SSC CGL Reasoning Inequality: Concepts, Rules, Either/Or & Coded Inequality

Inequality is a logical reasoning topic that involves determining relationships between variables, letters, or elements using comparison symbols such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), and equal to (=).

Questions are generally based on a set of statements followed by conclusions. Candidates must determine whether the conclusions logically follow from the given statements.

Since inequality questions are frequently asked in SSC CGL examinations, understanding the underlying rules and concepts is essential for scoring well in the reasoning section.

Types of Inequality Questions in SSC CGL

SSC CGL generally asks questions from the following types of inequality:

• Direct Inequality

• Coded Inequality

• Statement and Conclusion Based Inequality

• Either/Or Inequality Questions

Among these, coded inequality and Either/Or questions are commonly considered more challenging.

Important Inequality Symbols

Candidates must be comfortable interpreting these symbols before attempting inequality questions.

Introduction to Inequality Rules

When presented with statements and conclusions, the goal is to determine which conclusions are correct based on the given information. This relies on two fundamental rules:

Consistent Sign Direction:

• All signs must be in a single, consistent direction when establishing a path between two elements. For example, all signs should point left (<, <=) or all signs should point right (>, >=).

• If the direction of signs reverses along the path, the connection between the elements is considered blocked, and no definite conclusion can be drawn.

Rule: When evaluating a path between two elements, the highest priority sign present in the clear path dictates the resultant relationship:

• If all three signs (Grandfather, Father, Neighbor) are present, the Grandfather sign is the resultant.

• If Grandfather and Father signs are present, the Grandfather sign prevails.

• If Father and Neighbor signs are present, the Father sign prevails.

Either/Or Conditions

The Either/Or condition applies when a definite conclusion cannot be drawn, but the two given conclusions, when combined, cover all possible scenarios.

General Conditions for Either/Or:

1. Both conclusions must be individually incorrect.

2. Subjects and predicates must be the same in both conclusions.

Types of Either/Or Cases:

• Case 1: Consistent Sign Direction (Expected Result)

• This occurs when signs between elements are in a single direction, and a definite resultant sign (e.g., Grandfather, Father) is expected. However, this exact resultant is not presented in either conclusion individually.

• If the two conclusions, when combined, accurately represent the expected resultant (e.g., if the expected result is >= and the conclusions are > and =, then Either/Or applies).

• Case 2: Opposite Sign Direction (No Relation)

• This applies when signs between elements are in opposite directions, indicating no definite relation (a "no result" scenario).

• In this situation, the two conclusions must collectively cover a minimum of three distinct signs (Greater Than, Less Than, and Equal To).

• Example: If the relationship between A and B is uncertain due to opposite signs, and the conclusions are A > B and A <= B, then Either/Or applies because A > B, A < B, and A = B are all collectively covered.

Coded Inequality

Coded Inequality is an advanced topic often appearing in examinations like the CGL Mains. It requires careful decoding of symbols before applying the standard inequality rules.

Decoding Symbols

In Coded Inequality, conventional symbols (like #, @, *, $ or =) are used to represent standard inequality signs (<, >, <=, >=, =).

Strategy: Always write down the meaning of each symbol first to convert the coded statement into a regular inequality statement.

Example Decoding:

• # means Greater Than (e.g., A # Q means A > Q).

• @ means Equal To (e.g., T @ R means T = R).

• * means Greater Than or Equal To.

• $ means Smaller Than.

• = means Smaller Than or Equal To.