Inequality: Notes for IBPS PO & SBI PO

Reading a chain

An inequality chain such as A > B >= C = D < E is a row of comparisons between neighbours. To compare any two elements, walk along the chain between them and look at every sign on the way. If all signs point the same way, the elements can be compared; if even one sign points the other way, they cannot.

When does a conclusion follow?

• Find the path between the two elements in the conclusion.
• If the signs are mixed, the conclusion does not follow (unless it forms an either-or pair).
• If the signs agree, work out the result and compare it with the conclusion. A conclusion 'P > Q' does not follow when the chain gives only P >= Q.
• A conclusion that says the opposite of the chain is simply false.

The either-or rule

Choose 'either I or II' only when all three conditions hold: neither conclusion follows on its own, both conclusions use the same two elements, and between them they cover every possibility. Typical pairs: 'A > B' with 'A = B' when the chain gives A >= B; 'A < B' with 'A = B' when it gives A <= B; and 'A >= B' with 'A < B' (or 'A > B' with 'A <= B') when there is no relation at all.

Worked example: Statement G <= H = K. Conclusions: I. K > G II. K = G. The chain gives K >= G. Neither alone is certain, but one must be true — either I or II follows.

Combining statements

When two or three statements are given separately, join them at the shared element and write one chain. Example: 'M > N >= P' and 'Q < P = R' combine at P as M > N >= P > Q, with R = P. Now M > Q follows, R > Q follows, and M > R also follows through M > N >= P = R. Check each path in turn.

Coded inequalities

Symbols such as #, @, $, % and & are assigned meanings in words. Make a decoding table first and rewrite every statement and conclusion with normal signs. Then solve as usual.

Which expression is true?

Some questions give four chains and ask in which one a relation (say P < T) definitely holds. Check only the path between the two named elements in each option: it must have all signs pointing the same way and at least one strict sign if the relation asked is strict. Another version gives blanks to fill (P _ Q _ R _ S) — try each option's signs in the blanks and apply the same test.