Premises:
Sharp decline in population causes tax revenue to reduce.
But the areas which this revenue supports is still the same such as police protection and maintenance of water lines.
We cannot make up by increasing tax rate since more people will leave.

We need a conclusion. Something that follows from what is given. There should be no new information.

A. If, in a city with sharply declining population, police protection and water line maintenance do not deteriorate, some other service previously provided by the city will deteriorate or be eliminated.
The tax revenues decrease when population decreases. Since the revenues cannot be recovered by raising tax rate (since it will mean more people leaving and consequently lower collection points), it means the revenue will reduce. The need for the revenue does not reduce for at least some services. Hence, some services will certainly suffer. If police protection and water line maintenance do not suffer, something will suffer.
This follows what is given to us in the argument. There is nothing called "this option is incorrect due to usage of extreme language". If the premises give you extreme data, the option will use extreme language.
If the premises give you: "If A happens, B will happen." and "A has happened", what will you conclude? That B WILL HAPPEN. Can you say that the language is too extreme here? No.

B. If a city's tax rates are held stable over a period of time, neither the population nor the levels of city services provided will tend to decline over that period.
We do not know what causes the population to decline. Irrelevant.

C. If a city's population declines sharply, police protection and water line maintenance are the services that deteriorate most immediately and most markedly.
Not known. When the revenue declines, which services take the hit, we don't know. All we can say is that some service will take a hit.

D. A city that suffers revenue losses because of a sharp decline in population can make up some of the lost tax revenue by raising tax rates, provided the city's tax rates are low in relation to those of other cities.
What happens when the city increases tax rate, we cannot say. The premises give us that we cannot make up for lost revenue by increasing tax rate. Are we able to make up for it partially provided the tax rate still remains low, we cannot say. Note that we have no information on why people choose a certain city to live in. Perhaps its tax rate is lower but the quality of air and water isn't that great. Perhaps its cost of living is high. What happens when the tax rate is increased slightly (but is still less than other cities), overall it may not make financial sense for people to stay. The point is, we don't know how people will react if the taxes are raised even a tiny bit. We do know that raising tax rates cannot make up the loss in revenue and that is all. The argument tells us nothing else. We have to stick to the universe created by our argument.

E. A city that is losing residents because tax rates are perceived as too high by those residents can reverse this population trend by bringing its tax rates down to a more moderate level.
Irrelevant. We don't know how to reverse population trend and whether it can be reversed in the first place.

Answer (A)