This sentence contrasts William's abilities in English to his lack of abilities in math. Apparently, he cannot do any math problems at all. This means that he has no capability whatsoever. In other words, he is totally incapable of completing such problems.

The clues for this sentence are pretty obvious. The wealthy family apparently wants to use their money to help neighbors who cannot afford to buy food. This implies that the other family is poor or impoverished. Though this is a pretty obvious answer, it is clearly the correct one based on the context clues!

The important thing to note is Robert's fear. He was afraid that having many people in charge of the food would lead to the food coming up missing. (Rations can refer to the limited food that is given to people in fixed amounts. The word can also be used in the plural like this just to mean "the food that is available.") Therefore, Robert wanted to have complete control over the food. That is, he wanted exclusive control—control that excluded everyone else from making decisions.

This sentence implies that the friends kept a supply of candy in common. Apparently no one person owned the candy, but anyone in the group could take from it at his or her desire. Now, perhaps this was a generous, large, or (in a broader sense) "wealthy" pile of candy. We just don't know. All that is implied is that they held it in common. Thus, the adjective "communal" is the best option among those provided. Communal goods are ones that are held by the group for the sake of members of the group.

This sentence clearly is contrasting Regina and her sister. Regina is a careful planner who seems to set out to do exactly what she plans. From what we can tell, she does not deviate from these plans.  A person who is impulsive is just the opposite of this. He or she follows his or her impulses (wishes or desires), often going from one thing to the next without much explanation. Now, this can seem to be irrational, but these two words are not quite the same. An irrational person can also be someone who just can't "think straight" because he or she is angry. An impulsive person is a closer contrast to Regina's personality.

The key word in this sentence is "shock." It is stating that a suggestion that is shocking is able to make people pay attention. Now, a violent suggestion can do this, but really that is more than is being said by the sentence. The word "outrageous" is much closer to "shocking." Something that is outrageous is shockingly "over the top." It is extreme.

The most important clue in this sentence is the clause, "fearing that he might be misunderstood if he were completely clear about the meaning of his words." Harry did not want to be unclear with his words. Therefore, he apparently wanted to spell out every detail, meaning that he wanted to be explicit in what he stated. When something is "implicit", it is unstated even if it is assumed. An explicit matter is discussed completely "in the open."

The key clue in this sentence is the fact that the argument being made in the book can't be found in any other books. This does not necessarily mean that the argument is controversial, though it might be.  Likewise, this doesn't mean that it is necessarily amazing—though such rare things are often amazing. Instead, it just means that it is a rare argument. Whenever something is so rare that it is not found anywhere else, it is "unique."

For this sentence, it is true that scientists must be attentive when they do their experiments. The point of the sentence, however, is most directly that they must avoid mistakes. This implies that they must be very "exact" with their measurements. They must not be sloppy but instead must try to find the measurement that is closest to reality as is possible.

Based on the description, this must have been a very stately dinner. It had a very elevated dignity and importance about it. Whenever something is "dignified", it is important and serious. This well describes the dinner, given the remarks made in the clause at the end of the sentence. Given all of the important people at the meal, it must have been a very serious, majestic, and dignified affair.