Inequalities

Inequalities

Overview

Inequalities is one of the most scoring and time-efficient topics in SBI Clerk Prelims Reasoning section. Questions test your ability to interpret relationship symbols (>, <, =, ≥, ≤) between elements and derive valid conclusions.

This topic comes in two forms: Direct Inequalities (symbols given as-is) and Coded Inequalities (symbols replaced by codes like @, #, $, %). Mastering the logical chain rules and recognizing invalid combinations is the key to accuracy. Since there's no calculation involved, this is pure logic — ideal for quick marks.

Key Concepts

• 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, the weakest link determines the final relationship. If any link includes "=" along with >, the combined result becomes ≥.
• Complementary Pairs: > and ≤ are complementary (opposite). Similarly, < and ≥ are complementary. A relationship must be one or the other.
• Coded Inequality Decoding: Always write out the code key first. Convert coded statements to standard symbols before analyzing.

Formulas / Key Facts

Must-Remember Rules:

1. Same direction symbols → Definite conclusion possible
2. Opposite direction symbols → No definite conclusion
3. "Either-or" applies when both individual conclusions are false but are complementary
4. Always trace the chain from the first element to the last element mentioned in the conclusion
5. For coded inequalities, decode ALL symbols before attempting any question

Worked Examples

Example 1: Direct Inequality

Statement: P > Q ≥ R = S < T

Conclusions: I. P > S II. T > Q

Solution:

For I (P > S): Trace P → Q → R → S P > Q ≥ R = S All symbols point in the same direction (left to right: P is greater) P > Q ≥ R = S → P > S is TRUE

For II (T > Q): Trace T → S → R → Q T > S = R ≤ Q From T's perspective: T > S = R, then R ≤ Q Directions conflict (> then ≤) → T > Q is NOT DEFINITE

Answer: Only conclusion I follows.

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Example 2: Coded Inequality

Code: @ means >, # means <, $ means =, % means ≥, & means ≤

Statement: A @ B $ C # D % E

Decode first: A > B = C < D ≥ E

Conclusions: I. A > C II. E < B

Solution:

For I (A > C): A > B = C → A > C is TRUE

For II (E < B): Trace E → D → C → B E ≤ D > C = B Directions: ≤ then > then = → Mixed directions E < B is NOT DEFINITE

Answer: Only conclusion I follows.

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Example 3: Either-Or Case

Statement: M ≥ N = O ≤ P

Conclusions: I. M > P II. M = P

Solution:

Trace M → N → O → P: M ≥ N = O ≤ P Directions: ≥ then = then ≤ → Opposite directions (≥ vs ≤)

M > P → Not definite (FALSE) M = P → Not definite (FALSE)

But together, M ≥ P or M ≤ P must be true. Since we have M ≥ N = O and O ≤ P, the only certainty is M could be >, =, or < compared to P.

Wait — let's check: These conclusions are M > P and M = P. Together they make M ≥ P. But the chain doesn't guarantee M ≥ P.

Either-or does NOT apply here because M could also be < P.

Answer: Neither conclusion follows.

Common Mistakes

• 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: If any link has "=", the combined result includes "=" possibility.
• Applying either-or incorrectly → Using either-or when conclusions aren't complementary. Fix: Either-or only works when one conclusion is ">" and other is "=" for the same pair, or "<" and "=".
• Decoding errors in coded inequalities → Misremembering which symbol means what. Fix: Write the code key on rough sheet before solving. Never decode mentally.
• Reversing the chain direction → Checking Q > P when asked about P > Q. Fix: Always trace FROM the first element TO the second element as written in the conclusion.

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 ≤
• Trace conclusion elements in exact order given