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OG18-数学分册
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A triangle has side lengths of a, b, and c centimeters. Does each angle in the triangle measure less than 90 degrees?(1) The 3 semicircles whose diameters are the sides of the triangle have areas that are equal to 3 $$cm^{2}$$, 4$$cm^{2}$$, and 6 $$cm^{2}$$, respectively.(2) c < a + b < c + 2
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OG18-数学分册
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A certain list consists of 400 different numbers. Is the average (arithmetic mean) of the numbers in the list greater than the median of the numbers in the list?(1) Of the numbers in the list, 280 are less than the average.(2) Of the numbers in the list, 30 percent are greater than or equal to the average.
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OG18-数学分册
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[y] denotes the greatest integer less than or equal to y. Is d < 1?(1) d = y - [y](2) [d] = 0
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OG18-数学分册
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K is a set of numbers such that (i) if x is in K, then -x is in K,and (ii) if each of x and y is in K, then xy is in K.Is 12 in K?(1) 2 is in K.(2) 3 is in K.
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OG18-数学分册
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In the equation $$x^{2} + bx + 12 = 0$$, x is a variable and b is a constant. What is the value of b?(1) x - 3 is a factor of $$x^{2} + bx +12.$$(2) 4 is a root of the equation $$x^{2} + bx + 12 = 0$$.
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OG18-数学分册
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M and N are integers such that 6 < M < N. What is the value of N?(1) The greatest common divisor of M and N is 6.(2) The least common multiple of M and N is 36.
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OG18-数学分册
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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.
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OG18-数学分册
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If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?(1) The range of the n integers is 14.(2) The greatest of the n integers is 17.
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OG18-数学分册
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 In the xy-plane shown, the shaded region consists of all points that lie above the graph of $$y = x^{2} - 4x$$ and below the x- axis. Does the point (a,b) (not show ) lie in the shaded region if b < 0?(1) 0 < a < 4(2) $$a^{2} - 4a < b$$
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OG18-数学分册
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On monday morning a certain machine ran continuously at a uniform rate to fill a production order.At what time did it completely fill the order that morning?(1) The machine bagan filling the order at 9:30 a.m.(2) The machine had filled $$\frac{1}{2} $$ of the order by 10:30 a.m. and $$\frac{5}{6} $$ of the order by 11:10 a.m.
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OG18-数学分册
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A small school has three foreign language classes, one in French, one in Spanish, and one in German. How many of the 34 students enrolled in the Spanish class are also enrolled in the French class?(1) There are 27 students enrolled in the French class, and 49 students enrolled in either the French class, the Spanish class, or both of these classes.(2) One - half of the students enrolled in the Spanish class are enrolled in more than one foreign language class.
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OG18-数学分册
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If N is a positive odd integer, is N prime?(1) $$N = 2^{k} + 1$$ for some positive integer k.(2) N + 2 and N + 4 are both prime.
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OG18-数学分册
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If m and n are positive integers, is m+n divisible by 4?(1) m and n are each divisible by 2.(2) Neither m nor n is divisible by 4.
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OG19-数学分册
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If a and b are positive integers, is $$\sqrt[3]{ab}$$ an integer?(1) $$\sqrt{a}$$ is an integer.(2) $$b = \sqrt{a}$$
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OG18-数学分册
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If p, q, x, y,and z are different positive integers, which of the five integers is the median?(1) p + x < q(2) y < z
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OG18-语文分册
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Commemorative plaques cast from brass are a characteristic art form of the Benin culture of West Africa. Some scholars, noting that the oldest surviving plaques date to the 1400s, hypothesize that brass-casting techniques were introduced by the Portuguese, who came to Benin in 1485 A.D. But Portuguese records of that expedition mention cast-brass jewelry sent to Benin's king from neighboring Ife. So it is unlikely that Benin's knowledge of brass casting derived from the Portuguese.Which of the following, if true, most strengthens the argument?
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OG18-语文分册
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Many gardeners believe that the variety of clematis vine that is most popular among gardeners in North America is jackmanii. This belief is apparently correct since, of the one million clematis plants sold per year by the largest clematis nursery in North America, ten percent are jackmanii.Which of the following is an assumption on which the argument depends?
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OG18-语文分册
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Jay: Of course there are many good reasons to support the expansion of preventive medical care, but arguments claiming that it will lead to greater societal economic gains are misguided. Some of the greatest societal expenses arise from frequent urgent-care needs for people who have attained a long life due to preventive care.
Sunil: Your argument fails because you neglect economic gains outside the health care system: society suffers an economic loss when any of its productive members suffer preventable illnesses. Sunil's response to Jay makes which of the following assumptions?
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OG18-语文分册
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Typically during thunderstorms most lightning strikes carry a negative electric charge; only a few carry a positive charge. Thunderstorms with unusually high proportions of positive-charge strikes tend to occur in smoky areas near forest fires. The fact that smoke carries positively charged smoke particles into the air above a fire suggests the hypothesis that the extra positive strikes occur because of the presence of such particles in the storm clouds. Which of the following, if discovered to be true, most seriously undermines the hypothesis?
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OG18-语文分册
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Music critic: Fewer and fewer musicians are studying classical music, decreasing the likelihood that those with real aptitude for such music will be performing it. Audiences who hear these performances will not appreciate classical music's greatness and will thus decamp to other genres. So to maintain classical music's current meager popularity, we must encourage more young musicians to enter the field. Which of the following, if true, most weakens the music critic's reasoning?
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