30 seconds each. They are among the few reasoning questions where there is nothing to draw and no case to split. You read a chain of signs, trace a path between two letters, and decide.

The trouble is that the traps are small: a ≥ where you expected a >, or a sign pointing the wrong way halfway along the path. This guide gives you the rules as a short checklist, then the three forms IBPS PO uses: direct chains, several statements that share letters, and coded symbols.

The rules

1. Find the path in the chain that links the two letters in the conclusion.
2. If every sign on that path points the same way (only > and ≥, or only < and ≤, with any number of =), a relation exists.
3. If the path has signs pointing opposite ways (a > and a <, or a ≥ and a ≤), no relation can be drawn.
4. The relation is strict (> or <) if at least one strict sign appears on the path. If every sign is ≥ or = (or ≤ or =), the relation is ≥ (or ≤).
5. An = never breaks a chain and never changes its direction.

The either-or case

Suppose the chain gives J ≥ M and the conclusions are "J > M" and "J = M". Neither is certain, but one must be true. The answer is either I or II.

Either-or needs all three conditions:

• both conclusions are about the same two letters,
• neither follows on its own, and
• together they cover the only possibility the chain allows (≥ split into > and =, or ≤ split into < and =).

If the chain gives no relation at all between the two letters, the answer is neither, not either-or.

Worked examples

Example 1: a direct chain

A > B ≥ C = D < E ≤ F. Conclusions: I. A > D. II. F > C. III. A > E.

• I: A > B ≥ C = D. All signs point one way and one is strict. True.
• II: C = D < E ≤ F, which reads F ≥ E > D = C. True.
• III: A > … D < E. The signs turn round at D. Does not follow.
• Answer: I and II.

Example 2: several statements

Statements: M ≥ N > O; O = P; Q < P ≤ R. Conclusions: I. M > Q. II. R ≥ O. III. N > R.

Join the statements at the shared letters: M ≥ N > O = P > Q, and P ≤ R.

• I: M ≥ N > O = P > Q. True.
• II: O = P ≤ R. True (R ≥ O, not R > O).
• III: N > O = P ≤ R. The signs turn at P. Does not follow.
• Answer: I and II.

Example 3: either-or

J ≥ K = L ≥ M. Conclusions: I. J > M. II. J = M.

• The path is ≥, =, ≥, so J ≥ M.
• J > M alone is not certain, and J = M alone is not certain. Together they cover J ≥ M.
• Answer: either I or II.

Example 4: coded inequality

In a code: P @ Q means P > Q; P # Q means P < Q; P $ Q means P ≤ Q; P % Q means P ≥ Q; P & Q means P = Q.

Statements: A @ B, B % C, C & D, D # E. Conclusions: I. A @ D. II. E @ B. III. B % D.

• Decode first: A > B, B ≥ C, C = D, D < E. So A > B ≥ C = D < E.
• I: A > D. True.
• II: E > B? The path E > D = C ≤ B turns at C. Does not follow.
• III: B ≥ D. B ≥ C = D. True.
• Answer: I and III.

Example 5: which expression makes it true?

Which expression makes "P > S" definitely true?

Answer: (c). For "fill the blank" versions of this question, the same check works: try each sign in the gap and keep the one that makes the path one-way with a strict sign.

Common mistakes

• Reading ≥ as >. "A ≥ B > C" gives A > C, but "A ≥ B ≥ C" gives only A ≥ C.
• Missing a turn in the middle. Trace the whole path, not just the two ends.
• Choosing either-or when there is no relation. Either-or needs a ≥ or ≤ between the two letters.
• Choosing either-or when one conclusion already follows. If J > M is certain, "J = M" is simply false.
• Decoding symbols in the wrong direction in coded questions. Write "@ = >" at the top of your rough sheet.

Practice set

1. A ≥ B > C ≤ D = E. Conclusions: I. A > C. II. E ≥ C.
2. P > Q ≥ R = S < T. Conclusions: I. P > S. II. T > Q.
3. W ≤ X = Y < Z. Conclusions: I. W < Z. II. Z > X.
4. K ≥ L ≥ M. Conclusions: I. K > M. II. K = M.
5. F < G ≤ H > I. Conclusions: I. F < H. II. G > I.
6. Statements: T > U ≥ V; W ≤ V; X = W. Conclusions: I. T > X. II. X < V.
7. Using the codes in Example 4: G $ H, H & J, J @ K. Conclusions: I. G # K. II. K # H.
8. Statements: R > S ≤ T; U < T. Conclusions: I. R > T. II. U > S.

Answers

1. Both. A ≥ B > C gives A > C. C ≤ D = E gives E ≥ C.
2. Only I. P > Q ≥ R = S gives P > S. For II, the path T > S = R ≤ Q turns at R.
3. Both. W ≤ X = Y < Z gives W < Z, and X = Y < Z gives Z > X.
4. Either I or II. K ≥ M, and the two conclusions split it.
5. Only I. F < G ≤ H gives F < H. G ≤ H > I turns at H.
6. Only I. T > U ≥ V ≥ W = X gives T > X. For II, the chain gives only V ≥ X, so X < V is not certain.
7. Only II. Decoded: G ≤ H = J > K. For I, G ≤ … > K turns at J. For II, H = J > K gives K < H.
8. Neither. R > S ≤ T turns at S, and U < T > S turns at T. No relation exists in either, so either-or does not apply.

What to do next

• Write the four-row rule table from memory, then solve the practice set again in under four minutes.
• Do 15 inequality questions a day for a week, half of them coded.
• Pair this topic with syllogism, since both reward the same habit of asking "must this be true?", and see the reasoning plan for where to attempt them in the section.