Ram is taller than Shyam, and Jay is shorter than Vikram. Who is the shortest among Ram, Shyam, Jay, and Vikram? I. Ram is the tallest. II. Shyam is taller than Vikram.

Difficulty: Medium

Correct Answer: Statement II alone is sufficient to answer the question but Statement I alone is not.

Explanation:


Introduction / Context:
This is an order-comparison Data Sufficiency question. We must decide if the given statements allow us to identify the shortest person uniquely, using the base relations from the stem.


Given Data / Assumptions:

  • Base facts: Ram > Shyam; Jay < Vikram (here > means taller).
  • Statement I: Ram is the tallest.
  • Statement II: Shyam > Vikram.


Concept / Approach:
Combine the base facts with each statement independently to see whether a unique shortest person emerges.


Step-by-Step Solution:
With II: Shyam > Vikram and Jay < Vikram ⇒ Jay is shorter than Vikram, who is shorter than Shyam. From the base, Ram > Shyam, so the complete order is Jay < Vikram < Shyam < Ram. The shortest is Jay ⇒ II alone is sufficient.With I: Ram is tallest, and we know Ram > Shyam. But we do not know how Shyam compares to Jay (we only know Jay < Vikram) or how Vikram compares to Shyam. Jay could be shorter than all, or Shyam could be shorter than Jay, leaving ambiguity ⇒ I alone is not sufficient.


Verification / Alternative check:
Construct examples consistent with I where different shortest persons are possible, confirming insufficiency of I alone.


Why Other Options Are Wrong:
Claiming that I suffices contradicts the ambiguity; claiming both are needed is false because II alone already resolves the order.


Common Pitfalls:
Ignoring the base relationships embedded in the stem when evaluating each statement independently.


Final Answer:
Statement II alone is sufficient; Jay is the shortest.

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