The phrase "reached through faulty logic" is an interrupting phrase, or one that gives crucial information to the meaning of the sentence, but is not necessary to the sentence's construction. All interrupting phrases must be set apart from the rest of the sentence by commas, making "The conclusion, reached through faulty logic, proved" the correct answer choice.

The phrase "a former player for the team" is an interrupting phrase, a phrase that provides extra information, but is apart from the structure of the sentence. All interrupting phrases must be separated from the rest of the sentence by commas, making "The new manager, a former player for the team, commented" the correct answer choice.

The phrase "worn out from his travels" is an interrupting phrase, or a phrase that provides additional meaning to the sentence, but stands apart from its essential structure. To show this, all interrupting phrases must be set off by commas on each end. This makes "The executive, worn out from his travels, barely" the correct answer choice.

The phrase "a close confidante for years" is an interrupting phrase, or a phrase that gives additional information without being crucial to the structure of the sentence. All such phrases need to be separated by commas, making "The advisor, a close confidante for years, gave" the correct answer choice.

The phrase "all still in high school" is an interrupting phrase, one that provides extra information to the sentence but is not a part of the sentence's main structure. Because of this separation, all interrupting phrase should be surrounded by commas; therefore, the correct answer choice is "The debaters, all still in high school, showed a maturity beyond their years."

When additional elements are put after or before the subject (in this case, "unaware of their country's") it should be separated by commas. Also look for the answer where "country" is in its proper possessive state: "their country's tense foreign relationship."

The phrase "a long time civic activist" is an appositive, a noun that renames a previously introduced noun while providing more information about that previously introduced noun. Appositives that can be removed from a sentence without affecting the sentence's meaning must be set apart by commas. "The speaker, a long time civic activist, urged" is the only answer choice that actually does this.

The phrase "all rescued from local shelters" is an interrupting phrase, a phrase that gives additional information to the sentence but remains apart from its structure. All interrupting phrases must be set apart from the rest of the sentence by commas. The only answer choice that appropriately does this is "The dogs, all rescued from local shelters, took quite a while to adjust to their new foster homes."

The phrase "held every four years" is an adjectival participle phrase, one that sits outside the structure of the sentence, but provides extra information. Any such phrase must be set apart by commas. "The tournament, held every four years, is" is the only answer choice that appropriately does this.

The phrase "originally scheduled for three hours" is an interrupting phrase, or one that sits outside the sentence's structure but provides extra information. All interrupting phrases must be set apart by commas. The only answer choice that appropriately does this is "The dance, originally scheduled for three hours, had to be cut short after just an hour.