Inequalities for IBPS Clerk

Inequality questions give you a chain of relations such as A > B ≥ C = D and ask which conclusions must be true. There is no diagram to draw and no arrangement to build. With the rules below, most of them take 15 to 25 seconds, which makes them some of the cheapest marks in the reasoning section.

They usually come as a small set in the prelims, often in the opening minutes of your attempt because they are quick. In the mains the same logic appears in a disguised form: the signs are replaced by codes, or the statements are split up and have to be joined first. The method does not change.

The one rule that matters

You can combine two relations only when they point the same way.

• A > B ≥ C. Both signs open towards the left, so A > C. The chain holds.
• A > B < C. The signs point in opposite directions from B, so A and C have no fixed relation. A could be larger, smaller or equal.

Put your finger on the first letter of the conclusion and slide along the chain to the second letter. If every sign you cross points the same way (ignoring = signs), a relation exists. The moment the direction flips, stop. No relation.

Combining signs

When the direction holds, the result is the strongest sign on the path. A single strict sign (> or <) anywhere on the path makes the whole result strict.

Either–or conclusions

Sometimes neither conclusion follows on its own, but between them they cover every case. Then the answer is "Either I or II follows". All three conditions must hold:

1. Both conclusions are about the same two letters.
2. Neither conclusion follows on its own.
3. Together they cover every possibility. The usual pair: the chain gives A ≥ C, and the conclusions are A > C and A = C.

If one conclusion already follows, the answer is never either–or.

Question types you will meet

Worked examples

Example 1 (direct). Statement: A > B ≥ C = D < E.
Conclusions: I. A > D. II. E > C.

1. A to D: >, ≥, =. Same direction, one strict sign. A > D. I follows.
2. E to C: E > D = C. E > C. II follows.
3. Both follow.

Example 2 (direction break). Statement: P ≤ Q < R > S ≥ T.
Conclusions: I. P < R. II. Q > T.

1. P ≤ Q < R gives P < R. I follows.
2. Q to T crosses Q < R > S. The direction flips at R. No relation. II does not follow.
3. Only I follows.

Example 3 (either–or). Statement: M ≥ N = O ≤ P.
Conclusions: I. M > O. II. M = O.

1. M ≥ N = O gives M ≥ O. Neither "M > O" nor "M = O" is certain on its own.
2. Both are about M and O, and together they make M ≥ O.
3. Either I or II follows.

Example 4 (jumbled). Statements: J > K, K ≥ L, L = M, N > M.
Conclusions: I. J > M. II. N > K.

1. Join the statements at shared letters: J > K ≥ L = M < N.
2. J to M: >, ≥, =. J > M. I follows.
3. N to K: N > M = L ≤ K. The direction flips at L. II does not follow.
4. Only I follows.

Example 5 (coded, mains style). Codes: A @ B means A > B; A # B means A ≥ B; A $ B means A = B; A % B means A < B; A & B means A ≤ B.
Statements: R @ S, S $ T, T & U, U % V.
Conclusions: I. R @ T. II. V @ S.

1. Decode: R > S, S = T, T ≤ U, U < V. Chain: R > S = T ≤ U < V.
2. I says R > T. R > S = T, so R > T. I follows.
3. II says V > S. V > U ≥ T = S, so V > S. II follows.
4. Both follow.

Example 6 (sign-filling). Which sign should replace the blank so that X > Z definitely holds? X ≥ Y __ Z. Options: >, ≥, =.

1. With >: X ≥ Y > Z. One strict sign on the path, so X > Z. Works.
2. With ≥: X ≥ Y ≥ Z gives only X ≥ Z. Fails.
3. With =: X ≥ Y = Z gives only X ≥ Z. Fails.
4. The answer is >.

Common mistakes

• Treating ≥ as >. From A ≥ B ≥ C you get A ≥ C, never A > C.
• Reading past a direction change. In A > B < C, the shared letter B is smaller than both, so A and C can be in any order.
• Marking either–or when one conclusion already follows. Check each conclusion alone first.
• Mixing up codes. In the mains, "not greater than" means ≤ and "not smaller than" means ≥. Translate these slowly.
• Reversing a conclusion by accident. "E > C" and "C > E" look alike when you are rushing. Read the conclusion aloud in your head before you check it.

Practice

Set a five-minute timer. For questions 1 to 6 and 8, choose: only I, only II, either I or II, neither, or both.

1. W > X ≥ Y > Z. Conclusions: I. W > Z. II. X > Z.
2. A < B ≤ C > D. Conclusions: I. A < C. II. B > D.
3. G ≥ H = K ≤ J. Conclusions: I. G ≥ K. II. J > G.
4. F ≤ G = H < I. Conclusions: I. F = H. II. F < H.
5. Statements: P > Q, R ≥ Q, S < R, S = T. Conclusions: I. P > S. II. R > T.
6. Using the codes in Example 5. Statements: M # N, N @ O, O $ P, Q % P. Conclusions: I. M @ O. II. Q $ M.
7. Which sign sequence makes A < D definitely true in A __ B __ C __ D? (a) ≤, =, < (b) <, >, ≤ (c) =, ≥, < (d) ≤, ≤, ≤
8. Statements: E > F, F ≥ G, G ≥ H, H > I. Conclusions: I. I > F. II. G > H.

Answers:

1. Both. W > X ≥ Y > Z gives W > Z. X ≥ Y > Z gives X > Z.
2. Only I. A < B ≤ C gives A < C. B ≤ C > D flips at C, so B and D have no relation.
3. Only I. G ≥ H = K gives G ≥ K. From K, G and J point in opposite directions, so II fails.
4. Either I or II. F ≤ G = H gives F ≤ H. Neither part is certain alone, and together they cover it.
5. Only II. P > Q ≤ R flips at Q, so P has no relation to R, S or T. R > S = T gives R > T.
6. Only I. Decoded: M ≥ N > O = P > Q. So M > O, and Q < M, which means Q = M is false.
7. (a). A ≤ B = C < D contains a strict sign and no flip. (b) and (c) flip direction, and (d) gives only A ≤ D.
8. Neither. I is false, because F ≥ G ≥ H > I means F > I. G ≥ H allows G = H, so II is not certain.

What to do next

• Do 20 direct inequality questions a day for a week. Target: 10 questions in 4 minutes with no errors.
• In week two, switch to coded and jumbled statements, since those are the mains versions.
• Keep a short list of your own slips (≥ read as >, missed flips) and reread it before each mock.
• Pair this with syllogism, the other half of the quick-types block, and use data sufficiency to practise the same logic in a different format.