The phrase "which is one of the largest buildings in the world" is an example of a relative clause, which gives more information about its antecedent: the Willis Tower. Any such phrase that occurs in the middle of a sentence must be introduced and completed with a comma. The correct answer choice is "The Willis Tower, which is one of the largest buildings in the world, was built."

The phrase "which might decide the fate of thousands of workers' jobs" is an example of a relative clause, which gives more information about its antecedent: announcement. Any such phrase that occurs in the middle of a sentence must be introduced and completed with a comma. The correct answer choice is "The company's upcoming announcement, which might decide the fate of thousands of workers' jobs, put everyone on edge."

The phrase "who lives in Asia" is an example of a relative clause, which gives more information about its antecedent: his family. Any such phrase that occurs in the middle of a sentence must be introduced and completed with a comma. The correct answer choice is "He speaks with his family, who lives in Asia, every week."

The phrase "which was supposed to make their jobs easier" is an example of a relative clause, which gives more information about its antecedent: "machinery." Any such phrase that occurs in the middle of a sentence must be introduced and completed with a comma. The correct answer choice is "They were investing in new machinery, which was supposed to make their jobs easier, but cost much money."

"The GMAT builds character" and "it is full of challenging sentences" are independent clauses. They are related, but independent; therefore, the best way of separating them within the same sentence is with a semicolon rather than a comma.

The phrase "which he had had since childhood" is an example of a relative clause, which gives more information about its antecedent: the man's routine. Any such phrase that occurs in the middle of a sentence must be introduced and completed with a comma. The correct answer choice is "The man decided to change his morning routine, which he had had since childhood, because he wanted to try something new."

This sentence misuses the commas in this sentence. When the word "that" is used, what would be a relative clause becomes part of the main clause, therefore making commas inappropriate, as it no longer separates anything. "Which" would be an appropriate choice, but only if both commas are there: none of the options offer this choice. The best choice is, "inventions that we use every day had their start."

This sentence misuses a comma. This sentence is a simple sentence, so no punctuation of any sort is needed. The comma should be omitted because it comes in the middle of an independent clause. The correct choice is, "Many elements on the periodic table."

This sentence does not contain a comma where one is needed. The phrase "after running" is an example of an introductory phrase, explaining information necessary to the context of the sentence, but outside of the main sentence, grammatically. These types of phrases must be followed by a comma in order to separate them from the rest of the sentence. The correct choice is: "After running, he decided to eat a snack and watch."

This sentence does not contain a comma where one is necessary. The phrase "While looking through the company's books" is an example of an introductory phrase, explaining information necessary to the context of the sentence, but outside of the main sentence, grammatically. These types of phrases must be followed by a comma in order to separate them from the rest of the sentence. The correct answer choice is, "the company's books, the accountant found many errors."