This is a strengthen with sufficient premise question. Remember that a sufficient premise is sufficient for a conclusion, if and only if the existence of the premise guarantees or brings about the existence of the conclusion. Therefore, we need to find the premise that 100% guarantees the conclusion. The way you want to attack these answer choices is two-pronged. Ask yourself, does it strengthen? If it doesn't, then cross it out and continue to the next answer choice. If it does strengthen, however, then ask yourself whether or not the premise guarantees the conclusion.
Conclusion: the new library will not be completed on schedule.
Why? We are given the following principle rule: if the new library is completed on schedule, then the building permit is obtained by February 1st or some of the other activities necessary for construction of the new library can be completed in less time than originally planned.
P1: NLCS ==> BPOF1 or OANCLT not BPOF1 and not OANCLT ==> not NLCS
We also know that the building permit cannot be obtained by February 1st.
P: not BPOF1
What's the issue here? We need the negation of BOTH "BPOF1" and "OANCLT" in order to conclude that the new library will not be completed on schedule.
Answer choice (A) does exactly this: "All of the other activities necessary for construction of the library will take at least as much time as originally planned," i.e. "not OANCLT." Thus, not only does answer cohice (A) strengthen the argument, but it also guaranteed the conclusion since the sufficient condition of the contrapositive of the principle rule is triggered when we have (A) so that we can definitely conclude the necessary condition, i.e. our conclusion.
Hope that helps! Please let us know if you have any other questions.
