If n and k are positive integers, is n divisible by 6?
(1) n = k(k + 1)(k – 1)
(2) k – 1 is a multiple of 3.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

In the xy-plane, point (r, s) lies on a circle with center at the origin. What is the value of r^2 + s^2?

(1) The circle has radius 2.
(2) The point (v2, -v2) lies on the circle.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

A conventional view of nineteenth-century Britain holds that iron manufacturers and textile manufacturers from the north of England became the wealthiest and most powerful people in society after about 1832. According to Marxist historians, these industrialists were the target of the working class in its struggle for power. A new study by Rubinstein, however, suggests that the real wealth lay with the bankers and merchants of London. Rubinstein does not deny that a northern industrial elite existed but argues that it was consistently outnumbered and outdone by a London-based commercial elite. His claims are provocative and deserve consideration.

Rubinstein’s claim about the location of wealth comes from his investigation of probate records. These indicate the value of personal property, excluding real property (buildings and land), left by individuals at death. It does seem as if large fortunes were more frequently made in commerce than in industry and, within industry, more frequently from alcohol or tobacco than from textiles or metal. However, such records do not unequivocally make Rubinstein’s case. Uncertainties abound about how the probate rules for valuing assets were actually applied. Mills and factories, being real property, were clearly excluded: machinery may also have been, for the same reason. What the valuation conventions were for stock-in-trade (goods for sale) is also uncertain. It is possible that their probate values were much lower than their actual market value: cash or near-cash, such as bank balances or stocks, were, on the other hand, invariably considered at full face value. A further complication is that probate valuations probably took no notice of a business’s goodwill (favor with the public) which, since it represents expectations about future profit-making, would today very often be a large fraction of market value. Whether factors like these introduced systematic biases into the probate valuations of individuals with different types of businesses would be worth investigating.

The orthodox view that the wealthiest individuals were the most powerful is also questioned by Rubinstein’s study. The problem for this orthodox view is that Rubinstein finds many millionaires who are totally unknown to nineteenth-century historians: the reason for their obscurity could be that they were not powerful. Indeed, Rubinstein dismisses any notion that great wealth had anything to do with entry into the governing elite, as represented by bishops, higher civil servants, and chairmen of manufacturing companies. The only requirements were university attendance and a father with a middle-class income.

Rubinstein, in another study, has begun to buttress his findings about the location of wealth by analyzing income tax returns, which reveal a geographical distribution of middle-class incomes similar to that of wealthy incomes revealed by probate records. But until further confirmatory investigation is done, his claims can only be considered partially convincing.

1) The main idea of the passage is that
(A) the Marxist interpretation of the relationship between class and power in nineteenth-century Britain is no longer viable
(B) a simple equation between wealth and power is unlikely to be supported by new data from nineteenth-century British archives
(C) a recent historical investigation has challenged but not disproved the orthodox view of the distribution of wealth and the relationship of wealth to power in nineteenth-century Britain
(D) probate records provide the historian with a revealing but incomplete glimpse of the extent and location of wealth in nineteenth-century Britain
(E) an attempt has been made to confirm the findings of a new historical study of nineteenth-century Britain, but complete confirmation is likely to remain elusive

2) The author of the passage implies that probate records as a source of information about wealth in nineteenth-century Britain are
(A) self-contradictory and misleading
(B) ambiguous and outdated
(C) controversial but readily available
(D) revealing but difficult to interpret
(E) widely used by historians but fully understandable only by specialists

3) The author suggests that the total probate valuations of the personal property of individuals holding goods for sale in nineteenth-century Britain may have been
(A) affected by the valuation conventions for such goods
(B) less accurate than the valuations for such goods provided by income tax returns
(C) less, on average, if such goods were tobacco-related than if they were alcohol-related
(D) greater, on average, than the total probate valuations of those individuals who held bank balances
(E) dependent on whether such goods were held by industrialists or by merchants or bankers

4) According to the passage, Rubinstein has provided evidence that challenges which one of the following claims about nineteenth-century Britain?
(A) The distribution of great wealth between commerce and industry was not equal.
(B) Large incomes were typically made in alcohol and tobacco rather than in textiles and metal.
(C) A London-based commercial elite can be identified.
(D) An official governing elite can be identified.
(E) There was a necessary relationship between great wealth and power.

