Direct and coded inequalities for SBI PO

Inequality questions are free marks if your method is mechanical and a trap if it is not. The chains look simple, but a single sign pointing the other way breaks the link, and the options are built to catch anyone who reads the chain too quickly.

The good news: one rule, one table and one habit (decode first, then answer) cover every version you will meet in SBI PO.

How it is asked

• Direct inequality (prelims): a chain such as J ≥ K = L > M with two or three conclusions.
• Coded inequality (mains, sometimes prelims): the signs are replaced by symbols such as @ or #, and you decode them first.
• Multi-statement sets: two or three separate chains that share a letter, so you must join them at that letter.
• Missing-sign questions: "Which sign should replace the question mark so that A > D is definitely true?"

The number of questions varies, so check recent papers. What does not vary is that each one should take well under a minute.

The one rule

You can combine two relations only if they point in the same direction. Follow the chain from one letter to the other. If every sign on the way points the same way (all > or ≥, or all < or ≤, with = anywhere), there is a definite relation. If the direction changes even once, there is no definite relation.

Reading a chain backwards

A chain can be read in either direction. A > B means B < A. When a conclusion is written the other way round, such as "M < J" for a chain that starts at J, flip it before you compare: M < J is the same as J > M.

The either–or test

Sometimes neither conclusion follows alone but one of them must be true. Mark "either I or II follows" only if all three hold:

1. Both conclusions use the same two letters.
2. Neither follows on its own.
3. Together they cover every possibility. The usual pairs are > with =, when the chain gives ≥; and > with ≤, or < with ≥, when there is no relation at all.

Worked examples

Example 1 (direct). J ≥ K = L > M

Conclusions: I. J > M. II. L ≥ J.

• J to M: ≥, =, >. All point the same way and one is strict, so J > M. I follows.
• J to L: ≥, = gives J ≥ L, which means L ≤ J. II claims the opposite. It does not follow.
• Only I follows.

Example 2 (either–or). R ≥ S = T

Conclusions: I. R > T. II. R = T.

• R ≥ T. Neither I nor II is certain, but R ≥ T means one of them must be true.
• Either I or II follows.

Example 3 (two statements). Statements: P > Q ≥ R; R < S ≤ T.

Conclusions: I. P > S. II. T > R. III. Q ≥ S.

• Join at R: P > Q ≥ R < S ≤ T.
• P to S: the direction changes at R. I does not follow.
• T to R: read backwards, T ≥ S > R, so T > R. II follows.
• Q to S: the direction changes at R. III does not follow.
• Only II follows.

Example 4 (coded). Use these codes throughout this guide:

Statement: A @ B # C $ D % E

Conclusions: I. A @ D. II. E @ C. III. B @ E.

• Decode once: A > B ≥ C = D < E.
• I (A > D): >, ≥, = all point one way, with a strict sign. Follows.
• II (E > C): read backwards, E > D = C. Follows.
• III (B > E): the direction changes at D. Does not follow.
• I and II follow.

Example 5 (missing sign). A > B ? C ≥ D. Which sign in place of ? makes A > D definitely true? (a) < (b) ≤ (c) = (d) none of these

• The chain already runs downwards from A with a strict sign. Any sign that keeps the direction works: >, ≥ or =.
• < and ≤ reverse the direction and break the chain.
• (c) = is the only valid option offered.

Common mistakes

• Answering from the first and last letters only, without checking the direction at every step.
• Getting ≥ instead of >. One strict sign anywhere on the path makes the result strict.
• Marking either–or for different letters, such as "A > B or C = D".
• Decoding the same symbol twice for every conclusion. Decode the statement once on rough paper and answer everything from that line.
• Forgetting to flip a reversed conclusion. "E < A" is the same as "A > E".

Practice set

Use the codes from Example 4 where symbols appear.

1. W @ X $ Y # Z. I. W @ Z. II. Z & X.
2. D % E & F @ G. I. D % F. II. E @ G.
3. H # J $ K. I. H @ K. II. H $ K.
4. F < G ≤ H = I; I > J ≥ K. I. F < I. II. K < H. III. G > J.
5. U ≥ V > W; X < W ≤ Y. I. U > X. II. Y > V. III. V > X.
6. B & C $ D @ E; E # F % G. I. B & D. II. D @ F. III. G @ E.
7. L > M ≥ N = O < P. I. M > P. II. M ≤ P.
8. S ≥ T ? U > V. Which sign in place of ? makes S > V definitely true? (a) < (b) ≤ (c) ≥ (d) none of these

Answers:

1. Both. W > X = Y ≥ Z gives W > Z. X = Y ≥ Z gives Z ≤ X.
2. Only I. D < E ≤ F > G. D < F follows; E to G changes direction at F.
3. Either I or II. H ≥ J = K gives H ≥ K, so H > K or H = K.
4. I and II. F < G ≤ H = I gives F < I. K ≤ J < I = H gives K < H. G and J change direction at I.
5. I and III. U ≥ V > W > X gives U > X, and V > W > X gives V > X. Y and V change direction at W.
6. I and II. Decoded: B ≤ C = D > E ≥ F < G. B ≤ D follows. D > E ≥ F gives D > F. G and E change direction at F.
7. Either I or II. M to P changes direction at O, so there is no relation. But the two conclusions are about the same letters and together cover every case.
8. (c) ≥. S ≥ T ≥ U > V gives S > V. The signs < and ≤ reverse the chain.

What to do next

• Write the combining table from memory, including when the result is strict.
• Do 20 direct and 20 coded inequalities a day for five days. Time yourself: under 30 seconds each is the target.
• Practise joining two statements at a shared letter until it feels routine.
• Next, take on syllogism. For the quant version of the same idea, see quadratic inequalities.