Statements:\nI. Best performance in the Olympics fetches a gold medal.\nII. Player X got a gold medal but later was found to be using a prohibited drug.\n\nConclusions:\nI. X should be allowed to keep the gold medal.\nII. The gold medal should be withdrawn and given to the next eligible athlete.

Introduction / Context:
Competitive sport operates on the rule that awards are contingent on fair play. The statements assert that gold reflects best performance and add that athlete X tested positive for a prohibited drug after receiving gold. We examine which conclusion is compelled by these premises without relying on external sporting codes by name.

Given Data / Assumptions:

• Gold is awarded for the best performance.
• X used a prohibited drug, discovered after receiving gold.
• Use of a prohibited drug invalidates the performance as a fair contest result (implicit in the meaning of prohibited).

Concept / Approach:
When the premise includes the term prohibited drug, it implicitly asserts an illegitimate advantage that vitiates the status of best performance. The core entitlement to gold evaporates if the winning mark was achieved under prohibition violation. Therefore, the logical corrective is withdrawal and reassignment, not retention.

Step-by-Step Solution:
1) Best performance → gold (Statement I).2) X’s performance used a prohibited means (Statement II).3) A performance tainted by prohibited means cannot qualify as best in the legitimate sense → X’s entitlement fails.4) The rightful gold should therefore pass to the next eligible athlete → Conclusion II follows; Conclusion I does not.

Verification / Alternative check:
Suppose prohibited had no effect on entitlement; then prohibited would be irrelevant. That contradicts the conventional force of the word prohibited embedded in the premise itself.

Why Other Options Are Wrong:
Only I or Both: deny the normative effect of prohibition. Neither: ignores the premise’s clear implication that an invalidating condition occurred.

Common Pitfalls:
Appealing to sympathy or non-logical considerations (e.g., crowd favor or prior career) which are outside the given statements.

Final Answer:
Only Conclusion II follows.