In several cities, the government is going ahead with ambitious constr

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For this particular question, I will only discuss (A) & (E), since those are the two that confuse you.

In several cities, the government is going ahead with ambitious construction projects despite the high office-vacancy rates in those cities. The vacant offices, though available for leasing, unfortunately do not meet the requirements for the facilities needed, such as court houses and laboratories. The government, therefore, is not guilty of any fiscal wastefulness.
Which of the following is an assumption on which the argument above depends?
(A) Adaptation of vacant office space to meet the government's requirements, if possible, would not make leasing such office space a more cost-effective alternative to new construction.
The classic test for an assumption, as folks above have said, is the "negation test" --- negate the statement, and if that devastates the argument, that's an assumption. You may find this blog helpful.
https://magoosh.com/gmat/2012/arguments- ... -the-gmat/

Here, let's assume the opposite of (A). Assume that we would save money, that it would be more cost effective, to renovate and adapt those existing offices spaces, rather than build whole new ones. Well, if that's true, then building new ones, the more expensive option, would definitely be more wasteful. That obliterates the conclusion of this argument, so this is a strong candidate for the the correct answer.

(E) Before embarking on any major construction project, the government is required by law to establish beyond any reasonable doubt that there are no alternatives that are most cost-effective.
This is a subtle point. Anything that involves extreme language is wrong on the GMAT Verbal section. Extremity can involve very strong emotions, very strong judgments, or, as in this case, extreme scenarios or standards or criteria. Consider the following hierarchy of scenarios ----
before embarking on any major construction project, the government .....
(a) has a policy of reviewing cost effectiveness with an advisory board
(b) must have the cost effectiveness approved by a majority (or 2/3) of the state assembly
(c) must submit the proposal to binding arbitration that will decide whether it is cost effective and hence, whether to permit it
(d) is required by law to establish, to a majority opinion of a panel of judges/jurors/experts, that it is cost effective [the judicial standard in civil cases]
(e) is required by law to establish beyond any reasonable doubt that it is cost effective [the judicial standard in criminal cases]
Notice that (e), the standard for decision in criminal cases, is the strictest decision-making criterion encoded in the law anywhere. Options (a) - (d) are all less serious, less imposing, than (e). In this sense, (e) is an extreme case --- saying that the judgment will be held to the highest standard known anywhere in the legal system. In essence, we are saying --- of 1000 potential projects, if even one cost ineffective project is allowed and goes through, that would be as great a tragedy as, in a 1000 criminal court cases, one innocent person is condemned to a criminal sentence. That latter is a true real-life tragedy, unfairly destroying some poor person's whole life! (That's exactly what the Founding Fathers were hoping to avoid by establishing such a demanding criterion.) Spending a bit too much money on a government construction project -- not ideal, but certainly not a tragedy of the same magnitude!! Do you see what I mean? Yes, it's not a good thing when the government overspends, but saying that it's so bad that it has to be held to the highest criterion that appears anywhere in the entire legal system --- that's extreme.
Obviously, if we negated option (E), which follows standard (e), any of (a)-(d) could still be true, and if any of those were true, it would support the conclusions. This is why (E) doesn't work.

(A) has to be the answer.

You don't have to be an expert on the legal system, but you do need to recognize that key phrase: "to establish beyond any reasonable doubt." That is the standard in every criminal case in the US legal system, again so extremely demanding and hard to demonstrate, because the system is trying to avoid the tragedy of condemning an innocent person to prison.
Nothing else in the entire legal system, in the entire government, is held to that lofty standard. Even in civil cases in the legal system, you only have to demonstrate it to a majority of the jurors to win. In a criminal cases, the decision must be unanimous --- all 12 people must agree that the person is guilty.
That's why, as soon as I saw those words in (E) --- some governmental fiscal thing held to the standard of "beyond any reasonable doubt" --- right away, I knew that was far to extreme to be a correct answer on the GMAT.

Does all this make sense?

Mike