A man driving a car at a speed of 50 miles per hour on a road parallel to a railway track noticed a train coming towards him. Four seconds elapsed from the time the car was even with the front of the train to the time the car passed the end of the train. If the length of the train is 0.1 miles and the length of the car is negligible, what was the speed in miles per hour of the oncoming train?

If function f(z) represents the sum of the distinct prime factors of z, then what is the value of f(f(250))?

After winning the World Cup this year, the Indian team were touted as the world’s best cricket team; no coach or critic had anything but praise for the young sportsmen.

If $x={\left(\frac{1}{64}\right)}^{-\frac{1}{6}}$, what is $x$?

In what proportion should a 2% alcohol solution and a 40% alcohol solution be mixed in order to produce a 15% solution?

Research conducted by the University of California has discovered that about 1 in 8 women develop depression at some point in their lives and that women are doubly likely to struggle with chronic depression as men are.

Is the integer x even?

(1) x³ + x² is even

(2) 3x is divisible by 6

John takes the same route from home to work every day. How long did it take John to reach work today?

(1) Today, it took John twice his usual time to reach work, which was 10 minutes more than his usual time.

(2) The distance between John's home and work is 20 miles.

Is x even?

(1) x² = x

(2) x³ = x

All four vertices of quadrilateral ABCD lie on a circle. What is the measure of ∠BAD?

(1) AC = CD

(2) $\angle \mathrm{ADC}$= $70°$

According to several Russian analysts, the failure of military reform in Russia has not resulted from a lack of consensus regarding the substance of the reform but a shortage of financial resources in the country and conflicts in Chechnya.

A set contains eight consecutive integers. What is the product of all the integers?

(1) The greatest integer in the set is 5

(2) The set contains both positive and negative integers

In the last 100 years, the amount of sulfates in the atmosphere decreased considerably over the past century, while the concentration of greenhouse gases is more than twice what it was.

     The term "glass ceiling" as a discriminatory barrier limiting females from reaching senior management positions was used in the early 1990s, around the time that females first surpassed males in annual university degrees obtained in the United States. Studies of employment in various cities, such as the 2003 study of employment data in Sweden conducted by Albrecht, Bjӧrklund, and Vroman, have found a consistent gap between men's and women's wages after these are controlled for gender differences in age, education level, education field, sector, industry, and occupation. However, empirical studies as early that of Powell and Butterfield in 1994 have suggested that gender, as a job-irrelevant variable in consideration of promotions to top management positions, may actually work to women's advantage. Whereas the gender gap in pay is strongly supported by data, the glass-ceiling notion itself as a discriminatory force has been harder to account for in empirically proven terms.      Studies that have been considered by some a partial repudiation of the glass-ceiling theory have indicated that men and women differ in their preferences for competition and that such differences impact economic outcomes. If women are less likely to compete, they are less likely to enter competitive situations and hence less likely to win. For example, in a laboratory experiment featuring a non-competitive option and a competitive incentive scheme, men selected the latter twice as often as did women of equal ability. One explanation is that men are inherently more competitive; another is that the social influences limiting women's presence in executive leadership generally make their impact long before women are near the ceiling.    

     The outsourcing of production factories to locations overseas from companies' home countries has been a hallmark practice of multinational brands since the 1990s and is lauded by some economists as advancing the well-being of people in both the home country and the production country. However, not all of the benefits attributed to this globalization practice necessarily accrue, and there are concerns about outsourcing that are not readily addressed within the formulations of economic theory. First, a home company that separates its brand and its product as completely as possible and places the brand as paramount hardly sends a message that product quality is central to its operations; more likely, all of its innovation attempts will focus on branding, and such a company will settle with a product that is merely (and maybe barely) good enough. Dismissing this point, economists may cite the law of comparative advantage: outsourcing allows both companies involved to pursue greater profit and well-being according to their capabilities. Specifically, workers in the companies of manufacture should be paid more than they would be paid otherwise, even if they are paid less than factory workers in the original country; meanwhile, workers in the home country should be pushed to increase their skills and education and move to higher-skill jobs that are less available in the country of manufacture. Whether displaced workers in the home country acquire skills and make this shift in any reasonable timeframe is hardly demonstrated, however, and while outsourcing may create value by lowering costs, it has been asserted that workers in the countries of production are making no more after outsourcing than previously and hence in effect are enjoying none of the new profit. The CEO of one outsourcing company, when pressed on this point by a reporter, explained that, as the employees of those factories were not employees of his company, he could not be responsible for them. He asked the reporter whether journalists should be expected to know, and be responsible for, the manufacturing conditions of the paper on which their articles are printed. This comment, as much as it defends corporations, highlights the broadest form of worry about outsourcing: in global supply chains with increasingly distant and opaque connections, responsibility is too easy to shirk and maybe even impossible to determine.  

