More government action is necessary to maintain the affordability of higher education than subsidizing loans. It is true to say that as the costs of education rise, the necessity of government subsidized student loans increases, where the size of each loan is determined by the financial needs of a student, the price of a desired institution, and the student's likelihood to succeed in a college environment. However, subsidized loans are unsustainable unless a reasonable degree of educational “value” (an increase in income as a result of a bachelor's degree) is received by the student. The value necessary to repay the loans is difficult to ascertain when students vary wildly as to the costs of the institutions they attend, the financial circumstances of their families, and their chosen academic specializations. If the value of a student's education is ever less than the amount of money she was given through government loans, repayment drops sharply and the government is left with a lending deficit. Net government deficits (in this instance the relevant expense is money loaned to students) do not increase when more students apply to, attend, and graduate from institutions of higher learning. Indeed, government reaps the benefits of expanded education in the form of taxes collected from incomes increased as a result of college graduation—that is, value added by the attainment of a degree—but the value added by education is not increasing at the same rate as the costs of that education—students are being charged more and receiving fewer benefits.

     The necessity of introducing more stringent regulations on educational costs is obvious if one understands the benefits government enjoys from high rates of scholastic attainment. The prices colleges set for themselves are dictated not by the costs of operation, but by the prices students and the organizations supporting them are willing to pay. Once this high price of education is established, college administrations have little incentive to lower costs. Governments must circumscribe educational costs within reasonable bounds to ensure their subsidization programs remain effective. Governments must ensure that students procure substantial value from the educations they receive. And governments must make it so the individuals to whom they lend money will reliably pay it back at reasonable intervals.

     As understandings of the solar life cycle developed, scientists were confronted by a nagging question: If, early in the history of Earth's planetary formation, the sun was significantly dimmer than it is now, how do we explain evidence for the presence of liquid water on the planet's surface during this period? It is understood that during the early Earth period our sun would have shone at about 70 percent of its current luminosity, significantly below the level necessary to sustain the presence of liquid oceans on the planet's surface. But paleontological and geological records indicate with substantial certainty that liquid water was present on the Earth's surface during this time. If scientific models of solar development and the early geological history of Earth are to be reconciled, there must have been some other, intervening factor affecting surface temperatures during this early period of geologic history.

     Our method of reconciling these two apparently contradictory bodies of evidence has been to analyze the characteristics and chemical composition of Earth's atmosphere during its various periods of geological development. We have known for decades that the presence of certain vapors in the air, commonly known as “greenhouse gases,” increases the amounts of heat retained by an atmosphere to a degree proportionate to the concentration of greenhouse gases within it. If the Earth was warmer in the past than solar luminosity would suggest—and we have strong evidence that it was—then we can expect that the distribution of greenhouse gases in its atmosphere would be of paramount value in explaining that discrepancy. Heightened greenhouse gas levels would trap and magnify the sun's heat as it struck the atmosphere, enabling liquid water to exist on the surface of Earth. However, we have discovered little evidence that greenhouse gases during the early Earth period were present in larger quantities than previously assumed. These surprising findings indicate that the discrepancy between solar-astronomical and geological evidence related to the development of Earth's oceans cannot be explained by the presence of carbon in the atmosphere.

     One likely alternative is that another, non-solar source for atmospheric heat during the early Earth period. Earth and its moon were much closer together in the early geologic history of the planet, and tidal heating caused by the moon's rotation around Earth was likely much greater. While it is unclear how much influence this phenomenon might have exerted over atmospheric temperatures, scientists are increasingly convinced that it could play a part in explaining the unlikely presence of liquid water on our infant planet, perhaps in combination with indeterminate geological activity, solar flares, or irregularities in Earth's magnetic field.

     Felicia Durkhart's assertion that women in ancient Rome “enjoyed relatively equal standing” with ancient Roman men has served as a rallying point for feminist scholars eager to demonstrate that misconceptions about gender in history abound. For instance, Darla Moore's seminal 1981 essay “The Women Who Nurtured an Empire” showed that the ancient Romans might have recognized the necessity of women to the empire's continuance, but habitually treated them with contempt and abuse. More recently, however, feminist scholars have recognized that neither Durkhart's glib assessment of women's situation nor Moore's dour one adequately describes the dynamics of power and gender in ancient Rome. Several recent studies by these scholars give special attention to the ways in which women's rights and status changed over time, injecting much-needed nuance into the discussion.

     The criticism that Durkhart and Moore oversimplify matters is also leveraged against those works that examine women's status with little or no attempt to take into account the quality of evidence available. Since details of the lives of often-oppressed populations are notoriously difficult for historians to ascertain, any description of women's lives in ancient times should be tempered by some acknowledgment that what evidence does exist can only offer limited perspectives. John Evans, among others, attempts to remedy these errors by contextualizing each source used in its immediate setting, as well as describing the larger social and historical forces, from household traditions to wartime conventions and symbols, that his interpretations take into account. Evans is therefore able to integrate studies that have previously been siloed due to the methods and concerns of the subjects' usual scholars and allows the insights of feminist studies and political analysis to be brought to bear on one another, and moreover focuses on the changes to household dynamics and economies over years of war and imperial expansion. Evans does acknowledge that upper-class women's fortunes did, at least, improve as the empire enriched itself, but concludes that the average woman likely faced increasing economic uncertainty and violence in times of war, demonstrating that men's decisions in remote centers of power affected more than just their immediate subordinates.

Six distinct pairs of shoes are in a closet. If three shoes are selected at random from the closet, what is the probability that no two of the chosen shoes make a pair?

A mayor has proposed a fee of five dollars per day for private vehicles entering the city, claiming that the fee will alleviate the city’s traffic congestion. The mayor reasons that, since the fee will exceed the cost of round-trip bus fare from many nearby points, many people will switch from using their cars to using the bus. Which of the following statements, if true, provides the best evidence that the mayor’s plan will fail to accomplish its goal?  

If a freight train travels at an average speed of 30 mph, it will arrive at its destination 1.5 hours late. If the train instead travels at an average speed of 45 mph, it will arrive 1 hour early. At what average speed, in miles per hour, should the train travel in order to arrive at its destination exactly on time?

Is an integer?

(1) is a prime number

(2) is divisible by

Is ?

(1)

(2)

According to architects, the reason a dome was used in traditional Mughal architecture was not because it was more aesthetic, but because it was structurally stronger.

How many 5-digit multiples of 3 can be formed using only the digits 0, 1, 2, 3, 4, and 5, without repeating any digits?

Two sides of a triangle have lengths 4 and 6. How many different integer values of the third side are possible?