Inequalities

Why This Chapter Matters

Inequalities (symbol-based) appear in every Banking exam — 5 marks. Both direct and coded inequality questions need fast solving. Systematic approach is key.

Core Concepts

1. Basic Symbols

2. Rules for Combining Inequalities

If A > B and B > C: then A > C (transitive)

If A > B and B = C: then A > C

If A = B and B > C: then A > C

If A ≥ B and B > C: then A > C

If A ≥ B and B ≥ C: then A ≥ C

CANNOT COMBINE: If A > B and C > B (B is not a bridge)

3. Conclusion Types

"A > B" is definitely true | "A < B" is definitely false

"A ≥ B" is true means A is greater than or equal (either OR relationship)

"Either A > B or A = B" — conclusion is "A ≥ B"

4. Coded Inequalities

Replace symbols with codes:

Decode first, then apply normal rules.

5. New Pattern

Given: A $ B (A ≥ B), B > C, C @ D (C < D), D # E (D = E)

Conclusions: (I) A > C (II) E > B (III) D < B

Step-by-step: A ≥ B > C < D = E

From A ≥ B > C: A > C (✓ conclusion I follows)

From B > C < D: can't compare B and D directly. Conclusion II (E > B): E = D > C but B > C too, can't determine E vs B. Doesn't follow.

Conclusion III (D < B): Same issue. Doesn't follow.

Key: Break the chain where inequality direction changes (< to > or > to <). Conclusions only follow within unbroken chains.

Practice Problems

Q1: A > B ≥ C = D > E < F

(I) A > D? Yes — A > B ≥ C = D, so A > D. ✓

(II) F > C? Cannot determine — F > E but E < D = C, so F could be more or less than C. ✗

(III) B > E? Yes — B ≥ C = D > E, so B > E. ✓

Q2 (Either-Or): A ≥ B, B ≤ C, A > C?

A ≥ B, C ≥ B. Relation between A and C? Not determined.

But: "A > C OR A = C OR A < C" — so "A ≥ C" or "A ≤ C" — without more info, "Either I or II" can only be used when I and II are complementary.

Previous Year Questions

SBI PO 2023: 5 statements, 5 conclusions. Coded with letters P@Q meaning P

IBPS Clerk 2022: "P ≥ Q > R = S < T ≤ U". Which conclusions follow?

Revision Notes

TRANSITIVE RULE:
Same direction chain: A>B>C → A>C, A>C
Mixed direction: STOP — cannot conclude

CODED INEQUALITY:
1. Decode all symbols first
2. Write out the chain in standard notation
3. Apply transitive rules

EITHER-OR CASES:
Used when two conclusions together cover all possibilities
If (I) A>B and (II) A=B, then "Either I or II" if A≥B is given (but not alone)
Common: either I or II follows when they are complementary and one must be true

QUICK TIPS:
Break chain at direction change (> to < or < to >)
Same inequality can be strengthened: A≥B + B>C → A>C (not A≥C)
Weakened: A>B + B≥C → A>C still (because B≥C includes B=C, and A>B>C or A>B=C both give A>C)