     In the realm of the psychology of decision-making, the role of expert intuition is under attack. People's inclination is to trust intuition and to point to many examples, across various disciplines, in which experts are able to make difficult judgments in seemingly negligible amounts of time. But this trust of intuition has been undermined by the research of other psychologists who have taken care to expose and document thoroughly the cognitive biases that can impede both our use of intuition and our ability to judge the use of intuition in a broader sense. How, then, can we know when expert intuition is to be trusted?      Gary Klein's research has provided a basis on which to establish how expert intuition, also known as naturalistic decision making, works at its best, which it does according to a recognition-primed decision model. One of his studies examined the thought process of experienced fireground commanders, the leaders of firefighter teams. One finding was that fireground commanders do not only consider a small number of options in deciding how to approach a firefighting situation; they tend to consider only one option. When presented with a situation, the commander was observed to think of one option spontaneously and then mentally simulate acting on that proposed course of action to see whether it would work. More specifically, Klein formulated the recognition-primed decision model as occurring in two steps. In the first step, a tentative plan comes to the mind of the expert by an automatic function of associative memory; the situation provides one or more clues recognized by the expert. Second, the plan is mentally simulated to see whether it will work.      When, then, can expert intuition be tested? Klein's model implies that the successful application of expert intuition will be limited to circumstances in which situational clues are reproduced and can be recognized over time. Situational regularity and individual memory are critical components of success. Reliable intuition is primarily — and, arguably, nothing more than — recognition. By this somewhat controversial inference, intuition is essentially memory. Consequently, all cases in which we might anticipate expert intuition to be valid are not equally conquerable by this faculty. Some environments may not be sufficiently regular to be predictable, and, of course, even in regular environments, the presumed expert must draw on a sufficient depth of practice. We can conclude, for example, that if a dedicated stock picker is to make judgments as skilled as those of a dedicated chess player, that person will do so not by relying primarily on intuition. One might note that, with or without intuition, it is incumbent on any true expert to know the limits of his or her knowledge.    

     M. Norton Wise's examination of the calorimeter, a machine invented in the 1780s to measure heat, elucidates his theory of a role that technology plays in society outside of the applications for which it has been developed.      In the schema given to us by Thomas Kuhn, as popularly understood, cultural differences are mediated through the paradigms that underlie theories-the theories' interconnected assumptions. According to Wise's theory, however, technologies act as cultural mediators, reconciling differences among different fields of thought and study, such as chemistry, political economy, and mathematics, and also connecting ideas with realities. When Antoine-Laurent Lavoisier and Pierre-Simon de Laplace first invented the calorimeter, they thought of it in comparison to a simple physical device, the balance scale: the calorimeter balanced quantities of heat against quantities of melted ice. In fact, Lavoisier and Laplace conceived of the device somewhat differently, and in this respect the calorimeter performed mediation of the first kind. Lavoisier, who is remembered as a chemist, viewed the calorimeter as measuring a balance between chemical substances, whereas Laplace, who is remembered as a mathematician and physical astronomer, viewed the calorimeter as balancing forces.      The differing interests of Lavoisier and Laplace (who tried at least once to rid himself of the partnership in order to work on pure mathematics) caused tension. This tension between the otherwise distinct fields of chemistry and physical astronomy was resolved, in part, by the calorimeter itself; it provided a common ground to the two fields in its own concrete existence and quantitative measure, if not entirely in concept. Secondly, the calorimeter, in providing commonly accepted measurements, gave commonly accepted meanings to the ideas involved in interpreting those measurements: caloric fluid and the physical force of heat.      We are typically more inclined to view a new technological invention in the terms of Kuhn--it supports an existing paradigm, or, rarely, massively disrupts it and causes a paradigm shift. Wise would agree with Kuhn that our conception of the electron is reinforced by the television and the fiberoptic cable, but while Kuhn sees the theoretical relationship as one of champion against challenger, arbitrated through defeat and continued reigning victory, technologies per Wise arbitrate by harmonizing.    

