Which inequality must hold — Aptitude Question
Which inequality must hold: If P ≥ Q, Q > R and S < R, which of the following is definitely true? Answer and worked solution on CodeKairo.
- Topic: Mathematical Reasoning
- Section: Logical Reasoning
- Difficulty: Medium
- Time target: 75 seconds
Question
If P ≥ Q, Q > R and S < R, which of the following is definitely true?
Options
- P > S
- S > Q
- P = R
- Q < S
Show the answer and the worked solution
Correct answer: A. P > S
Worked solution
- The chain is P ≥ Q > R > S.
- Since at least one link is strict, P > S definitely holds.
- The other options reverse the chain or claim equality that is not forced.
Answer: P > S.
The idea
A mixture of ≥ and > still yields a strict conclusion, provided at least one link is strict. All links being ≥ would only give ≥.
Shortcut. S < R < Q ≤ P puts S below everything, so any option placing S above a term (S > Q, Q < S) dies at sight, and Q > R rules out P = R.
Common trap. "P = R" — reading the ≥ as allowing equality further down the chain; it only lets P equal Q, and Q > R keeps P strictly above R.