Inequalities

Overview

Inequalities is one of the most reliable scoring topics in IBPS PO Prelims Reasoning section. Unlike puzzles that can consume 10+ minutes, inequality questions—when mastered—take 15–30 seconds each. You'll typically see 3–5 questions in the exam, appearing either as direct inequalities (symbols given explicitly) or coded inequalities (symbols replaced by codes like @, #, $, %).

The core skill is simple: chain multiple two-variable relationships and determine whether a definite relationship exists between two variables that aren't directly compared. Once you internalize the chaining rules, this becomes a near-guaranteed scoring area. Most errors come from rushing or misreading coded symbols—not from conceptual difficulty.

Key Concepts

• **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 directly—you must reverse one.

• **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.

• **Coded Inequalities**: The symbols are replaced with arbitrary codes. Your first job is to decode and write down the symbol meanings. Then solve exactly as direct inequalities.

• **Negation Trap**: "A is not greater than B" means A ≤ B. "A is neither greater than nor equal to B" means A < B. Read negations carefully.

Formulas / Key Facts

| Combination | Can Chain? | Result | |-------------|------------|--------| | > with > | Yes | > | | < with < | Yes | < | | > with ≥ | Yes | > | | ≥ with ≥ | Yes | ≥ | | < with ≤ | Yes | < | | ≤ with ≤ | Yes | ≤ | | > with = | Yes | > | | < with = | Yes | < | | > with < | No | Indefinite | | ≥ with < | No | Indefinite |

**Priority Rule**: When chaining ≥ and =, result is ≥. When chaining > and =, result is >. The "strict" symbol dominates over "equal."