Height ordering with partial comparisons: Mukesh is taller than Suresh but shorter than Rakesh. Rakesh is taller than Harish but shorter than Amar. Who is the shortest?
-
AMukesh
-
BSuresh
-
CHarish
-
DCannot be determined
-
ERakesh
Answer
Correct Answer: Cannot be determined
Explanation
Introduction / Context:Height-ranking questions require building partial order chains. Sometimes the data are sufficient to determine extremes; other times, uncertainty remains. Recognizing insufficiency is a key reasoning skill.
Given Data / Assumptions:
- Mukesh > Suresh.
- Mukesh < Rakesh.
- Rakesh > Harish.
- Rakesh < Amar.
- No direct comparison between Suresh and Harish, or between Amar and others except via Rakesh.
Concept / Approach:Construct a chain that is consistent: Amar > Rakesh > Mukesh > Suresh and Rakesh > Harish. The unknown link is between Suresh and Harish; either could be shorter.
Step-by-Step Solution:
Step 1: From “Rakesh is taller than Harish but shorter than Amar,” build Amar > Rakesh > Harish.Step 2: From “Mukesh taller than Suresh but shorter than Rakesh,” insert ⇒ Rakesh > Mukesh > Suresh.Step 3: Combine chains: Amar > Rakesh > (Mukesh, Harish in some order) > Suresh OR Amar > Rakesh > Mukesh > Suresh and also Rakesh > Harish; relative order of Harish vs. Suresh unresolved.Verification / Alternative check:Try two consistent placements: (a) Harish taller than Suresh ⇒ Suresh shortest; (b) Suresh taller than Harish ⇒ Harish shortest. Both satisfy the given constraints, proving non-uniqueness.
Why Other Options Are Wrong:
- Picking Mukesh/Harish/Suresh outright assumes an ordering not supported by data.
Common Pitfalls:Forcing a total order when only partial comparisons are given. Always check if multiple arrangements fit.
Final Answer:Cannot be determined