If and represent the length and width, respectively, of the rectangle above, what is the perimeter?

(1)

(2)

If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

(1) 60 percent of the guests who ordered dessert also ordered coffee.

(2) 90 percent of the guests who ordered coffee also ordered dessert.

In the -plane, lines k and l intersect at the point (1,1). Is the -intercept of k greater than the -intercept of l?

(1) The slope of k is less than the slope of l.

(2) The slope of l is positive.

If arc PQR above is a semicircle, what is the length of diameter PR?

(1) a = 4

(2) b = 1

If a and b are positive integers, is ?

(1)

(2)

The annual rent collected by acorporation from a certain building was percent more in 1998 than in 1997 and percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997?

(1)

(2) 

If is an integer, is ?

(1) 

(2)

Six shipments of machine parts were shipped from a factory on two trucks, with each shipment entirely on one of the trucks. Each shipment was labeled either S1, S2, S3, S4, S5, or S6. The table shows the value of each shipment as a fraction of the total value of the six shipments. If the shipments on the first truck had a value greater than of the total value of the six shipments, was S3 shipped on the first truck?

(1) S2 and S4 were shipped on the first truck.

(2) S1 and S6 were shipped on the second truck.

In the figure above, what is the value of x + y?

(1) x = 70

(2) and are both isosceles triangles.

There were several factors that led to the downfall of the Tughlaq Empire. The Tughlaq empire was a Turkic dynasty of Delhi sultanate, whose reign started in the fourteenth century in Delhi. Around the year 1321, Ghiyas Tughlaq ascended the throne and was given the title Ghiyath al-Din Tughlaq. The Tughlaq dynasty was able to hold its rule because it had their strong allies like the Turks, Afghans and the Muslim warriors of south Asia. The Tughlaqs established the most extensive empire among the Delhi Sultanate. Ghiyas-ud-din Tughlaq took advantage of a previous conquest of the south and annexed a larger part of it. His son, Muhammad Bin Tughlaq, contributed most towards the extension of the Empire both as a prince and a Sultan. But the process of disintegration began during his reign. He became notorious for ill-advised policy experiments such as shifting the capital from Delhi to Daulatabad and introducing copper coins without effective regulation against forgery. Tughluqi has as a result become a synonym for brilliant if stubborn eccentricity in the Urdu language. The annexation of the south, the failures of Muhammad Tughlaq, the weakness of Firoz Shah Tughlaq, the incompetence

of his successors, the incompetence and demoralization of the nobility, and the invasion of Timur were the chief factors responsible for the downfall of this vast Empire.

Ghiyas-ud-din Tughlaq waged a gruesome battle against Khusrao Khan, who killed the last Khilji ruler. His successful defense against the Mongols made him an able ruler and the founder of a dynasty in India. He conquered many areas including the eastern portion of Bengal, a huge territory. In addition, Ghiyas-ud-din Tughlaq adopted the policy of annexing the conquered territories of the south, which was p

of his successors, the incompetence and demoralization of the nobility, and the invasion of Timur were the chief factors responsible for the downfall of this vast Empire.

Ghiyas-ud-din Tughlaq waged a gruesome battle against Khusrao Khan, who killed the last Khilji ruler. His successful defense against the Mongols made him an able ruler and the founder of a dynasty in India. He conquered many areas including the eastern portion of Bengal, a huge territory. In addition, Ghiyas-ud-din Tughlaq adopted the policy of annexing the conquered territories of the south, which was p

d Tughlaq. But this measure was against the permanent interest of the empire. Because of the lack of efficient transportation, it was difficult for the rulers of the north to keep the south under control for long. Thus the south became independent during the later period of Muhammad Tughlaq. The conquest of the south brought no advantages to the Tughlaqs. On the contrary, it adversely affected the resources and the strength of the Empire.

