Inequalities
About 7 min · Reasoning Ability · English
Time worked out from the lesson's 534 words at 150 words a minute, plus a minute for each question.
Inequalities is a topic in IBPS PO Prelims Reasoning section. Unlike puzzles, inequality questions—when mastered—are quick to solve.
Key ideas
- The Six Symbols: The relationships are > (greater than), < (less than), = (equal to), ≥ (greater than or equal), ≤ (less than or equal), and ≠ (not equal). Every question tests your ability to chain these.
- Chaining Rule: You can only chain relationships when the connecting variable sits at opposite ends. A > B and B > C chains to A > B > C. A > B and C > B does NOT chain—rewriting C > B as B < C gives A > B < C, where the directions are opposite, so nothing follows about A and C.
- Definite vs. Indefinite: A conclusion is definite only if ALL elements in the chain point the same direction (all > or all <, with = allowed in between). If directions conflict or "either-or" is needed, the relationship is indefinite.
- Equal Sign Behavior: The = sign acts as a "pass-through." A ≥ B = C means A ≥ C. The equal sign doesn't block the relationship—it transfers it.
- Complementary Pairs (Either-Or): When neither X > Y nor X < Y is individually true, but together they cover all possibilities, "either (i) or (ii)" becomes the answer. This happens when the chain shows X and Y are definitely not equal, but direction is unclear.
Watch out for
- Reversing without flipping the symbol: When you need to write B > A instead of A < B to chain, students forget that the inequality direction must flip. A < B is the same as B > A—always rewrite to make chains flow one direction.
- Treating ≥ as strictly >: A ≥ B does NOT mean A > B. If the conclusion asks "A > B" and the statement only gives A ≥ B, the conclusion is not definite (A could equal B).
- Misreading coded symbols: Under exam pressure, students decode @ as > once, then accidentally read it as < later. Write the decoded statement fully before solving.
Quick reference
- Same-direction symbols chain; opposite directions break the chain.
- Strict symbol (> or <) dominates when chained with ≥, ≤, or =.
- "Either-or" is valid only when both conclusions are individually false but one MUST be true.
- For coded inequalities: decode first, solve second—never decode on the fly.
- "Not greater" = ≤; "Not less" = ≥; "Neither greater nor equal" = <.
Check yourself: 3 questions
1. Statements: P ≥ Q > R = S; T < S Conclusions: I. P > T II. Q > T Which conclusion(s) logically follow(s)?
2. Statements: A > B ≥ C; D = C; E < D Conclusions: I. A > E II. B = D Which conclusion(s) logically follow(s)?
3. Statements: M < N ≤ O = P; Q > P Conclusions: I. Q > M II. N < Q Which conclusion(s) logically follow(s)?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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