Politician: Nobody can deny that homelessness is a problem, yet there

Politician: Nobody can deny that homelessness is a problem, yet there seems to be little agreement on how to solve it. One thing, however, is clear: ignoring the problem will not make it go away. Only if the government steps in and provides the homeless with housing will this problem disappear, and this necessitates increased taxation. For this reason, we should raise taxes.

Which one of the following principles, if valid, most supports the politician's argument?

The big thing about this problem isn't breaking it down into premises/conclusions. The thing to understand is context, similar to that of an SC question. To begin, the question splits into two categories: the "only if" vs "if". Most people catch that the question stem says "only if", pushing people to (A) or (B). This is what LSAT wants you to do; they want you to fall into this trap. As I explain below, watch the context. They want you to reverse a sufficient condition for a necessary condition, which is where most get tripped up in (A)

Diagram: Homelessness problem -- little being done -- ignoring doesn't work -- only if Gov. helps (and leads to taxes) will it go away (this is our conclusion)

Breaking down A and C further:
A: Measure should be adopted ---> Measure is required to solve a problem
C: Measure is required to solve a problem ---> then it should be adopted

(A) Only if a measure is required to solve a problem should it be adopted -- The measure is taxation. Is taxation required to solve the problem? Nope. Government intervention is required, which will bring taxation. In other words: Only if taxation is required to solve a problem, it should be adopted. Reverses the correct answer.
(B) Only if a measure is sufficient to solve a problem should it be adopted -- This is not our conclusion. This says that if sufficient -- do it.
(C) If a measure is required to solve a problem, then it should be adopted -- This is word for word what we want. If taxation is required to solve a problem, it should be adopted. Bingo
(D) If a measure is sufficient to solve a problem, then it should be adopted -- This says if it is sufficient then we should adopt. That is not what our conclusion is saying, so this is out
(E) If a measure is sufficient to solve a problem, any steps necessitated by that measure should be adopted -- "any steps" is way off, as we only talk about one solution. Beyond this, same issue as D