It is well known that many homeless people frequent public libraries as a kind of sanctuary. Now, several dozen public libraries across the country have made their facilities more useful to homeless people by offering free job training programs, for adults and free activities for homeless children. While the administrators of these libraries mean well, the homeless do not pay property taxes to support the library, so these people are getting something for nothing, a dangerous practice for all concerned.

Which of the following is assumed by the author of this argument?

A. None of the sales tax paid by homeless people who use the free services is used by the libraries.
Correct answer,passes the negation test. as the argument will break if the taxes paid by the homeless are reaching to libraries in some form or the other.
B.The general public that uses the libraries does not mind the services provided to the homeless.
The opinion of the general public is not considered in the argument.
C. Many of the homeless people who use public libraries as sanctuaries check the library’s local newspapers for job listings.
Out of scope.
D. Some libraries that offer programs to the homeless cannot afford these programs.
The affordability for the libraries is not the correct answer because it may raise concern for the people concerned but running the program is a decision taken by some libraries not all,and those which cannot afford may not implement the program.
E. Property taxes are used predominantly to support public libraries.
Option A is better answer,than E also predominantly does not means entirely and libs may be getting funds apart from the property taxes.

Did u notice the subtle shift in A which talks about sales tax while the argument talks about property taxes.

Bro Conclusion is important here.

IMO A is the best answer
Nagating A it says that they are not getting something for free , and breaks apart the conclusion .
in D : So what if libraries pay for the homeless - It does not do anything if we negate - i.e. They still get something for free which is dangerous concern to some. . This is the conclusion "They still get something for free which is dangerous concern to some" .

Good question. A part of solving the question starts from identifying the crux conclusion of the author - so these people are getting something for nothing, a dangerous practice for all concerned.
Since Homeless people dont pay anything, they shouldn't be getting anything.

Option A: touches on this aspect. On negating, sales tax paid by homeless people does infact get contributed to Libraries. This would imply that homeless people pay, not property taxes, but sales taxes for contributing to Libraries. This weakens the conclusion of the author. Hence A.

Option D: Negate D. Some libraries that offer programs to homeless can afford these programs. This does not impact the conclusion of the argument as stated above. Hence D is out.

Hope this helps.
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OA and explanation

Answer: A

Explanation: The author concludes that the homeless people are getting something for nothing because they don’t pay property taxes which are used to support the library. However, if these people are paying other kinds of taxes, such as sales taxes, that ARE used to support the library, then they are not getting something for nothing. Thus, saying that the sales tax paid by homeless does not go to the library strengthens the position that homeless people are getting something for nothing.

(B) The attitudes of the general public do not figure into the scope of this argument.

(C) Whether some homeless people already make use of the library is irrelevant to the scope of this argument, which deals with the free programs.

(D) Though this evidence might be used to oppose the program, it does not support the conclusion that people are getting something for nothing.

(E) The author does believe that at least some property taxes are used to support public libraries, but we cannot say that the author assumes most of the taxes are used that way.