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Inequality & Coded Inequalities for IBPS PO

Master direct and coded inequality questions with shortcut tricks, solved examples, and smart approaches. Learn how to solve 5-7 questions quickly in the Reasoning section.

5-7
Questions Expected
⭐⭐⭐⭐
Importance
3-4 min
Time Required
Easy-Moderate
Difficulty Level

What is Inequality in Reasoning?

Inequality is one of the most scoring topics in the IBPS PO Reasoning section. Typically, 5 to 7 questions are asked from this topic. These questions test your ability to compare quantities and determine relationships between different elements using mathematical symbols.

In inequality questions, you are given statements with symbols like > (greater than), < (less than), = (equal to), ≥ (greater than or equal to), ≤ (less than or equal to). Based on these statements, you need to check which conclusions are true.

Why this topic matters: Inequality questions are quick to solve if you understand the rules. With practice, you can solve 5 questions in under 3 minutes with 100% accuracy.

Basic Symbols and Their Meanings

SymbolMeaningExample
>Greater thanA > B means A is greater than B
<Less thanA < B means A is less than B
=Equal toA = B means A is equal to B
≥Greater than or equal toA ≥ B means A is greater than or equal to B
≤Less than or equal toA ≤ B means A is less than or equal to B
≠Not equal toA ≠ B means A is not equal to B

Types of Inequality Questions

  • Direct Inequality: Statements use standard symbols (>, <, =, ≥, ≤). You need to find which conclusions follow.
  • Coded Inequality: Symbols are replaced with letters (e.g., @ for >, # for <). You must decode the symbols first, then solve like direct inequality.
  • Either-Or Cases: When two conclusions are given and either one can be true but not both simultaneously.
  • Complementary Pairs: Conclusions like A ≥ B and A < B (all possibilities covered) form complementary pairs.

Golden Rules & Shortcut Tricks

Rule 1: Priority of Symbols

When combining inequalities, remember: = > ≥ > ≤ is not correct. Actually, treat each symbol separately. Always combine statements step by step.

Rule 2: The "Either-Or" Condition

Two conclusions form an Either-Or pair if:

  • Both conclusions are false individually
  • They cover all possible relationships (e.g., A > B and A ≤ B)
  • The elements are the same in both conclusions
Rule 3: Complementary Pairs

Common complementary pairs: (≥ and <), (≤ and >), (> and ≤), (< and ≥), (= and ≠)

Rule 4: Quick Elimination

If a conclusion contains a symbol that contradicts the given statements, it is definitely false. For example, if statements say A > B and B > C, then A = C is false.

Solved Example 1: Direct Inequality

Question:

Statements: P ≥ Q = R, S > R, T < S
Conclusions:
I. P ≥ R
II. T < Q
III. S > P
IV. Q < S

Which of the following is true?

Solution:

Step 1: Combine statements: P ≥ Q = R → P ≥ R. Also, S > R = Q → S > Q, and T < S.

Check Conclusion I: P ≥ R → From P ≥ Q = R, we get P ≥ R. TRUE

Check Conclusion II: T < Q → We know T < S and S > Q. But T and Q have no direct relation. FALSE

Check Conclusion III: S > P → We know S > R and P ≥ R. S could be > P or ≤ P. No definite relation. FALSE

Check Conclusion IV: Q < S → From S > R and R = Q, we get S > Q. TRUE

Answer: Conclusions I and IV are true.

Solved Example 2: Coded Inequality

Question:

Directions: In the following question, symbols @, #, $, %, & are used with following meanings:
P @ Q → P is greater than Q (P > Q)
P # Q → P is less than Q (P < Q)
P $ Q → P is greater than or equal to Q (P ≥ Q)
P % Q → P is equal to Q (P = Q)
P & Q → P is less than or equal to Q (P ≤ Q)

Statements: A $ B, B % C, C # D
Conclusions:
I. A $ C
II. A & C
III. B # D

Solution:

Step 1 - Decode the statements:
A $ B → A ≥ B
B % C → B = C
C # D → C < D

Step 2 - Combine: A ≥ B = C < D

Step 3 - Check conclusions:
I. A $ C → A ≥ C → From A ≥ B and B = C, we get A ≥ C. TRUE
II. A & C → A ≤ C → Not necessarily true because A ≥ C. FALSE
III. B # D → B < D → From B = C and C < D, we get B < D. TRUE

Answer: Conclusions I and III are true.

Solved Example 3: Either-Or Case

Question:

Statements: A > B ≥ C, D = B, E ≤ C
Conclusions:
I. A > E
II. A = E

Solution:

Combine statements: A > B ≥ C and B = D, E ≤ C

From A > B and B ≥ C ≥ E, we get A > C ≥ E → A > E (since A > C and C ≥ E, so A > E)

Therefore, Conclusion I (A > E) is TRUE. Conclusion II (A = E) is FALSE.

Note: This is NOT an Either-Or case because one conclusion is definitely true. Either-Or applies only when both are false individually but together cover all possibilities.

Practice Questions for Self-Assessment

Practice Question 1:

Statements: M ≥ N = O, P > O, Q ≤ P
Conclusions: I. M > O, II. Q > N, III. P ≥ Q
Which conclusions follow?

Practice Question 2 (Coded):

If P @ Q means P ≥ Q, P # Q means P < Q, P $ Q means P = Q, then statements: A @ B, B # C, C $ D. Conclusions: I. A # C, II. B $ D, III. A @ D. Find true conclusions.

Practice Question 3:

Statements: X > Y ≤ Z, W = Y, V ≥ Z
Conclusions: I. X > W, II. V ≥ Y, III. W < Z
Which conclusions are true?

Answers: Q1: Only III follows | Q2: Only III follows | Q3: I, II, and III all follow

Frequently Asked Questions about Inequality

Q1: How many questions come from Inequality in IBPS PO?
Typically, 5 to 7 questions are asked from Inequality in both Prelims and Mains. In some papers, it can go up to 8-9 questions.
Q2: What is the difference between direct and coded inequality?
Direct inequality uses standard symbols (>, <, ≥, ≤, =). Coded inequality replaces these symbols with letters or special characters, and you must decode them first before solving.
Q3: When does an "Either-Or" case occur?
An Either-Or case occurs when two conclusions are both false individually but together they cover all possible relationships between the elements (e.g., A > B and A ≤ B).
Q4: What are complementary pairs in inequality?
Complementary pairs are pairs of conclusions where one covers the opposite of the other. Examples: (≥ and <), (≤ and >), (= and ≠), (> and ≤), (< and ≥).
Q5: What is the best way to solve inequality questions quickly?
Practice combining statements step by step. Always write the combined chain clearly. Memorize complementary pairs. For coded inequalities, quickly decode all statements before solving.
Q6: Is there negative marking for inequality questions?
Yes, 0.25 marks are deducted for each wrong answer in IBPS PO objective tests. So accuracy is very important.

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