Understanding the Argument -
Population decline - tax revenue decline (which impacts the city services such as police protection and maintenance of water lines, as these are paid by taxes collected).
Ares to be policed and served with water line don't decrease.
A tax rate increase to recover the lost revenue is not feasible since it would push (hypothetical) even more residents out.
Option Elimination -
A. If, in a city with a 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.- That makes sense. Let's take an example: A person's salary is $10,000. Out of this, he spends $4000 on the mortgage, $2000 on children's education, $2000 on food, and $2000 in savings. Suppose the salary goes down to $8,000 while the mortgage and children's education are fixed, which accounts for $6,000. So obviously, the person will cut on food and savings. Isnt it? Yes. We can deduce this inference from the argument provided.
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 know if the population goes down, tax revenue goes down. Also, increasing the tax rate is not advisable as that would push more people to go out. Let's understand this 2nd part more as it is causing problems. Say 5000 people have a problem with Chicgao's cold weather and plan to relocate to Austin. All these 5000 lived in Cook County in Chicago, which will result in the county's tax revenue. Now, say, the Cook County authorities raise the tax from 10.25 to 20.25%. There may be additional people for whom this tax increase makes living complex, and more people, as a result, move out of Chicago. This option says, "If the tax rates stay stable, say 10.25%, neither population nor services will decline. Did you notice the 5000 are leaving because of cold weather? Even if the tax is stable, it doesn't matter. More people can leave because of the cold or job relocation or any other reason. So, this is out of scope.
C. If a city's population declines sharply, police protection and water line maintenance are the services that deteriorate most immediately and most markedly. We don't know which will be impacted the most. Nothing is mentioned in the argument. These are just examples "such as." Out of scope.
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. - In my example, say Chicago's tax rate is 10.25, and another city X is 12.25%. So if Chicago raises to 11.25% less than city X, people can still leave for other reasons? Yes. Distortion.
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. - While the passage discussed the impact of tax increases, it doesn't discuss the solution to reverse the population declines as described in this option, which is to tax rate to a moderate level. Distortion.
By the way, Chicago is a wonderful city that I love.

. People who live here enjoy the diverse culture, architecture, culinary delights, winter wonderfest at Navy Pier, and ice skating, to name a few.