5) The author mentions that goodwill was probably excluded from the probate valuation of a business in nineteenth-century Britain most likely in order to
(A) give an example of a business asset about which little was known in the nineteenth century
(B) suggest that the probate valuations of certain businesses may have been significant underestimations of their true market value
(C) make the point that this exclusion probably had an equal impact on the probate valuations of all nineteenth-century British businesses
(D) indicate that expectations about future profit-making is the single most important factor in determining the market value of certain businesses
(E) argue that the twentieth-century method of determining probate valuations of a business may be consistently superior to the nineteenth-century method

6) Which one of the following studies would provide support for Rubinstein’s claims?
(A) a study that indicated that many members of the commercial elite in nineteenth-century London had insignificant holdings of real property
(B) a study that indicated that in the nineteenth century, industrialists from the north of England were in fact a target for working-class people
(C) a study that indicated that, in nineteenth-century Britain, probate values of goods for sale were not as high as probate values of cash assets
(D) a study that indicated that the wealth of nineteenth-century British industrialists did not appear to be significantly greater when the full value of their real property holdings was actually considered
(E) a study that indicated that at least some members of the official governing elite in nineteenth-century Britain owned more real property than had previously been thought to be the case

7) Which one of the following, if true, would cast the most doubt on Rubinstein’s argument concerning wealth and the official governing elite in nineteenth-century Britain?
(A) Entry into this elite was more dependent on university attendance than on religious background.
(B) Attendance at a prestigious university was probably more crucial than a certain minimum family income in gaining entry into this elite.
(C) Bishops as a group were somewhat wealthier, at the point of entry into this elite, than were higher civil servants or chairmen of manufacturing companies.
(D) The families of many members of this elite owned few, if any, shares in iron industries and textile industries in the north of England.
(E) The composition of this elite included vice-chancellors, many of whom held office because of their wealth.

Affording strategic proximity to the Strait of Gibraltar, Morocco was also of interest to the French throughout the first half of the twentieth century because they assumed that if they did not  hold it, their grip on Algeria was always insecure.

(A) if they did not hold it, their grip in Algeria was always insecure
(B) without it their grip on Algeria would never be secure
(C) their grip on Algeria was not ever secure if they did not hold it
(D) without that, they could never be secure about their grip on Algeria
(E) never would their grip on Algeria be secure if they did not hold it

Who types at a faster rate, John or Bob?
(1) The difference between their typing rates is 10 words per minute.
(2) Bob types at a constant rate of 80 words per minute.

Virtually everything astronomers known about objects outside the solar system is based on the detection of photons—quanta of electromagnetic radiation. Yet there is another form of radiation that permeates the universe: neutrinos. With (as its name implies) no electric charge, and negligible mass, the neutrino interacts with other particles so rarely that a neutrino can cross the entire universe, even traversing substantial aggregations of matter, without being absorbed or even deflected. Neutrinos can thus escape from regions of space where light and other kinds of electromagnetic radiation are blocked by matter. Furthermore, neutrinos carry with them information about the site and circumstances of their production: therefore, the detection of cosmic neutrinos could provide new information about a wide variety of cosmic phenomena and about the history of the universe.

But how can scientists detect a particle that interacts so infrequently with other matter? Twenty-five years passed between Pauli’s hypothesis that the neutrino existed and its actual detection: since then virtually all research with neutrinos has been with neutrinos created artificially in large particle accelerators and studied under neutrino microscopes. But a neutrino telescope, capable of detecting cosmic neutrinos, is difficult to construct. No apparatus can detect neutrinos unless it is extremely massive, because great mass is synonymous with huge numbers of nucleons (neutrons and protons), and the more massive the detector, the greater the probability of one of its nucleon’s reacting with a neutrino. In addition, the apparatus must be sufficiently shielded from the interfering effects of other particles.

Fortunately, a group of astrophysicists has proposed a means of detecting cosmic neutrinos by harnessing the mass of the ocean. Named DUMAND, for Deep Underwater Muon and Neutrino Detector, the project calls for placing an array of light sensors at a depth of five kilometers under the ocean surface. The detecting medium is the seawater itself: when a neutrino interacts with a particle in an atom of seawater, the result is a cascade of electrically charged particles and a flash of light that can be detected by the sensors. The five kilometers of seawater above the sensors will shield them from the interfering effects of other high-energy particles raining down through the atmosphere.

