Types
Direct inequality (A > B ≥ C = D) with two conclusions, combined multi-statement inequality (three or four separate statements that must be joined), and "which symbol should replace the question mark" problems. Expect 3-5 questions in Prelims.
Core rules
- A conclusion is true only if the chain between the two elements has signs in one direction: >, ≥, = (or <, ≤, =). A > B ≤ C gives no relation between A and C.
- The resulting sign is the strongest one in the chain: if any > appears with ≥ and =, the result is >. Only ≥ and = gives ≥. Only = gives =.
- Combine statements through common elements: A ≥ B > C and C = D ≤ E join at C.
The either-or rule
If neither conclusion is definitely true, but both are about the same pair and together give the established relation, the answer is "Either I or II". The standard pairs are:
| Established | Conclusions |
|---|---|
| Q ≥ S | I. Q > S, II. Q = S |
| Q ≤ S | I. Q < S, II. Q = S |
| no relation (Q vs S) | I. Q ≥ S, II. Q < S (or Q ≤ S / Q > S) |
Worked example
Statements: W > X ≥ Y; Y = Z; Z ≥ U; V < U. Conclusions: I. X > U, II. W > V. From X ≥ Y = Z ≥ U we only get X ≥ U, so I is not definite. W > X ≥ Y = Z ≥ U > V has one direction and contains >, so W > V is true. Answer: Only II.
Trap: when the chain gives X ≥ U, the conclusion "X > U" is false and so is "X = U" - but together they make an either-or pair. Look at both conclusions before marking "Neither".
Speed method
- Write all statements as one line, aligning common letters.
- For each conclusion, trace from one letter to the other and read the signs on the way.
- Opposite signs on the path means no relation - stop.
Time target
30-40 seconds per question. Combined three-statement versions: under a minute.