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OG19-数学分册
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In the sequence $$x_0$$, $$x_1$$, $$x_2$$, ... , $$x_n$$, each term from $$x_1$$ to $$x_k$$ is 3 greater than the previous term, and each term from $$x_k+1$$ to $$x_n$$ is 3 less than the previous term, where n and k are positive integers and k < n. If $$x_0 = x_{n} = 0 $$ and if $$x_{k} = 15$$ , what is the value of n?
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OG19-数学分册
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Two numbers differ by 2 and sum to S. Which of the following is the greater of the numbers in terms of S ?
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OG19-数学分册
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The figure shown above consists of three identical circles that are tangent to each other. If the area of the shaded region is $$64\sqrt{3} - 32\pi$$, what is the radius of each circle?
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OG19-数学分册
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The infinite sequence $$a_1$$, $$a_2$$, ... , $$a_n$$, ... is such that $$a_1 = 2$$, $$a_2 = -3$$, $$a_3 = 5$$, $$a_4 = -1$$, and $$a_n = a_{n-4}$$ for n > 4. What is the sum of the first 97 terms of the sequence?
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OG19-数学分册
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The sequence $$a_1$$, $$a_2$$, ... $$a_n$$, ... is such that $$a_n= 2a_{n-1} - x$$ for all positive integers $$ n\geq 2$$ and for a certain number x. If $$a_5 = 99$$ and $$a_3 = 27$$, what is the value of x?
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OG19-数学分册
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In a certain medical survey, 45 percent of the people surveyed had the type A antigen in their blood and 3 percent had both the type A antigen and the type B antigen. Which of the following is closest to the percent of those with the type A antigen who also had the type B antigen?
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OG19-语文分册 OG20-语文分册
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Meat from chickens contaminated with salmonella bacteria can cause serious food poisoning. Capsaicin, the chemical that gives chili peppers their hot flavor, has antibacterial properties. Chickens do not have taste receptors for capsaicin and will readily eat feed laced with capsaicin. When chickens were fed such feed and then exposed to salmonella bacteria, relatively few of them became contaminated with salmonella.
In deciding whether the feed would be useful in raising salmonella-free chicken for retail sale, it would be most helpful to determine which of the following?
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OG19-语文分册 OG20-语文分册
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Which of the following most logically completes the passage?
Leaf beetles damage willow trees by stripping away their leaves, but a combination of parasites and predators generally keeps populations of these beetles in check. Researchers have found that severe air pollution results in reduced predator populations. The parasites, by contrast, are not adversely affected by pollution; nevertheless, the researchers' discovery probably does explain why leaf beetles cause particularly severe damage to willows in areas with severe air pollution, since ___
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OG19-语文分册 OG20-语文分册
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Most banks that issue credit cards charge interest rates on credit card debt that are ten percentage points higher than the rates those banks charge for ordinary consumer loans. These banks' representatives claim the difference is fully justified, since it simply covers the difference between the costs to these banks associated with credit card debt and those associated with consumer loans.
Which of the following, if true, most seriously calls into question the reasoning offered by the banks' representatives?
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OG19-语文分册 OG20-语文分册
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Often patients with ankle fractures that are stable, and thus do not require surgery, are given follow-up x-rays because their orthopedists are concerned about possibly having misjudged the stability of the fracture. When a number of follow-up x-rays were reviewed, however, all the fractures that had initially been judged stable were found to have healed correctly. Therefore, it is a waste of money to order follow-up x-rays of ankle fractures initially judged stable.
Which of the following, if true, most strengthens the argument?
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OG19-语文分册 OG20-语文分册
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The chemical adenosine is released by brain cells when those cells are active. Adenosine then binds to more and more sites on cells in certain areas of the brain, as the total amount released gradually increases during wakefulness. During sleep, the number of sites to which adenosine is bound decreases. Some researchers have hypothesized that it is the cumulative binding of adenosine to a large number of sites that causes the onset of sleep.
Which of the following, if true, provides the most support for the researchers' hypothesis?
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OG19-语文分册 OG20-语文分册
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Most scholars agree that King Alfred (A.D. 849-899) personally translated a number of Latin texts into Old English. One historian contends that Alfred also personally penned his own law code, arguing that the numerous differences between the language of the law code and Alfred's translations of Latin texts are outweighed by the even more numerous similarities. Linguistic similarities, however, are what one expects in texts from the same language, the same time, and the same region. Apart from Alfred's surviving translations and law code, there are only two other extant works from the same dialect and milieu, so it is risky to assume here that linguistic similarities point to common authorship.
The passage above proceeds by
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OG19-语文分册
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The primary purpose of the passage is to
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OG19-语文分册
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The author of the passage mentions the effect of acquisitions on national economies most probably in (8l Most such acquisitions produced only order to
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OG19-语文分册
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According to the passage, during the 1970's and 1980's bidding firms differed from the firms for which they bid in that bidding firms
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OG19-语文分册 OG20-语文分册
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In the first paragraph, the author of the passage
mentions a contention that would be made by an
anthropologist most likely in order to
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OG19-语文分册 OG20-语文分册
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The passage suggests that the historians referred to in
line 1 make which of the following assumptions about
Renaissance Europe?
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OG19-语文分册 OG20-语文分册
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The author mentions the fact that baryons are the
source of stars' luminosity primarily in order to explain
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OG19-语文分册 OG20-语文分册
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The passage suggests that bank managers failed
to consider whether or not the service improvement
mentioned in lines 18-20
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Antonia Castaneda has utilized scholarship from
women's studies and Mexican-American history to
examine nineteenth-century literary portrayals of
Mexican women. As Castaneda notes, scholars of
women's history observe that in the United States,
male novelists of the period-during which, according
to these scholars, women's traditional economic role
in home-based agriculture was threatened by the
transition to a factory-based industrial economy-
define women solely in their domestic roles of wife and
mother. Castaneda finds that during the same period
that saw non-Hispanic women being economically
displaced by industrialization, Hispanic law in territorial
California protected the economic position of
"Californianas'' (the Mexican women of the territory) by
ensuring them property rights and inheritance rights
equal to those of males.
For Castaneda, the laws explain a stereotypical
plot created primarily by male, non-Hispanic novelists:
the story of an ambitious non-Hispanic merchant or
trader desirous of marrying an elite Californiana.
These novels' favorable portrayal of such women
is noteworthy, since Mexican-American historians
have concluded that unflattering literary depictions
of Mexicans were vital in rallying the United States
public's support for the Mexican-American War
(1846-1848). The importance of economic alliances
forged through marriages with Californianas explains
this apparent contradiction. Because of their real-
life economic significance, the Californianas were
portrayed more favorably than were others of the
same nationality.
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