What it looks like
Symbols such as @, #, $, %, & are given meanings like 'P @ Q means P is greater than Q' or 'P % Q means P is not smaller than Q'. Statements and conclusions are written in these codes. The site generates practice sets for this topic; these notes give the decoding method.
Typical code definitions
| Coded phrase | Decoded sign |
|---|---|
| P is greater than Q | P > Q |
| P is either greater than or equal to Q / P is not smaller than Q | P ≥ Q |
| P is equal to Q / P is neither greater nor smaller than Q | P = Q |
| P is smaller than Q | P < Q |
| P is either smaller than or equal to Q / P is not greater than Q | P ≤ Q |
Method
- Write a decoding key beside the question once (for example @ = >, # = ≥, $ = =, % = <, & = ≤) and use it for all five questions.
- Convert every statement into normal signs before reading any conclusion.
- Convert each conclusion too, then solve as ordinary inequality: same-direction chain, strongest sign wins, opposite signs means no relation.
- Apply the either-or rule exactly as in normal inequality.
Worked example
Let 'P @ Q' mean P > Q, 'P # Q' mean P ≥ Q and 'P $ Q' mean P = Q. Statements: A # B, B @ C, C $ D. Decoded: A ≥ B > C = D. Conclusion 'A @ D' means A > D: the chain runs in one direction and contains >, so it is true. Conclusion 'D $ B' means D = B, but B > D, so it is false.
Trap: "not greater than" is ≤ and "not smaller than" is ≥ - candidates often flip these. Also read the direction carefully: 'P % Q' (P < Q) is the same as Q > P.
Common errors
- Decoding the statements but forgetting to decode the conclusions.
- Mixing the key of one question set with another set in the same paper.
- Treating "≥" from the chain as ">".
Time target
After the key is written, 30-40 seconds per question.