Governments have only one response to public criticism of socially nec

The LSAT arguments are typically harder than GMAT CR arguments, so if you have run out of challenging GMAT CR practice questions, the LSAT questions can be an excellent source of further practice.

This argument is a complex syllogism.
General case: public complains --- government forced to regulate ---- more money spent on the necessary social service.
Then, we apply this general case scenario the specific example of child care
folks are complaining about child care --- the government will have to regulate it --- then it will cost more money to run the child care programs

Now, let's look at the answers:
(A) The quality of child care will improve.
We know that it's quite likely that the government will spend more money on child care to regulate it. Does this necessarily mean that the quality of the child care programs will improve. Perhaps in a magical fairyland, anything at which the government throws money automatically improves, but in the real world, there are oh-so-many examples of the best intentions of government spending going astray, and programs not improving despite increased spending. It's very helpful to have a real world sense of these things ---- both GMAT CR and LSAT argument questions are consistent with the push & pull of real world forces.
(A) is incorrect.

(B) The cost of providing child-care services will increase.
This is the direct result of the parallel logic. Notice --- we don't know to whom the costs increase: will that increased cost be paid by the parents who want childcare, or by the government (i.e. by all taxpayers)? We don't know, but this is irrelevant. Regardless of who pays, the cost will be increased. (B) is a promising and plausible answer.

(C) The government will use funding to foster advances in child care.
Similar to (A). Yes, the government is going to through money at the programs in the form of regulating it, but will these regulations produce radically improved programs? Of course, that's the idealized hope, but there's no guarantee that this will be the outcome.
(D) is incorrect.

(D) If public criticism of policy is strongly voiced, the government is certain to respond.
Very tricky. This passage is very specifically about "socially necessary services". The government funds a whole bunch of things that are not in the category of socially necessary services (the arts, environmental protection, diplomacy & foreign aid, etc. etc.) Will the government respond to strong criticism about any of these? We don't know. It's well outside the scope of this argument.
(D) is incorrect.

(E) If child-care services are not regulated, the cost of providing child care will not increase
This is the one about which smartmanav asked. Technically, this answer choice is relying on a logical mistake known as the equivalence of a conditional statement and its inverse. In formal language, the mistake is
Starting with (if P, then Q), we conclude (if not P, then not Q).
This is a logical fallacy.
Consider these examples:
Original: If I am in the SF Bay Area, then I am in California. True
Inverse: If I am not in the SF Bay Area, then I am not in California. False --- I could be in LA or San Diego or Tahoe or Yosemite or etc. California is a big state!

Original: If a shape is a square, then it is a quadrilateral. True
Inverse: If a shape is not a square, then it is not a quadrilateral. False --- it could be a trapezoid, a slanted rhombus, an elongated rectangle, etc. etc.

The argument makes the case that
If government regulates, then costs increase.
For the purposes of this question, we have to accept the prompt evidence as true.
Essentially, answer choice (E) leaps from here to the inverse:
If government does not regulate, then costs will not increase.
If the government does not regular child care, that particular source of cost increase is eliminated, but that is certainly not a guarantee that nothing else at all will cause the price to increase. There could be a labor dispute, lawsuits from parents, insurance increases, etc. etc. --- any one of a thousand other things that could cause the price of child care to increase. We don't have a guarantee that the cost of child care will increase, but we certainly can't conclude definitively that the cost won't increase. The truth is: if the government does not regular child care, we have absolutely no idea whether the cost of child care will increase or not. We can draw no conclusion. We have absolutely no grounds for concluding the inverse from the original conditional statement ---- this is a fundamental logical fallacy.
(E) is incorrect.

The only possible answer is (B).

Does all of this make sense?

Mike