One of the most controversial rulers in India, Mohammed bin Tughlaq was the successor of Ghazi Tughlaq. Under his rule, the empire spread and his reign grew. Many theorize that he was a brilliant person who had full command over mathematics and medicine. Yet, he was considered crazy by members of his court. He was known to mete out very cruel and brutal punishment to people who were found guilty of even small offenses. Eventually, Muhammad Tughlaq failed both in his internal and foreign policy. While Bengal and the south regained independence and the hold of the Delhi Sultanate became weak over Gujarat and Sindh, no significant territor

on, his policies and severe measures resulted in widespread revolts and further taxed the energy and resources of the empire.

Antitrust laws — statutes that supposedly keep any one firm or group of firms from dominating the marketplace — are thought by some to be the bulwark of free enterprise. These laws are founded on the idea that without the continued vig

. Collectively, such laws not only have a negative effect on economic efficiency, but also negatively affect the appropriate distribution of wealth and income in society and the allocation of political and consumer power and rights.

Often, antitrust laws are fluid, non-objective and retroactive. Because of murky statutes and conflicting case law, companies can never be sure what constitutes permissible behavior. Normal business practices — price discounts, product improvements and exclusive contracting — can somehow morph into an antitrust violation when examined by government antitrust regulators. Companies can be accused of monopolistic price gouging for charging more than their competitors, or accused of predatory pricing for charging less, or accused of collusion for charging the same.

In one of the most brazen examples of misuse of antitrust laws for competitive and strategic benefit, Digital Equipment Corp. filed a lawsuit against Intel in 1990, when the firm`s attempt to persuade Intel to incorporate Digital Equipment`s technology as part of its next-generation chip design ended in failure. Alpha, then Digital`s flagship product, was at the time the fastest chip in the industry. In spite of Alpha`s relative superiority, more computers, including computers manufactured by Digital itself, employed Intel`s lower-powered Pentium chip than Digital`s counterpart. In 1997, Digital threatened Intel with antitrust action in a bold attempt to reposition itself in the computer industry. Robert B. Palmer, Digital`s chief executive, denied analysts` suggestions that the lawsuit was in fact a veiled strategic effort to prevent Intel from developing competing technology in the microprocessor market.

The origin of life remains one of the world's greatest mysteries even to this day. Several theories have attempted to explain this phenomenon, but thus far, there has been no conclusive evidence to support one theory over another. One of the most popular theories is the primordial soup theory. This model purports that all life on the planet was created out of a “primordial soup." Oparin and Haldane, the scientists who developed this model, hypothesized that all life forms originated in a warm pond or ocean from a combination of chemicals that created amino acids. All the building blocks of life were already available in the atmosphere. These molecules were then “energized” by lightning, and combined to form amino acids which, in turn, folded into complex proteins. The first organisms to evolve were simple heterotrophs, which survived by consuming other organisms. Theoretically, this is plausible. Miller and Urey, in 1950, carried out a rather famous experiment to test this theory. They mixed gases believed to have been present in the primordial atmosphere and then energized the mixture with an electric spark. They discovered that all 20 amino acids could be produced in this manner.

However, there are several major flaws in this theory. First, the formation of proteins from amino acids is an extremely complex process. There are over a trillion ways amino acids can combine to form proteins, and hitting upon the right protein by accident is extremely improbable. Moreover, the primordial soup would have been way too diluted to achieve anything. In short, there is just too much left to chance. As one critic put it, “What are the chances that a monkey playing with an old typewriter will accidentally type out a bestseller?” An alternative theory is that life originated deep underground, not in a water body. One could argue that “superbugs," which are present in deep soil even today, were the first life forms to evolve. They may have originated as microbes thriving on intense heat. However, there has been no satisfactory account of how these superbugs evolved from a mass of chemical compounds.

