In this logical reasoning problem, two related statements about luck, hard work, and success are given. Treat both statements as true and then decide which of the following conclusions logically follow. Statement I: If we are lucky, then things automatically fall into place. Statement II: Luck follows only when we work hard. Conclusions: I. Hard work is the key to success. II. If you do not work hard, luck will not follow you.

Introduction / Context:
This question examines your ability to connect conditional statements and derive meaningful conclusions. The ideas of luck, hard work, and success are tied together in two premises. From these, you must decide which conclusions necessarily follow. While the language is everyday, the underlying structure is logical: one statement describes what happens when we are lucky, and the other describes when luck appears. Taken together, they give a chain from hard work to success.

Given Data / Assumptions:

• Statement I: If we are lucky, then things automatically fall into place. This suggests that luck leads directly to favorable outcomes or success.
• Statement II: Luck follows only when we work hard. This means hard work is a necessary condition for luck to appear.
• Conclusion I: Hard work is the key to success.
• Conclusion II: If you do not work hard, luck will not follow you.
• All statements are to be treated as logically true premises, ignoring any real world exceptions.

Concept / Approach:
Both statements can be expressed as conditional relationships. Statement I links Luck to Success: Luck implies Success. Statement II links Hard Work to Luck: only when you work hard does luck appear, which translates to Luck implies Hard Work or equivalently, no Hard Work implies no Luck. By combining these, we can trace a path from Hard Work to Luck and then to Success, and we can also derive the contrapositive about what happens when there is no Hard Work. The conclusions must be checked against these derived relationships.

Step-by-Step Solution:
Step 1: Rewrite Statement I in logical form: Luck leads to things falling into place, which we can interpret as success or favorable outcomes. So Luck implies Success. Step 2: Rewrite Statement II in logical form: “Luck follows only when we work hard” means that having Luck requires that Hard Work has been done. In logic, this is Luck implies Hard Work. The contrapositive is also true: if there is no Hard Work, then Luck does not follow. Step 3: Combine the two statements. From Statement II we have Luck implies Hard Work, and from Statement I we have Luck implies Success. Hard Work is therefore necessary for Luck, and Luck is a pathway to Success. In everyday language, this strongly supports the idea that Hard Work is a central factor or key to success. Step 4: Check Conclusion I. It says, “Hard work is the key to success.” Since success in the premises comes only when Luck appears, and Luck appears only when there is Hard Work, Hard Work becomes a necessary precondition in the chain that leads to success. This conclusion captures the overall message of the two statements and therefore follows. Step 5: Check Conclusion II. We already derived the contrapositive of Statement II: if you do not work hard, Luck does not follow. This is exactly what Conclusion II states. Hence, Conclusion II also follows directly.

Verification / Alternative check:
To verify, imagine two scenarios. In the first, someone works very hard; then according to the statements, Luck may follow them, and once they are lucky, things fall into place, meaning they achieve success. In the second scenario, a person does not work hard at all. Then, according to Statement II, Luck cannot follow, so the first link in the chain to success is broken. This illustrates both that Hard Work is the key factor enabling success and that without Hard Work, Luck does not appear. Thus both conclusions are consistent with and supported by the given premises.

Why Other Options Are Wrong:
Option a: “Only conclusion II follows” is incorrect because it ignores the overall chain created by the two statements, which clearly elevates Hard Work as the central condition for success, justifying Conclusion I as well. Option c: “Neither conclusion I nor conclusion II follows” is wrong because we have clearly derived both from the original premises. Option d: “Only conclusion I follows” is incomplete because the contrapositive of Statement II exactly matches Conclusion II. Option e: Suggesting that the conclusions are unrelated is incorrect; they are directly connected to the logical structure of the statements.

Common Pitfalls:
A common mistake is to treat luck and hard work as independent and to assume that success can happen without any one of them, which is not allowed once you accept the premises as absolutely true. Another error is failing to use contrapositives: many learners overlook that “Luck follows only when we work hard” also implies that lack of hard work stops luck from appearing. Always convert “only when” statements into a clear conditional and then use its contrapositive to find additional valid conclusions.

Final Answer:
Both conclusion I and conclusion II logically follow from the given statements.