This is a formal logic question that calls for an inference based upon the logical structure of the argument. It is best to reformulate the statements into simple conditional declarations (if-then statements) and then note the contrapositive. Here is a suggested reformulation: If masterpiece (M), then tight melodic structure (TMS). Contrapositive: If no TMS, then not M. If not appealing to aficionados (not A), then not M. Contrapositive: If M, then A. Some recent classical music (R) are masterpieces. Therefore, some R have TMS and are M. All of the answer choices that express one of these conditional statements follow logically from the argument presented. Those are the incorrect responses. The correct response—in effect, If TMS, then A (“Only classical music that has a tight melodic structure appeals to classical music aficionados”)—does not comport with any of these logical conditional statements.

This is a formal logic problem.  First, note the conclusion:  If Omega, then not Homunculus.  Second, note the evidence/premises:  If Xenon, then not Alpha (or you can put it in its contrapositive form:  If Alpha, then not Xenon).; and If Omega, then Xenon.  To find the assumption, look for the missing term in the evidence/premises that does not appear in the conclusion---namely, Alpha.  So we can eliminate any answer choice that does not mention Alpha.

To elaborate in order to select the proper answer choice, we can see that the premises come down to this (combining the two propositions):  If Omega, then not Alpha.  The conclusion states:  If Omega, then not Homunculus.  Therefore, the assumption has to be If not Alpha, then not Homunculus.  Take the contrapositive of that:  If H, then A.  And that is what credited answer choice states.

The conclusion here is readily identifiable.  It advocates the use of PUBLIC FUNDS to support PBS news programs.  Why?  The answer to this "why?" question is our evidence:  the appearance of public intellectuals on news programs often lead to high-level discussions that many might find disturbing or controversial.  So the assumption needs to speak to the issue of "high-level discussions" that disturb many people since that is a term or idea that does not appear in the conclusion.  Moreover, that key term or idea must operate in a way to link the evidence to the key idea in the conclusion, which is the notion of "public funding."  The credited response does precisely that, whereas the wrong answer choices tend to go off in irrelevant or non-essential directions.

Nothing in the argument as written explains why the greatness of a film cannot be determined upon its release. To draw that conclusion, the argument requires a connecting premise indicating that a period of time (in this case, twenty years) must elapse to determine greatness because initial impressions might be inaccurate. The other answer choices either restate premises already contained in the argument, or state premises which do not support the conclusion.

The argument states that giving the price up front will help people make a more informed decision than if they are charged hidden fees and given the total price later. For this statement to be valid, it must be true that decisions are less informed in the latter scenario. People’s awareness or preference as to the timing of prices are irrelevant; the key is whether they are more or less informed as a result of a particular advertising strategy.

First we must identify the conclusion: It is wrong to conclude that the Tibutu do not understand the concept of private property. Second we must articulate the premise or evidence for that conclusion: drinking and using water can lead to knowledge of water, even without attaching a name to it (experiencing something is enough to gain knowledge of that thing). The assumption must link the premise or evidence to the conclusion. To do that, we must identify the word, phrase, or concept (or idea) in the premise or evidence that does not appear in the conclusion. That is relatively easy here—the idea of experiencing water as a way to gain knowledge of it is the key point that must appear in the assumption. The correct response expresses the key idea in the premise and links it to the conclusion. Note that the answer choice that invokes the idea of experiencing something as a way to know it states something extreme—namely, that is “better” to experience something than to have a name for it when it comes to gaining knowledge of it. While perhaps true, that qualitative judgment is not expressed or implied in the argument, so it is not the correct answer choice.

To derive the assumption, we must first identify the conclusion of the argument—to wit, “Non-analytical thought offers a more profound way to engage with reality than does analytical thought.” What is the evidence or premise to that conclusion? We can express it as something like this, as a paraphrase of what is expressed fully in the argument: “Analytical thought ignores ‘unity’ of all things.” What is a term or concept in the premise that does not appear in the conclusion? Answer: the notion of “unity.” So the assumption must contain within it some expression of that notion. More particularly, the assumption involves some notion of “grasping unity” as a way to penetrate “reality” in a more profound way. The credited answer choice expresses that notion precisely. The others miss the mark inasmuch as they do not express the key idea of “grasping unity” as a way to understand “reality” in a “profound” way.

The psychologist gives a description of a certain repeated pattern of behavior which involves an addict and another person to whom the addict is close. That pattern reflects how one person’s behavior triggers responding behavior by the other, such that the behavior of both people is constantly being reinforced. The credited response must capture this mutual-reinforcement phenomenon. The argument by the psychologist is not calculated to tag all addicts as manipulative and untrustworthy; nor does it warn against having an intimate relationship with all addicts. Finally, the argument does not concern itself with how an addict develops his or her behavior pattern. So all of the other answer choices, to one degree or another, miss the mark.

First, identify the conclusion:  "Rapid but foolhardy change may occur in a society that quickly improves its public education system at the high school level but does not address the problem of money in politics."

Second, identify the key terms in the evidence/premises with a paraphrase of what is presented in the passage:  for example, you might say, "campaign contributions (money in politics) distorts the electoral process."

What key term in the evidence/premises does not appear in the conclusion? Obviously, something relating to unbridled campaign contributions (i.e., the distorting affects of money in politics).  That key term or idea must be at work in the assumption, and therefore it must appear in the correct answer choice.  So we can quickly eliminate any answer choice that does not speak to this key term or idea.

The credited response speaks directly to the distorting effects of uncontrolled money in politics without the use of extreme language and without resort to unnecessary "ought" or "should" assertions.  Note how the wrong answers either use extreme language or resort to claims that urge some kind of action (whereas the argument does not assume something about action that is needed---though it may lead to an INFERENCE that certain action would be wise, but that is not an assumption).

Providing students access to healthier liquids would not improve nutrition among students if the students didn’t actually drink the liquids.  Therefore, the argument assumes that at least some portion of students (enough to be significant) would replace their normal soda drinking with mineral water drinking.  The other answer choices, while they may be relevant, are not required for the argument to be sound.