Another hypothesis is that life did not originate on the earth at all. The Panspermia theory suggests that life seeds came from outer space. This theory has found considerable support, as it explains the sudden spurt in life forms after millions of years of nothingness. Also, statistics show that 7.5% of rocks from Mars reach earth. Such rocks, from Mars or elsewhere, could have transported bacteria, which can easily survive the harsh environs of space. After all, there is evidence that meteorites contain amino acids and bacteria. Panspermia states that these meteorites carried bacteria, amino acids, methane and carbon. These substances were then deposited on earth, either in warm oceans or underground, and eventually grew into simple life forms. This theory merits further research because it has potential to explain not only the origin of life on earth, but also prove the presence of life beyond the earth.

By far the most common cause of hair loss in men is androgenetic alopecia, also referred to as “male pattern” or “common” baldness. It is caused by the effects of the male hormone dihydrotestosterone (DHT) on genetically susceptible scalp hair follicles. This sensitivity to DHT is present mainly in hair follicles that reside in the front, top, and crown of the scalp (rather than the back and sides), producing a characteristic and easily identifiable pattern.

It is frequently stated that “hair loss comes from the mother's side of the family.” The truth is that baldness can be inherited from either parent. However, recent research suggests that the reasons for hair loss and balding may be a bit more complex than originally thought. Factors on the X-chromosome have been shown to influence hair loss, making the inheritance from the maternal side of the family slightly more important than the paternal one. The identification of an androgen receptor gene (AR) on the X-chromosome helps to explain why the hair loss pattern of a man resembles his maternal grandfather more often than his father. However, this is clearly not the whole story since a direct inheritance of baldness from the father is observed as well. An autosomal (non-sex) linked gene would explain this type of transmission — but this gene has not yet been found.

DHT is formed by the action of the enzyme 5-alpha reductase on testosterone, the hormone that causes sex characteristics in men. DHT causes male hair loss by shortening the growth, or the anagen, phase of the hair cycle, causing miniaturization of the follicles, and producing progressively shorter, finer hairs. Eventually these hairs totally disappear.

      Despite views that globalization has reached its peak, a period beginning in the nineteenth century and extending into the early-twentieth century, in fact, is the interval during which international barriers to trade fell most steeply, as can be seen in the case of price convergence in commodities. The prices of cloves, pepper, and coffee failed to converge between Amsterdam and East Asia or between England and India from as far back as 1580 but began in 1820 to draw closer. Similarly, the difference in wheat prices in the United States and England fell from one hundred percent in the early-nineteenth century to negligible levels late in the century and to no difference at all in the early-twentieth century. A similar story unfolded during this period for bacon, cotton, and rice.

     Peter Lindert and Jeffrey Williamson have summarized the price gaps in commodity markets between continents as evolving in three phases. From 1820 to 1914, these gaps fell by 81 percent; they attribute 72 percent of this decline to cheaper transport and 28 percent to trade policies. Second, during the wartime period of 1914 to 1950, the gaps doubled, due to a reversal in trade policies. Finally, from 1950 to 2000, they fell again by 76 percent, ending up 92 percent lower than in 1820, with about four-fifths of the total change attributable to cheaper transport and one-fifth to more favorable trade policies.

     Trade data for this period are typically articulated in terms of ratio of total trade volume to gross domestic product, since commodity price information is not universally available. These ratios in many advanced economies were higher in the mid-1990s than in the early 1900s, but not by much. In Japan, notably, the percentage of GDP for which trade accounted in 1995 was 17 percent, far under its 1910 level of 30 percent, as measured in current prices. Sure enough, the ratios have risen somewhat in other economies over that same time period—by 13 percentage points in the United Kingdom, 8 points in France, and from 11 percent to 24 percent in the United States; this latter spike may explain why the attention to globalization has been especially acute in America. These increases, nevertheless, are modest given the fact that the world economy grew roughly twice as quickly in the twentieth century as in the nineteenth.

     The ratios above, and hence the substantiation for the argument that globalization peaked a century ago, grow much more dramatically if they are computed in constant prices rather than in current prices, because the prices of goods relative to services fell due to sustained increases in productivity in the sectors producing these goods. Trade has grown most in those sectors in which prices have most strikingly fallen, so the proportions of GDP in constant prices have risen more than those in current prices.