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题目： Is x an integer?(1)$$\frac x 2$$ is an integer.(2)2x is an integer.

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题目： A family-size box of cereal contains more cereal and costs more than the regular-sizebox of cereal. What is the cost per ounce of the family-size box of cereal?(1)The family-size box of cereal contains 10 ounces more than the regular-size box of cereal.(2)The family-size box of cereal costs $5.40.

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题目： When 200 gallons of oil were removed from a tank, the volume of oil left in the tank was $$\frac 3 7$$ of the tank's capacity. What was the tank's capacity?(1)Before the 200 gallons were removed, the volume of oil in the tank was $$\frac1 2$$ of the tank's capacity.(2)After the 200 gallons were removed, the volume of oil left in the tank was 1,600 gallons less than the tank's capacity.

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题目： If r is a constant and $${a}_{n}$$ = rn for all positive integers n, for how many values of n is $${a}_{n} < 100$$ ?(1)$${a}_{50} = 500$$(2)$${a}_{100}+{a}_{105} = 2,050$$

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题目： Carlotta can drive from her home to her office by one of two possible routes. If she must also return by one of these routes, what is the distance of the shorter route?(1)When she drives from her home to her office by the shorter route and returns by the longer route, she drives a total of 42 kilometers.(2)When she drives both ways, from her home to her office and back, by the longer route, she drives a total of 46 kilometers.

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题目： Is $$x >{y}$$?(1)$$x = y + 2$$(2)$$\frac x 2 = y-1$$

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This year, the number of applications at College X increased by nearly 5%, while the size of the entering class and the structure of the admissions process remained the same. However, the admissions director of College X claims that this year a greater proportion of its applicants received offers of admission from the college than in years past.

Which of the following statements best reconciles the claim of the admissions director with other evidence presented in the argument?

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Zoologists warn of an imminent surge in the number of bird species that will become extinct within this century. Nevertheless, these zoologists are wrong. One need only consider the information gathered on native North American raptors, such as bald eagles and peregrine falcons. Several of these species came close to vanishing between 1900 and 1970, but since 1970, the local populations of these raptors have rebounded.

The answer to which of the following questions provides information that would be most helpful in evaluating the argument above?

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Because of a rare type of fungus that killed off many cacao trees in Brazil, there was an unusually meager harvest of cacao beans this year. The wholesale price of cocoa solids and cocoa butter has increased significantly and is unlikely to fall in the foreseeable future. As a result, the retail price of chocolate is certain to increase within six months.

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

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The head baker at Barry's Bagels can either purchase flour in-person from the local flour mill, Larry's Local Mill, or order a shipment of flour from an out-of-state mill, Isadore's Interstate Mill. The cost of the flour from Isadore's Interstate Mill is 10 percent less than the cost of the flour from Larry's Local Mill. Even after shipping and handling fees are added, it is still cheaper to order flour that has to be shipped from Isadore's than to buy flour locally from Larry's.

The statements above, if true, best support which of the following assertions?

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In the United States, about $5,200 per person per year is spent on health care, while in Britain the amount is about half that. A recent study indicated that middle-aged white Americans have a significantly higher rate of diabetes and heart disease than do middle-aged white Britons. Even after eliminating from the study the lifestyle differences of diet, exercise, smoking, and drinking, the data showed that the Americans have poorer health than their British counterparts.

The statements above, if true, best support which of the following assertions?

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A researcher studying corporate executives found that they tend to have "take charge" personalities, with the predominant traits of assertiveness, decisiveness, and self-confidence. The researcher concluded that people who are more "take charge" than the average person are more likely to become corporate executives.

Which of the following, if true, most seriously weakens the researcher's conclusion?

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Ethanol is a derivative of corn and other grains. When burned as fuel, it emits significantly lower levels of carbon monoxide, a major atmospheric pollutant, than does gasoline. For that reason, environmentalists claim that ethanol is a better source of energy than gasoline.

Which of the following, if true, most strongly supports the environmentalists' claim?

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The Ergonomic Society conducted a study that indicated that many people develop severe back problems during adulthood, and that virtually all such people who received chiropractic treatment showed great improvement. Therefore, in order to minimize the proportion of the population that suffers from back pain, the Ergonomic Society recommended that chiropractic treatment be directed toward those adults who suffer from severe back problems.

Which of the following is an assumption on which the argument depends?

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Studies have demonstrated that people who keep daily diet records are far more successful at losing weight than people who don`t keep track of what they eat. Researchers believe that this occurs because people who don't record their diets eat more calories than they intend to consume. One study followed a group of patients who reported that they could not lose weight when consuming only 1,200 calories a day. The study found that the group consumed, on average, 47% more calories than it claimed and exercised 51% less. In contrast, when dieters record what they eat, their actual consumption more closely matches their reported consumption.

The two boldface portions in the argument above are best described by which of the following statements?