Archaeologists hypothesize that an eleventh-century Byzantine church in what is now Turkey was constructed in two distinct sections, separated by decades. They analyzed pigments from frescoes painted on walls in the two sections and confirmed the presence of different mineral compounds in each section's pigments. Additionally, the relatively rare ultramarine violet appears only in one section.

Which of the following would it be most useful to determine in evaluating the archaeologists' hypothesis?

Critics of a British surveillance system designed to recognize faces digitally point out that the system has not recognized any criminals committing a crime, even though scores of those with previous convictions have had their likenesses entered in the system's data banks and are known to live in the areas where the system is deployed. Nevertheless, proponents of the system rightly credit it with a 34 percent reduction of crime in those areas.

Given the information above, which of the following would, if true, most help to account for the system's contribution to the reduction of crime?

Psychologists spent three months training volunteers in a meditation technique that centers on minimizing distractions, while other volunteers received no training. Then all the volunteers were asked to pick out numbers from a stream of distracting letters that appeared on a video screen. The volunteers who had undergone meditation training were much better than the others at detecting the numbers. The psychologists concluded that practicing the concentration required by the meditation technique improves overall focus and attention.

In order to assess the strength of the psychologist's argument, it would be most helpful to know which of the following?

Draco Petrochemicals moves tens of tankers in and out of the heavily trafficked Port St. George every day. The company’s success depends on its ability to transport large chemical shipments with minimum delays. Consequently, Draco is planning to replace its largest tankers with new SPNSR tankers, whose cutting-edge architecture minimizes the need for routine maintenance. The SPNSR tankers’ durability in this regard results in both lower maintenance costs and less time lost to maintenance stops.

Which of the following, if true, could present the most serious disadvantage for Draco Petrochemicals in replacing its largest tankers with new SPNSR tankers?

United Lumber will use trees from its forests for two products. The tree trunks will be used for lumber and the branches converted into wood chips to make fiberboard. The cost of this conversion would be the same whether done at the logging site, where the trees are debranched, or at United's factory. However, wood chips occupy less than half the volume of the branches from which they are made.

The information given, if accurate, most strongly supports which of the following?

The contingency-fee system, which allows lawyers and their clients to agree that the lawyer will be paid only in the event of success, does not increase the number of medical malpractice lawsuits brought against doctors. As attorneys must cover the costs for their time and research, they want to be assured that any medical malpractice case they accept on a contingency-fee basis has substantial merit. Consequently, attorneys turn away many people who come to see them, for lack of a good case.

The argument above is most vulnerable to criticism on the grounds that it fails to

Unless tiger hunting decreases, tigers will soon be extinct in the wild. The countries in which the tigers’ habitats are located are currently debating joint legislation that would ban tiger hunting. Thus, if these countries can successfully enforce this legislation, the survival of tigers in the wild will be ensured.

The reasoning in the argument is most vulnerable to criticism on the grounds that the argument

A bag contains a total of 20 only red and white marbles, fewer than half of which are red. Two marbles are to be drawn simultaneously from the bag. How many marbles in bag are red?

(1) The probability that the two marbles to be drawn will be red is .

(2) The probability that one marble to be drawn will be red and the other will be white is .

Installing scrubbers in smokestacks and switching to cleaner-burning fuel are the two methods available to Northern Power for reducing harmful emissions from its plants. Scrubbers will reduce harmful emissions more than cleaner-burning fuels will. Therefore, by installing scrubbers, Northern Power will be doing the most that can be done to reduce harmful emissions from its plants.

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

First-time computer buyers buying PXC home computers typically buy models that cost much less and have a smaller profit margin per computer than do PXC computers bought by people replacing their computers with more powerful models. Last year PXC's profits from computer sales were substantially higher than the previous year, although about the same number of PXC computers were sold and the prices and profit margins for each computer model that PXC sells remained unchanged.

If the statements above are true, which of the following is most strongly supported by them?