Coded and Direct Inequalities
Coded and Direct Inequalities
Inequality questions give a chain such as A > B ≥ C = D < E and ask which conclusions must be true. Coded versions replace the signs with symbols like @ or #. The rule is mechanical: two letters are comparable only if every sign between them points the same way (or is =), and the result is strict if any sign on the path is strict.
1. Rules Box
| Signs on the path between two letters | Conclusion |
|---|---|
| All > or ≥ or = (no <) | First ≥ second; strict > if at least one > |
| All < or ≤ or = (no >) | First ≤ second; strict < if at least one < |
| Mixed directions (> and <) | No definite relation |
| Only = | Equal |
Either-or: if A ≥ B, then "A > B" and "A = B" are each possibly false, but one of them must be true. Mark "either I or II follows" only for such a pair on the same two letters
In coded questions, decode the symbols into signs first, then use the table
✗ A > B < C, so A > C | ✓ Opposite signs on the path: no definite relation
✗ A ≥ B = C, so A > C follows | ✓ Only A ≥ C is certain; A > C and A = C form an either-or pair
हिंदी नोट: असमिका में दो अक्षरों के बीच सभी चिह्न एक ही दिशा में हों तभी निश्चित संबंध बनता है। रास्ते में कहीं भी एक सख्त चिह्न (> या <) हो तो निष्कर्ष सख्त होगा। विपरीत दिशा के चिह्न हों तो कोई निश्चित संबंध नहीं।
Exam Pointer: These patterns had no verified NTPC shift in our check (the verified NTPC symbol-code questions, March 2026 Graduate and August 2025 UG CBT-1, coded family relations and are covered in Blood Relations) and are tagged syllabus-based. Inequalities appear in the NTPC reasoning syllabus and in CBT-2.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Direct inequalities
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. Statement: A > B ≥ C = D < E. Conclusions: I. A > D. II. E > C. Which follow?
A to D: >, ≥, = all point one way with a strict sign, so A > D. E to C: E > D = C, so E > C. Both follow.
Answer: Both I and II
EXAMATLAS LEVEL
Q. Statement: P ≥ Q > R ≤ S < T. Conclusions: I. P > R. II. T > R. III. S > Q. Which follow?
P ≥ Q > R gives P > R. R ≤ S < T gives T > R. Between Q and S the signs are > and ≤ in opposite directions, so III does not follow.
Answer: I and II only
Pattern 2: Coded symbols
[Pattern: syllabus-based, PYQ-style]
Codes for both questions: P @ Q means P > Q; P # Q means P < Q; P © Q means P = Q; P % Q means P ≥ Q; P ★ Q means P ≤ Q.
EXAM LEVEL
Q. If A @ B © C, does A @ C follow?
Decoded: A > B = C, so A > C, which is A @ C.
Answer: Yes
EXAMATLAS LEVEL
Q. If M % N @ O ★ P # Q, which follow? I. M @ O. II. Q @ O. III. N @ P.
Decoded: M ≥ N > O ≤ P < Q. M ≥ N > O gives M > O (I follows). O ≤ P < Q gives Q > O (II follows). N > O ≤ P has mixed directions (III does not follow).
Answer: I and II only
Pattern 3: Either-or conclusions
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. Statement: A ≥ B = C. Conclusions: I. A > C. II. A = C.
A ≥ C is certain, but neither part alone is. The two cover every case for the same pair, so either I or II follows.
Answer: Either I or II
EXAMATLAS LEVEL
Q. Statement: X ≤ Y < Z ≥ W. Conclusions: I. X < Z. II. W < Y. III. Z = W. IV. Z > W.
X ≤ Y < Z gives X < Z (I follows). Y < Z ≥ W has mixed directions, so II does not follow. Z ≥ W makes III and IV an either-or pair.
Answer: I, and either III or IV
Pattern 4: Choosing signs or arrangements that make a conclusion true
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. Which pair of signs in A ? B ≥ C ? D makes A > D definitely true? (a) >, = (b) <, > (c) ≤, ≥ (d) =, <
(a) gives A > B ≥ C = D, so A > D. (b) and (c) start with signs pointing the wrong way, and (d) ends with C < D, so A > D is not certain.
Answer: (a)
EXAMATLAS LEVEL
Q. Which arrangement makes both P < S and R ≥ Q definitely true? (a) P < Q ≤ R = S (b) P ≤ Q < R > S (c) S > R < Q = P (d) R ≥ Q > P ≥ S
(a): P < Q ≤ R = S gives P < S, and R ≥ Q directly. (b) fails P < S (mixed signs). (c) gives R < Q. (d) gives P ≥ S.
Answer: (a)
60-Second Revision
- Same-direction path: definite relation; one strict sign makes it strict.
- Mixed directions: no relation.
- ≥ or ≤ alone: the > and = conclusions form an either-or pair.
- Decode symbols before reasoning.
Next Step: Mathematical Operations done. Try the operator and inequality questions in the ExamAtlas RRB NTPC 2026 mock tests; rewrite every coded sign before you calculate.