|
PREP07 Test 2
|
If k and t are integers and $$k^2 - t^2$$ is an odd integer, which of the following must be
an even integer?I. k+t+2II. $$k^2+2kt+t^2$$III. $$k^2+t^2$$
|
|
PREP07 Test 1
|
In the sequence of positive numbers $$x_1,x_2,x_3$$,. . ., what is the value of $$x_1$$ ?(1) $$x_l =\frac1 2 {x_{l-1}} $$ for all integers $$l > 1$$(2)$$x_5 = {x_4\over(x_4+1)}$$
|
|
PREP07 Test 1
|
If x is an integer, is $$(x^2 + 1)(x + 5)$$ an even number?(1) x is an odd number.(2) Each prime factor of $$x^2$$ is greater than 7.
|
|
PREP07 Test 1
|
Are x and y both positive?(1) 2x – 2y = 1(2) $$\frac{x}{y}>1$$
|
|
PREP07 Test 1
|
If p is a positive integer, what is the value of p ?(1) p/4 is a prime number.(2) p is divisible by 3.
|
|
PREP07 Test 1
|
Is y < 2x ?(1) $${y\over4} < \frac{x}{2}$$(2) $${(y-2x)\over3 }<0$$
|
|
PREP07 Test 2
|
If n is an integer, is n/7 an integer?(1) (3n)/7 is an integer(2) (5n)/7 is an integer.
|
|
PREP07 Test 2
|
If a > 0, b > 0, and c > 0, is a(b - c) = 0 ?(1) b – c = c - b(2)$$\frac{b}{c}=\frac{c}{b}$$
|
|
PREP07 Test 2
|
In the fraction x/y, where x and y are positive integers, what is the value of y ?(1) The least common denominator of $$\frac{x}{y}and \frac{1}{3} is 6$$.(2) x = 1.
|
|
Manhattan
|
A baseball card decreased in value 20% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?
|
|
|
The single-celled parasite known as Toxoplasma gondii infects more than half of the world's human population without creating any noticeable symptoms. Once inside the human body, Toxoplasma rapidly spreads to the heart and other organs. It can even penetrate the tight barrier that normally protects the brain from most pathogens. Yet, the blood of infected persons carries very few free-floating Toxoplasma cells. Scientists have long been puzzled by this ability of Toxoplasma to parasitize the human body without triggering an immune response and without an appreciable presence in the bloodstream. Recent research, however, has shed light on the ways in which Toxoplasma achieves its remarkable infiltration of the human body.Though there are few individual Toxoplasma cells coursing freely in the blood of an infected person, scientists have discovered that the parasite is quite common in certain cells, known as dendritic cells, involved in the human immune system. Dendritic cells are found in the digestive tract and frequently come into contact with the various pathogens that enter the human body through food and water. When the dendritic cells encounter pathogens, they travel to lymph nodes and relay this information to other immune cells that then take action against the reported pathogen. Scientists have found, however, that Toxoplasma is capable of hijacking dendritic cells, forcing them from their usual activity and using them as a form of transportation to infect the human body quickly. Without this transport mechanism, Toxoplasma could not reach the better-protected areas of the body.Toxoplasma invades the human body through consumption of the undercooked meat of infected animals, primarily pigs and chickens. Other animals, such as cats, can become infected as well. In fact, cats are a necessary component in the reproductive cycle of Toxoplasma, since the animal's intestines are the parasite's sole breeding ground. Toxoplasma creates egg-like cysts, known as oocysts, in the cats' intestines. These oocysts are shed in the cats' droppings and contaminate ground water and soil, eventually finding their way into the food chain. Because Toxoplasma must somehow find its way into a new host cat in order to reproduce, it cannot kill its current host. Instead, it waits for the host, usually a small rodent, to be eaten by a cat, thus providing Toxoplasma the opportunity to reproduce.
|
|
Manhattan
|
120% of $$\frac{5}{8} =$$
|
|
Manhattan
|
The author mentions "pigs and chickens" in the final paragraph in order to
|
|
Manhattan
|
Which of the following is the most likely outcome for Toxoplasma cells that invade the human body?
|
|
Manhattan
|
If Bob, working alone, can paint a certain room in 3 hours, how long does it take Bob and Richard working together to paint the room? (1) Richard, working alone, can paint the room in 2 hours.(2) Richard paints at a constant rate that is 50% greater than the rate at which Bob paints.
|
|
Manhattan
|
The portion of the interest earned on the state university's endowment that is set aside to fund merit scholarships for outstanding high school seniors is more numerous than that set aside to fund the university's high-powered athletic program.
|
|
Manhattan
|
If |a| = |b|, which of the following must be true? I. a = b II. |a| = -b III. -a = -b
|
|
Manhattan
|
Industry Analyst: This summer is expected to be particularly hot and dry in the major orange-growing regions of Florida, the state accounting for the largest share of orange production in the United States. While hot and dry weather usually leads to a substantial drop in the yield of oranges, my projections indicate that the revenues of Florida orange producers will not be substantially affected by these unfavorable conditions.Which of the following statements, if true, would support the claim of the Industry Analyst?
|
|
Manhattan
|
What is the value of y? (1) 2 x + 2 y = 14 (2) 2 y + 2 z = 14
|
|
|
Before the age of space exploration, astronomers assumed that the Moon's core was smaller than the Earth's, in both relative and absolute terms – the radius of the Earth's core is 55 percent of the overall radius of the Earth and the core's mass is 32 percent of the Earth's overall mass – but they had no way to verify this. Two sets of data gathered by Lunar Prospector have now given astronomers the ability to determine that the Moon's core accounts for 20 percent of the Moon's radius and for a mere 2 percent of its overall mass.First, scientists measured minute, relatively rapid variations in the wavelength of radio signals from Lunar Prospector as the craft moved towards or away from the Earth. Using these variations, scientists accurately determined even slight changes in the craft's velocity while the craft orbited the Moon, changes resulting from inconsistency in the gravitational pull of the Moon on the craft. The data were used to create a [hl:1]"gravity map"[/hl:1] of both near and far sides of the Moon, highlighting new details of the distribution of the Moon's internal mass. Scientists thus determined that the Moon has a small, metallic core, which, if composed mostly of iron, has a radius of approximately 350 kilometers. The second method involved examining the faint magnetic field generated within the Moon itself by the Moon's monthly passage through the tail of the Earth's magnetosphere. This approach confirmed the results obtained through examination of the gravity map.
The size and composition of the Moon's core have serious implications for our understanding of the Moon's origins. If the Moon and Earth developed as distinct entities, the sizes of their cores should be more comparable. In actuality, it seems that the Moon was once part of the Earth and broke away at an early stage in the Earth's evolution, perhaps due to a major asteroid impact that could have loosened a chunk of iron, allowing it to form the core around which the Moon eventually coalesced. Alternatively, according to fission theory, the early Earth may have spun so rapidly that it ejected a quantity of material by [hl:2]so-called[/hl:2] centrifugal force, material that later coalesced by mutual gravitational attraction into the Moon.
|