A machine makes widgets and gizmos. If it takes 6 minutes to make each widget and 10 minutes to make each gizmo, what is the total number of minutes it takes to make a batch of widgets and gizmos?

(1) A batch has 50 more widgets than gizmos.

(2) The ratio of the number of widgets to the number of gizmos in a batch is 3 to 1.

A cafeteria served hamburgers and hot dogs on a certain day. If the cost of each hamburger was $5 and the cost of each hot dog was $3, what was the total cost of the hamburgers and hot dogs served by the cafeteria that day?

(1) The total number of hamburgers and hot dogs served was 130.

(2) The ratio of the number of hamburgers to the number of hot dogs served was 3 to 2.

The Grand Bratislava Hotel, which has three floors, has requested that its elevator maintenance person decrease the speed of the hotel’s elevator by half. The elevator already meets safety requirements, and the change will cause the elevator to use slightly more energy per trip between floors. Nonetheless, the hotel’s management expects the hotel’s energy efficiency to increase as a result of the change without any concurrent change in other operating habits.

Which of the following, if true, provides the best reason for the expectation?

Plan: As part of its Healthy Students Initiative, Happy Meadows Elementary School decided two years ago to raise its school lunch budget by 20 percent in order to serve healthier food to its students. Result: The nutritional quality of Happy Meadows’ school lunches is no better now than it was two years ago. Further information: the annual rate of inflation since the budget change has been below 4 percent, and all of the money budgeted for lunches has been received by the school cafeteria.

In light of the further information, which of the following, if true, would best explain the result that followed from the implementation of the plan?

Agricultural expert: A new type of fertilizer, SynthaGro, promises to increase yields for corn farmers. Because the long-term costs of using it are unknown, however, I do not recommend its use at this time.

Corn Farmer: Your position is inconsistent with your usual course of action. You recommend many products that have substantial costs to farmers, so cost cannot be the real reason you do not recommend SynthaGro.

The corn farmer’s argument is flawed because it fails to consider that

Despite sky-high expectations, the global market for kale has remained stagnant for the last five years. However, although retail prices and the amount of kale produced have likewise varied little during the same period, kale farmers have increased their profits by 15 percent over the last two years.

Any of the following statements, if true about the last two years, helps to explain the rise in profits EXCEPT:

Many zoologists have taken to studying the DNA of American coyote populations in an attempt to learn more about ancient canid populations, the ancestors of modern dogs. One problem with this pursuit is that American coyote populations have interbred heavily with feral dog populations. Thus, any group of coyotes zoologists decide to study will have significant amounts of dog DNA in its communal genome.

Which of the following, if true, would most weaken the criticism made above of the zoologists’ pursuit?

Government spokesman: The least disruptive way for a government to recoup the cost of student loans is to increase borrowers' interest rates gradually over the life of each loan. But in the state of Vitulia, interest rates are as low as they have been in decades and legislators have promised to keep them that way. Therefore, the least disruptive way to collect student loans in Vitulia will be to increase the sums students are required to pay each month in order to shorten the life of each loan.

Which of the following is an assumption of the spokesman’s argument?

Classicist: Researchers studying a cache of documents discovered in Tuscany found that they contain vivid descriptions of a people we believe to be the ancient Chinese. The documents describe expeditions to and diplomatic transactions with a people far to the east dating back to the first century BCE. This shows that the Romans were aware of the Chinese as early as the period of the late Republic, long before historians thought contact was established.

Which of the following, if true, would most seriously weaken the classicist’s argument?

Increasing the prices of retail products and reducing the number of franchise locations are the two solutions Mighty-Mart can enact to substantially increase profit margins. Increasing the prices of products will produce more money through revenue than closing franchise locations will save in reduced real estate costs. Thus, increasing the prices of retail products is the most Mighty-Mart can do to improve its profit margins.

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

One renewable alternative to gasoline is ethanol fuel made from food crops, such as corn. Because turning corn into ethanol fuel requires intensive, unsustainable use of agricultural land, however, ethanol is no more a renewable resource than are traditional fossil fuels.

Which of the following, if true, most strengthens the argument above?

Productivity among workers has greatly declined, with fewer projects being completed. Because workers are increasingly assigned an unmanageable number of tasks, most work slower and accomplish less during the time they spend on the job. Therefore, an effective way for employers to increase productivity would be to minimize the number of tasks any individual worker is assigned at a given time, allowing her to focus on and complete a single project before moving on to the next one.

Which of the following, if true, would most support the recommendation above?

Teeth-whitening kits available for retail purchase are demonstrably effective at reducing plaque buildup and returning teeth to their natural shade, but only for periods of about two or three months. They require additional purchases and application. Professional cleaning by dental hygienists, however, can be effective at reducing plaque buildup and improving tooth appearance for six months to a year. Thus, for people looking to improve the appearance of their teeth in the long term, retail teeth-whitening kits should play no part in maintaining dental hygiene.

The argument is most vulnerable to the objection that it fails to

To increase productivity and prevent workers from leaving early, Company Z instituted a strict attendance policy dictating that all employees be present at work from 9 a.m. to 6 p.m. unless they are called away by an emergency. Six months after the policy had been implemented, however, internal analysis revealed that overall productivity during work hours had declined.

Which of the following, if true, would best explain why the policy produced the reverse of its intended effect?

Hypnerotomachia Poliphili is a romance published in 1499 that, though the author was originally anonymous, has been attributed to Francesco Colonna. Some academics, however, doubt that Colonna is the author because, as a Dominican monk, he would not have the skill or experience to produce such a work. One academic has recently made the assertion that the attribution is correct, citing as evidence Colonna’s proximity to the text’s publisher, Aldus Manutius, and the wealth of other complex Renaissance works of literature confirmed to be written and compiled by talented members of the clergy. In light of this argument, it is clear that it is indeed possible that a member of a monastic order may have produced such a text.

Which of the following, if true, would most support the academic’s recent hypothesis concerning the authorship of Hypnerotomachia Poliphili?

Polar bears depend on sea ice, which melts during exceptionally warm weather, for access to food. When warm weather lasts longer than normal, polar bears accumulate fat—energy stored for their long winter hibernation—more slowly and weigh less, on average, as a result. At the same time, during periods of prolonged cold, polar bears weigh significantly less than they usually do, on average.

Which of the following, if true, does most to explain the contrast described above?

To keep depleted batteries from polluting the environment, the government of Ulm is discussing a mandate that would require residents to dispose of them through a special pickup service. To offset the costs of maintaining such a service, Ulm expects to charge a fee, which would be collected when batteries are discarded. Collecting the fee at the time of sale would be more effective, however, because residents are more likely to make use of a service if they see themselves as already having paid for it.

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