The strongest motivation for the DUMAND project is that it will exploit an important source of information about the universe. The extension of astronomy from visible light to radio waves to x-rays and gamma rays never failed to lead to the discovery of unusual objects such as radio galaxies, quasars, and pulsars. Each of these discoveries came as a surprise. Neutrino astronomy will doubtless bring its own share of surprises.

1) Which of the following titles best summarizes the passage as a whole?
(A) At the Threshold of Neutrino Astronomy
(B) Neutrinos and the History of the Universe
(C) The Creation and Study of Neutrinos
(D) The DUMAND System and How It Works
(E) The Properties of the Neutrino

2) With which of the following statements regarding neutrino astronomy would the author be most likely to agree?
(A) Neutrino astronomy will supersede all present forms of astronomy.
(B) Neutrino astronomy will be abandoned if the DUMAND project fails.
(C) Neutrino astronomy can be expected to lead to major breakthroughs in astronomy.
(D) Neutrino astronomy will disclose phenomena that will be more surprising than past discoveries.
(E) Neutrino astronomy will always be characterized by a large time lag between hypothesis and experimental confirmation.

3) In the last paragraph, the author describes the development of astronomy in order to
(A) suggest that the potential findings of neutrino astronomy can be seen as part of a series of astronomical successes
(B) illustrate the role of surprise in scientific discovery
(C) demonstrate the effectiveness of the DUMAND apparatus in detecting neutrinos
(D) name some cosmic phenomena that neutrino astronomy will illuminate
(E) contrast the motivation of earlier astronomers with that of the astrophysicists working on the DUMAND project

4) According to the passage, one advantage that neutrinos have for studies in astronomy is that they
(A) have been detected for the last twenty-five years
(B) possess a variable electric charge
(C) are usually extremely massive
(D) carry information about their history with them
(E) are very similar to other electromagnetic particles

5) According to the passage, the primary use of the apparatus mentioned in lines 24-32 would be to
(A) increase the mass of a neutrino
(B) interpret the information neutrinos carry with them
(C) study the internal structure of a neutrino
(D) see neutrinos in distant regions of space
(E) detect the presence of cosmic neutrinos

6) The passage states that interactions between neutrinos and other matter are
(A) rare
(B) artificial
(C) undetectable
(D) unpredictable
(E) hazardous

7) The passage mentions which of the following as a reason that neutrinos are hard to detect?
(A) Their pervasiveness in the universe
(B) Their ability to escape from different regions of space
(C) Their inability to penetrate dense matter
(D) The similarity of their structure to that of nucleons
(E) The infrequency of their interaction with other matter

8) According to the passage, the interaction of a neutrino with other matter can produce
(A) particles that are neutral and massive
(B) a form of radiation that permeates the universe
(C) inaccurate information about the site and circumstances of the neutrino’s production
(D) charged particles and light
(E) a situation in which light and other forms of electromagnetic radiation are blocked

9) According to the passage, one of the methods used to establish the properties of neutrinos was
(A) detection of photons
(B) observation of the interaction of neutrinos with gamma rays
(C) observation of neutrinos that were artificially created
(D) measurement of neutrinos that interacted with particles of seawater
(E) experiments with electromagnetic radiation

The earth’s resources are being depleted much too fast. To correct this, the United States must keep its  resource consumption at present levels for many years to come.

1. The argument above depends on which of the following assumptions?
(A) Per capita resource consumption in the United States is at an all-time high.
(B) The United States wastes resources.
(C) The United States uses more resources than any other country.
(D) The United States imports most of the resources it uses.
(E) Curbing U.S. resource consumption will significantly retard world resource depletion.

Beatrix Potter, in her book illustrations, carefully coordinating them with her narratives,
capitalized on her keen observation and love of the natural world.
(A) Beatrix Potter, in her book illustrations, carefully coordinating them with her narratives,
(B) In her book illustrations, carefully coordinating them with her narratives, Beatrix Potter
(C) In her book illustrations, which she carefully coordinated with her narratives, Beatrix

Potter
(D) Carefully coordinated with her narratives, Beatrix Potter, in her book illustrations,
(E) Beatrix Potter, in her book illustrations, carefully coordinated them with her narratives