     For an online retailer, inventory represents a major source of cost. Every item of inventory represents an item that has not been sold and which therefore represents unrealized gains. Moreover, the greater the inventory a retailer must hold the anticipation of filling customer orders, the greater the amount of money it must have invested in something that cannot be used for other purposes. Two tenets of inventory management are to turn over inventory as quickly as possible and to hold the minimum amount of inventory necessary to fulfill tomorrow's orders efficiently. Those two challenges are related. If lower levels of inventory are needed, then less inventory will be on hand and it will be turned over more quickly. In competing with another online retailer, however, a company will be inclined to hold inventory of as many items as exist. If a particular type of item is not in stock at one retailer, a customer will turn to a competing retailer. Holding all of the possible stock items in stock adds to inventory cost. A solution to this issue has been previously for a company to have one central, monster-sized warehouse. Centralizing inventory allows a company to hold the widest possible range of items at the lowest necessary levels. But since customers also value speed of delivery time, the "monster warehouse model" has a flaw in that it involves shipping from a location which may not be as close to a customer's location as otherwise and which therefore would be vulnerable to a competitor who can deliver faster.      These considerations highlight the importance of information about consumer demand. At the basic level, knowing what items sell helps brick-and-mortar retailers determine what items to stock. In competitive online retail, companies with good data can stock minimum sufficient inventory levels. Even more significant, a national retailer that can forecast demand for specific items by region can move from the monster warehouse model to a system of regional warehouses, decreasing shipping time without increasing inventory costs.    

     Physical theory implies that the existence of astronomical entities above a certain mass is evidence for the existence of black holes. The Earth does not itself collapse upon itself under gravitational force because gravity is countered by the outward pressure generated by the electromagnetic repulsion between the atoms making up the planet. But if these forces are overpowered, gravity will always lead to the formation of a black hole. Assuming the validity of general relativity, we can calculate the upper bound for a star, the Tolman-Oppenheimer-Volkoff limit, to be 3.6 solar masses; any object heavier than this will be unable to resist collapse under its own mass and must be a black hole.     The search for entities more massive than the Tolman-Oppenheimer-Volkoff limit brings us to the examination of X-ray binary systems. In an X-ray binary, two bodies rotate around their center of mass, a point between them, while one component, usually a normal star, sheds matter to the other more massive component known as the accretor. The shedding matter is released as observable X-ray radiation. Since binary stars rotate around a common center of gravity, the mass of the accetor can be calculated from the orbit of the visible one. By 2004, about forty X-ray binaries that contained candidates for black holes had been discovered. The accretors in these binary systems did not appear visible, as is to be expected of black holes, but that fact alone does not distinguish them from very dense and hence less luminescent stars, such as neutron stars. More to the point is that these accretors were of mass far in excess of 3.6 solar masses. Famously, Cygnus X-1, an X-ray binary in the constellation Cygnus, has an accretor whose mass has been calculated to be 14 solar masses, plus or minus 4 solar masses. While it does not rule out other phenomena without further interpretation, it provides strong proof that black holes exist.     The conclusion that black holes exist depends on the reliability of the general-relativistic calculations involved. If more generous assumptions are made, the Tolman-Oppenheimer-Volkoff limit can be calculated to be as high as 10 solar masses. The finding also establishes plausibility, if not direct evidence, for the existence of supermassive black holes hypothesized to exist at the center of some galaxies.  

     How aquatic vertebrates evolved into land vertebrates has been difficult for evolutionary biologists to study, in part because the shift from water to land appears to have occurred rapidly and has thus has yielded a scarce fossil record. Prior to the advent of DNA sequencing, the primary guideposts in tracing the emergence of tetrapods had been morphological considerations, which highlighted the coelacanth and the lungfish as species of interest.      Coelacanths and lungfish are distinct from other fish in that they are lobe-finned species. Lobe-finned species, like ray-finned fishes such as tuna and trout, possess not cartilage but a bony skeleton, a key prerequisite for survival on land. Lobe-finned fish species are distinguished from ray-finned species by fins that are joined to a single bone, and which thus have the potential to evolve into limbs. Coelacanths and lungfish are two of the only lobe-finned species that are not extinct, and since they have evolved minimally since the time of the appearance of tetrapods, they are sometimes referred to as "living fossils." In fact, the first live coelacanth was discovered more than 100 years after the species had been discovered in fossilized form.      Whether the coelacanth in particular is rightly called a living fossil and whether it is the closest living relative of the original tetrapods are two questions that have been illuminated recently by genetic analysis. The coelacanth's sequenced genome, and this analysis has led to the conclusion that the lungfish is the closer relative of tetrapods. Moreover, coelacanth DNA has shown evolution over time, although at a rate much slower than that of most animals. The fish's morphology and its environment deep in the Indian Ocean may have created favorable conditions, allowing a more slowly evolving species to have survived for the last 400 million years.