This sentence is contrasting two things. The second item in the contrast is explicitly stated. It is the effect that showed itself after several days. In contrast to such a delayed effect, an "immediate" effect is one that shows itself right away.

This sentence implies that Daniel's accomplishments are not very extraordinary. They are just like everyone else's accomplishments. This means that they are not very impressive. Perhaps he has done some very good things. Still, they just don't "stand out."

This set of sentences is expressing the strange contrast between what we would expect from Robert when he finds out bad news and how he actually acts. It is surprising that he is not saddened by bad news. The implication is that his attitude is the opposite of sadness in these cases. That means that his attitude must be one of gladness or joy. Thus, it seems that the bad news would make him "rejoice"!

This sentence contrasts two things that are easy to do for other people. The implication of the logic of the sentence is that these are two different things. Thus, on the one hand it is said to be easy to annoy people. We are therefore looking for something opposite of annoying. Among the options provided, only one such word provides this kind of contrast, namely "please." The word "save" might seem like a positive contrast for "annoy."  While this is true, it is not a great contrast. The best option is "please," which is certainly a good opposite to "annoy."

Notice the important words that indicate a contrast being expressed in this sentence. Sally's current pie is surprising in that it is disgusting. This is contrasted with the normal state of affairs. The contrast is indicated by the use of the word "although" at the beginning of the sentence. Therefore, in contrast to "disgusting" her pies must have been rather tasty. This means that they were not merely nutritious, acceptable, or edible. They were quite delicious! 

You might be tempted to pick "majestic" or even "beautiful" as the answer to this question. Filbert apparently likes things that are "down to earth."  The real contrast here is between this kind of concrete and practical thinking and more abstract ways of thinking that are not so connected to common experience. Such abstract things can be majestic, beautiful, or even mathematical. The general term "abstract" best functions for the contrast, so stick to this!

The key word in all of this is "surprisingly." Since Theodore lived in extreme poverty for many years, it was likely thought that he would always be poor in this manner. Therefore, the surprise would come by him being very wealthy. Do not over-think this question. It is that simple of a contrast!

The key contrast being made in this sentence is between something that is theoretical and something that is practical. Theoretical things are often not able to be applied. For example, you might learn all about the nature of chemicals in a chemistry class. This is not, however, the same as learning how to apply this knowledge in particular experiments. Here, the contrast is very clearly between theoretical things in mathematics and the very practical matter of fixing the plumbing!

Notice that this sentence only discusses the fact that rich people often give money away. The implication is that not all rich people "hold onto" their money. Whenever someone does not want to give away his or her money, he or she might be greedy. Greed primarily deals with wanting to get money or something else. Whenever someone is "stingy," he or she "holds onto" what he or she has. This is the best option among those provided.

Notice that this sentence implies a contrast between two kinds of people. Some like to work on overall plans for a project.  We sometimes say that these people like to work on the "big picture." Such people don't like dealing with all of the little details involved in the project. This second kind of person is the kind of person being discussed at the beginning of the sentence. Therefore, the best option is the word "details."