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Magoosh
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In 1883, the Indonesian island Krakatoa, home to a massive volcano, seemingly disappeared overnight as an eruption rent the entire island apart, catapulting rock and debris into the atmosphere. For the next few years, as ash circled the entire globe, the average world temperature dropped by several degrees Fahrenheit. Therefore, an eruption of similar power in terms of the amount of debris ejected into the atmosphere will likely cause the average temperature around the world to drop by several degrees.Which of the following, if true, best challenges the main claim of the argument?
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Magoosh
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The CFO attributes our increased sales last year to the new markets in Eastern Europe. Nevertheless, a careful study of our revenue reveals a boom of sales in Southeast Asia, while the markets in Eastern Europe, after an early surge, settled at levels much lower than expected. After all, in Eastern Europe, our firm has fierce competition from both German and Russian exports, some of which offer exceptionally high quality at low cost. By contrast, no producers in this sector operate to the East of Turkey, and our firm is the only one in our sector with significant inroads into India, Thailand, Vietnam, and Taiwan. Current plans call for expansion into Eastern Europe, but the Southeast Asian markets hold much more promise. In the argument given, the two portions in boldface play which of the following roles?
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Magoosh
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If$${(\frac{1}{x}+x)}^{2}=16$$,then $${{1}\over{x^{2}}}+x^{2}=$$
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Magoosh
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At Funston Stores, a salesperson's salary is comprised solely of commissions from sales. A particular salesperson's annual salary was lower in 2009 than in 2008. In both years, all of this salesperson's sales were of only one item, product X, and he made the same number of product X sales in both years. The commission percentage for all Funston salespeople has remained unchanged over the past ten years. The information above most strongly supports which of the following?
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Magoosh
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When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 8, the quotient is 3y and the remainder is 2. What is the value of 13y – x ?
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Magoosh
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Despite the anti-virus protection program installed on its computers, SmartTech has received many complaints from consumers that their computers had become infected with viruses. In order to reduce the number of its computers vulnerable to viruses, the CEO of SmartTech Corp. has had the company's engineers install three different virus-blocking programs on each computer before shipping them to consumers. Nevertheless, customer reports of computer viruses have risen since the institution of this initiative.Which of the following, if true, most helps to explain why acting on the CEO's plan failed to achieve her goal?
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Magoosh
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If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference between the greatest and least of the five integers?
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Magoosh
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If 3x < 2y < 0, which of the following must be the greatest?
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Magoosh
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What is the sum of all integers from 45 to 155 inclusive?
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Magoosh
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If the ratio of the volume of cube A to the volume of cube B is 1 to 8, what is the ratio of the surface area of cube A to the surface area of cube B?
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Magoosh
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The city of Carina is considering implementing an Alternative Minimum Tax (AMT) for taxpayers earning more than 90% of the population, those individuals who earn more than $350,000 annually. Under this tax plan, Carina citizens in the AMT bracket would be exempt from paying taxes on the first $80,000 of their income and be taxed at a flat rate on the income thereafter. People paying the AMT would not be given allowances regular taxpayers are, such as deductions for children, healthcare expenses, or college tuition.Which of the following would be most important to determine in order to evaluate whether implementing the AMT plan would be profitable for the city of Carina?
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Magoosh
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2x + y years ago, Roberto was 3x + y years old. How many years old was Roberto x years ago?
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Magoosh
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The Aquipos toucan is able to use its long beak to reach inside apertures in a tree's bark and feed on the insects that dwell within and that are the toucan's main food source. Several noted ornithologists have speculated that because the toucan's beak is curved in a manner similar to the openings in the bark, the beak evolved so that the toucan can best take advantage of the insects lying deep inside. Which of the following, if true, argues most strongly against the ornithologists' speculation?
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Magoosh
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A study has recently shown that happier employees are more productive. Employees at Davis Industries are more productive over the course of the business day than those at Saturnine Corporation. Therefore, we can conclude that Davis Industries' employees must be happier than those at Saturnine Corp.The argument is most vulnerable to which of the following criticisms?
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Magoosh
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Playwright A is credited with being the first playwright to break the convention of having one character converse with a chorus, by casting two lead actors in a play. Yet, Playwright B, who was born several decades before Playwright A, also incorporates this theatrical device in two of his plays.Which of the following, if true, best helps to account for the inconsistency noted above?
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Magoosh
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If the average (arithmetic mean) of x, y and 15 is 9, and the average of x, 2y and 2 is 7, then y =
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Magoosh
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Walking at a constant rate of 8 kilometers per hour, Juan can cross a bridge in 6 minutes. What is the length of the bridge in meters? (1 kilometer = 1000 meters)
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Originally, scientists predicted small asteroids to be hard and rocky, as any loose surface material (called regolith) generated by impacts was expected to escape their weak gravity. Aggregate small bodies were not thought to exist, because the slightest sustained relative motion would cause them to separate. But observations and computer modeling are proving otherwise. Most asteroids larger than a kilometer are now believed to be composites of smaller pieces. Those imaged at high-resolution show evidence for copious regolith despite the weak gravity. Most of them have one or more extraordinarily large craters, some of which are wider than the mean ra dius of the whole body. Such colossal impacts would not just gouge out a crater—they would break any monolithic body into pieces. In short, asteroids larger than a kilometer across may look like nuggets of hard rock but are more likely to be aggregate assemblages—or even piles of loose rubble so pervasively fragmented that no solid bedrock is left. The rubble hypothesis, proposed decades ago by scientists, lacked evidence, until the planetologist Schumaker realized that the huge craters on the asteroid Mathilde and its very low density could only make sense together: a porous body such as a rubble pile can withstand a battering much better than an integral object. It will absorb and dissipate a large fraction of the energy of an impact; the far side might hardly feel a thing. At first, the rubble hypothesis may appear conceptually troublesome. The material strength of an asteroid is nearly zero, and the gravity is so low one is tempted to neglect that too. The truth is neither strength nor gravity can be ignored. Paltry though it may be, gravity binds a rubble pile together. And anybody who builds sandcastles knows that even loose debris can cohere. Oft-ignored details of motion begin to matter: sliding friction, chemical bonding, damping of kinetic energy, etc. We are just beginning to fathom the subtle interplay of these minuscule forces. The size of an asteroid should determine which force dominates. One indication is the observed pattern of asteroidal rotation rates. Some collisions cause an asteroid to spin faster; others slow it down. If asteroids are monolithic rocks undergoing random collisions, a graph of their rotation rates should show a bell-shaped distribution with a statistical “tail” of very fast rotators. If nearly all asteroids are rubble piles, however, this tail would be missing, because any rubble pile spinning faster than once every two or three hours fly apart. Recently, several astronomers discovered that all but five observed asteroids obey a strict rotation limit. The exceptions are all smaller than about 150 meters in diameter, with an abrupt cutoff for asteroids larger than 200 meters. The evident conclusion—that asteroids larger than 200 meters across are rubble piles—agrees with recent computer modeling of collisions. A collision can blast a large asteroid to bits, but those bits will usually be moving slower than their mutual escape velocity (the lowest velocity that a body must have in order to escape the orbit of a planet). Over several hours, gravity will reassemble all but the fastest pieces into a rubble pile.
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Magoosh
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Schumaker originally conceived of the rubble hypothesis because he surmised that
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Magoosh
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If $$72^{4}$$ is the greatest common divisor of positive integers A and B, and $$72^{6} $$is the least common multiple of A and B, then AB=
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