Inequalities
About 7 min · Reasoning Ability · English
Time worked out from the lesson's 545 words at 150 words a minute, plus a minute for each question.
Inequalities is a topic in SBI Clerk Prelims Reasoning section. Questions test your ability to interpret relationship symbols (>, <, =, ≥, ≤) between elements and derive valid conclusions.
Key ideas
- Basic Symbols: > means "greater than", < means "less than", = means "equal to", ≥ means "greater than or equal to", ≤ means "less than or equal to".
- Definite vs. Indefinite Relationships: A conclusion is definite only when all connecting symbols point in the same direction (all left-pointing or all right-pointing). Mixed directions yield no definite relationship.
- Chain Rule: You can combine relationships only when elements share a common link. For A > B ≤ C, the relationship between A and C is indefinite because > and ≤ conflict.
- Either-Or Conclusions: When two conclusions are individually false but together cover all possibilities (one uses > and other uses =, or one uses < and other uses =), "either-or" applies.
- Priority of Definite Symbol: In a chain running one way, one strict link (> or <) makes the result strict; the result is ≥ (or ≤) only when every link is ≥ (≤) or =.
Watch out for
- Ignoring direction conflicts → Students assume A > B < C means A > C. Fix: Check if all symbols point the same way; opposite symbols = no conclusion.
- Confusing ≥ and > → Writing "A > B" when chain shows "A ≥ B". Fix: The result includes the "=" possibility only when no link is strict (every link is ≥ or =).
- Applying either-or incorrectly → Using either-or when conclusions aren't complementary. Fix: Either-or works only for the same pair when the two conclusions together cover every case: complementary pairs (> with ≤, < with ≥), or > with = (< with =) when the chain gives ≥ (≤).
Quick reference
- Same direction symbols = Definite conclusion possible
- Opposite/mixed directions = No definite relationship
- Either-or = Both false individually + complementary pair
- Decode first, solve later (for coded inequalities)
- ≥ combines with ≥, >, or = to stay definite; breaks with < or ≤
Check yourself: 3 questions
1. Statements: P > Q ≥ R = S; T < R Conclusions: I. P > T II. Q > S
2. Statements: M ≤ N < O; P ≥ O; Q = P Conclusions: I. Q > M II. N < Q
3. In the following question, the symbols @, #, %, $ and * are used with the following meanings: A @ B means A is not greater than B A # B means A is neither greater than nor equal to B A % B means A is neither smaller than nor greater than B A $ B means A is not smaller than B A * B means A is neither smaller than nor equal to B Statements: K # L, L $ M, M * N Conclusions: I. K # M II. L * N
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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