Statement:\nNation X faced increased international opposition due to its decision to carry out eight nuclear explosions.\n\nConclusions:\nI. The citizens of Nation X favored the decision.\nII. Some powerful nations do not want other nations to become powerful.

Introduction / Context:
The statement reports a fact: international opposition increased after Nation X performed eight nuclear explosions. We must determine which conclusions necessarily follow from this diplomatic reaction without assuming internal public opinion or the detailed motives of every opposing nation beyond what is reasonably implied.

Given Data / Assumptions:

• Action: eight nuclear explosions by Nation X.
• Effect: increased international opposition.
• No information is provided about the domestic stance of citizens in Nation X.

Concept / Approach:
Conclusion I concerns internal public opinion (citizens favored the decision). The statement offers no data about citizen sentiment; opposition from abroad does not entail support at home, so I does not follow. Conclusion II generalizes that some powerful nations resist other nations becoming powerful. International opposition to nuclear testing reasonably implies that at least some influential states oppose proliferation or capacity-building that alters power balances; thus, II is a reasonable inference constrained to “some,” not “all.”

Step-by-Step Solution:
1) Opposition ≠ domestic approval; there is no link provided about citizens → I does not follow.2) International opposition to tests plausibly indicates resistance by influential states to capability expansion by others → II follows.

Verification / Alternative check:
If citizens were actually divided or opposed, the international reaction would still be as stated; hence I is independent and unsupported. But the existence of international opposition implies at least some states prefer others not to bolster nuclear capability—consistent with II’s “some.”

Why Other Options Are Wrong:
“Either/Both” overstate; “Neither” ignores the reasonable minimal inference in II; “Only I” relies on absent domestic data.

Common Pitfalls:
Assuming internal consensus from external reactions; overgeneralizing II to “all” nations (the conclusion wisely uses “some”).

Final Answer:
If only Conclusion II follows.