Historian: Newton developed mathematical concepts and techniques that are fundamental to modern calculus. Leibniz developed closely analogous concepts and techniques. It has traditionally been thought that these discoveries were independent. Researchers have, however, recently discovered notes of Leibniz` that discuss one of Newton's books on mathematics. Several scholars have argued that since the book includes a presentation of Newton's calculus concepts and techniques, and since the notes were written before Leibniz` own development of calculus concepts and techniques, it is virtually certain that the traditional view is false. A more cautious conclusion than this is called for, however. Leibniz` notes are limited to early sections of Newton's book, sections that precede the ones in which Newton's calculus concepts and techniques are presented.

In the historian's reasoning, the two portions in blodface play which of the following roles?

Five years ago, as part of a plan to encourage citizens of Levaska to increase the amount of money they put into savings, Levaska's government introduced special savings accounts in which up to $3,000 a year can be saved with no tax due on the interest unless money is withdrawn before the account holder reaches the age of sixty-five. Millions of dollars have accumulated in the special accounts, so the government's plan is obviously working.

Which of the following, if true, most seriously weakens the argument?

An overwhelming proportion of the most productive employees at SaleCo's regional offices work not eight hours a day, five days a week, as do other SaleCo employees, but rather ten hours a day, four days a week, with Friday off. Noting this phenomenon, SaleCo's president plans to increase overall productivity by keeping the offices closed on Fridays and having all employees work the same schedule-ten hours a day, four days a week.

Which of the following, if true, provides the most reason to doubt that the president's plan, if implemented, will achieve its stated purpose?

Which of the following most logically completes the argument below?

According to promotional material published by the city of Springfield, more tourists stay in hotels in Springfield than stay in the neighboring city of Harristown. A brochure from the largest hotel in Harristown claims that more tourists stay in that hotel than stay in the Royal Arms Hotel in Springfield. If both of these sources are accurate, however, the county's "Report on Tourism" must be in error in indicating that _______.

Although the earliest surviving Greek inscriptions written in an alphabet date from the eighth century B.C., a strong case can be made that the Greeks actually adopted alphabetic writing at least two centuries earlier. Significantly, the text of these earliest surviving Greek inscriptions sometimes runs from right to left and sometimes from left to right. Now, the Greeks learned alphabetic writing from the Phoenicians, and in the process they would surely have adopted whatever convention the Phoenicians were then using with respect to the direction of writing. Originally, Phoenician writing ran in either direction, but by the eighth century B.C. it had been consistently written from right to left for about two centuries.

In the argument given, the two portions in boldface play which of the following roles?

A significant number of complex repair jobs carried out by Ace Repairs have to be reworked under the company's warranty. The reworked jobs are invariably satisfactory. When initial repairs are inadequate, therefore, it is not because the mechanics lack competence; rather, there is clearly a level of focused concentration that complex repairs require that is elicited more reliably by rework jobs than by first-time jobs.

The argument above assumes which of the following?

The university science library, as most libraries, prohibits students to borrow rare, expensive, or popular reference materials; such materials are designated for use in the library only.

The art of Michelangelo, the inventions of Edison, and Shakespeare's plays all represent great achievements in human history.

Despite their numerous attempts to do so, scientists have not been able to sustain a controlled nuclear fusion reaction.

Art experts have attributed the enduring intrigue of Leonardo da Vinci's Mona Lisa to everything from having an enigmatic smile, which was never explained, to her association with the rich and powerful families of Europe.

Jack Nicklaus, who solidified his legendary status with an improbable victory at the famed Augusta National Golf Club in 1986, and Tiger Woods are widely regarded as two of the best golfers in the history of the sport.