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Inequality
Reasoning Ability · Core Logical Tools
Useful for: IBPS Banking
Overview
Inequality questions combine given relations through common terms and test which conclusions definitely follow.
Key points
- A > B ≥ C gives A > C.
- A ≥ B ≥ C gives A ≥ C.
- If the signs between two elements point in opposite directions (A > B < C), no relation follows.
- Coded inequalities: decode symbols first.
- Either-or applies when two conclusions (e.g. A > B and A = B) together cover all cases and neither follows alone.
Explanation
- Use the strongest sign: > combined with ≥ gives >.
- = with ≥ gives ≥.
- Write the chain left to right with common terms adjacent.
- Check each conclusion separately.
Step by step
- Set up the frame (table, rows, steps).
- Apply definite clues, then branch.
- Verify every clue before answering.
Examples
- A > B ≥ C = D → A > D (true); B ≥ D (true); C > A (false).
- P ≤ Q < R → P < R (true).
- M > N < O → no relation between M and O.
Traps and advanced points
- Trap: Combining opposite-direction signs.
- Trap: Missing the either-or case.
- Trap: Not decoding symbols.
Quick revision
- > with ≥ gives >.
- Opposite signs → no relation.
- Either-or for complementary pairs.
Practice MCQs
Five persons A, B, C, D, E sit in a row facing north. E is at the left end, A sits immediately right of E, B immediately right of A, and C immediately right of B. Who sits in the middle?
- C
- B
- D
- A
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Answer: (b) B. Place the fixed chain from left to right.
Five persons A, B, C, D, E sit in a row facing north. A is at the left end, B sits immediately right of A, C immediately right of B, and D immediately right of C. Who sits in the middle?
- B
- D
- A
- C
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Answer: (d) C. Place the fixed chain from left to right.
Five persons A, B, C, D, E sit in a row facing north. B is at the left end, C sits immediately right of B, D immediately right of C, and E immediately right of D. Who sits in the middle?
- D
- A
- C
- B
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Answer: (a) D. Place the fixed chain from left to right.
Five persons A, B, C, D, E sit in a row facing north. C is at the left end, D sits immediately right of C, E immediately right of D, and A immediately right of E. Who sits in the middle?
- C
- B
- E
- A
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Answer: (c) E. Place the fixed chain from left to right.
Five persons A, B, C, D, E sit in a row facing north. D is at the left end, E sits immediately right of D, A immediately right of E, and B immediately right of A. Who sits in the middle?
- D
- B
- C
- A
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Answer: (d) A. Place the fixed chain from left to right.
A > B ≥ C. Which follows?
- A > C
- A < C
- A = C
- C > A
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Answer: (a) A > C. Same direction; strict sign carries.
A > B < C. Relation between A and C —
- A = C
- cannot be determined
- A > C
- A < C
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Answer: (b) cannot be determined. Opposite directions.
P ≥ Q = R > S. Which follows?
- P < S
- S > Q
- P > S
- P ≥ S
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Answer: (c) P > S. A strict sign in the chain makes it strict.
M = N ≥ O. Conclusions: I. M > O, II. M = O.
- only I
- only II
- either I or II
- neither
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Answer: (c) either I or II. M ≥ O: one of them must hold.
X < Y ≤ Z. Which is true?
- X > Z
- X = Z
- Z ≤ X
- Z > X
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Answer: (d) Z > X. X < Z.
More topics in this chapter
Notes and questions are written by Kundali IQ for practice. They are not official papers; always check the latest official notification for the syllabus and pattern.