Inequality (Logical Reasoning)

1. What It Is

  • Inequality questions test your ability to compare two or more persons, numbers, or objects based on given relations.
  • Relations can be mathematical (> , <) or verbal (greater, smaller, taller, younger, etc.).
  • Objective: decide the correct relationship using the given statements.

Examples:

  • A > B, B = C → What is the relation between A and C?
  • Ram is taller than Shyam. Shyam is taller than Mohan. Who is tallest?

2. How to Approach

  1. Read all statements carefully – identify relationships.
  2. Convert verbal statements to symbols if needed:
    • “greater than” → >
    • “less than” → <
    • “equal to” → =
  3. Link the statements logically – combine the relations step by step.
  4. Determine final comparison – what exactly is asked?

3. Rules & Key Points

  • Transitive property applies:
    • If A > B and B > C → A > C
    • If A = B and B > C → A > C
  • Look for multiple steps – sometimes indirect relations are required.
  • Pay attention to negatives – “not equal,” “not taller,” etc.
  • Use short symbols for quick comparison → avoids confusion.

4. Tricks & Shortcuts

  1. Draw a diagram or chain: A > B > C …
  2. Start with strongest or fixed relationship first.
  3. Check carefully for equality signs.
  4. Use elimination method if multiple options given.
  5. Convert verbal to symbolic for faster analysis.

5. Types of Inequality Questions

  1. Direct Comparison – Compare two people/numbers directly.
  2. Three or More Entities – Use transitive property.
  3. Mixed Relations – Combination of >, <, =
  4. Coding / Symbol Substitution – Given symbols represent inequality.
  5. Positional / Rank-Based Inequalities – Heights, ages, marks, etc.

6. Stepwise Solving Strategy

  1. Identify all relations given in statements.
  2. Convert to symbols or draw comparison chains.
  3. Combine statements step by step.
  4. Check transitive relations → final answer.
  5. Choose answer based on direct or derived relation.

7. Easy Practice Questions

1. Direct Comparison

Statements:

  1. A > B
  2. B > C

Question: Which is true?

Solution:

  • A > B, B > C → A > C ✅
  • Answer: A is greatest among A, B, C

2. Three Entities

Statements:

  1. X = Y
  2. Y > Z

Question: Which is true?

Solution:

  • X = Y → X = Y
  • Y > Z → X = Y > Z → X > Z ✅

3. Mixed Relations

Statements:

  1. P < Q
  2. Q = R

Question: Relation between P and R?

Solution:

  • P < Q, Q = R → P < R ✅

4. Rank-Based

Statements:

  1. A is taller than B
  2. B is taller than C

Question: Who is shortest?

Solution:

  • Chain: A > B > C → Shortest = C

5. Symbol / Coding

Statements:

  • @ means >, # means =, $ means <
  • A @ B # C $ D

Question: Relation between A and D?

Solution:

  • A > B = C → A > C
  • C < D → A > D ❌ wait step: check chain
  • B = C → A > B = C → A > C
  • C < D → D > C → Compare A and D?
  • We cannot directly say → A > D ❌ insufficient info

8. Difficult Practice Questions

6. Multi-step Comparison

Statements:

  1. E > F = G
  2. H < G

Question: Who is smallest?

Solution:

  • F = G → E > F = G
  • H < G → H < G → H < F, H < E
  • Smallest = H ✅

7. Age Inequality

Statements:

  1. A is older than B but younger than C
  2. D is older than C

Question: Who is oldest?

Solution:

  • Chain: B < A < C < D
  • Oldest = D ✅

8. Rank-Based

Statements:

  1. 5 students, Ranks: P > Q > R > S > T
  2. S is taller than Q

Question: Who is tallest?

Solution:

  • First chain is rank by marks/height? Assuming rank for comparison.
  • If S taller than Q, new chain: P ? S ?
  • Need clarity – multiple possibilities → insufficient info

9. Symbol Substitution (Difficult)

Statements:

    • means <, % means >, & means =
  • X * Y & Z % W

Question: Relation X ? W

Solution:

  • X < Y, Y = Z → X < Z
  • Z > W → X < Z > W → X < W ✅

10. Complex Multi-Step

Statements:

  1. A > B, B = C
  2. C < D, D = E
  3. E > F

Question: Who is smallest?

Solution:

  • Chain: A > B = C < D = E > F
  • Arrange: F < C = B < D = E < A
  • Smallest = F ✅

✅ Quick Tips

  1. Convert words to symbols for faster solving.
  2. Draw a comparison chain or table.
  3. Use transitive property carefully.
  4. Handle equalities (=) correctly.
  5. Multiple-step inequalities → solve step by step.