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OG19-数学分册
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Is the perimeter of square S greater than the perimeter of equilateral triangle T?
(1) The ratio of the length of a side of S to the length of a side of T is 4:5.
(2) The sum of the lengths of a side of S and a side of T is 18.
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OG19-数学分册
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If $$xy = -6$$, what is the value of $$xy(x + y)$$ ?
(1) $$x - y= 5$$
(2) $$xy^{2} = 18$$
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OG19-数学分册
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If $$x^{2} = 2^{x}$$, what is the value of x?
(1) $$2x= (\frac{x}{2})^{3}$$
(2) $$x = 2^{x-2}$$
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OG19-数学分册
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The sequence $$s_1$$, $$s_2$$, $$s_3$$, ... , $$s_n$$, ... is such that $$s_n= \frac{1}{n} -\frac{1}{n+1}$$ for all integers $$n\geq 1$$. If k is a positive integer, is the sum of the first k terms of the sequence greater than $$\frac{9}{10}$$?
(1) $$k>10$$
(2) $$k < 19$$
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OG19-数学分册
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In the sequence S of numbers, each term after the first two terms is the sum of the two immediately preceding terms. What is the 5th term of S?
(1) The 6th term of S minus the 4th term equals 5.
(2) The 6th term of S plus the 7th term equals 21.
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OG19-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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OG19-语文分册 OG20-语文分册
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Many office buildings designed to prevent outside air from entering have been shown to have elevated levels of various toxic substances circulating through the air inside, a phenomenon known as sick building syndrome. Yet the air in other office buildings does not have elevated levels of these substances, even though those buildings are the same age as the "sick" buildings and have similar designs and ventilation systems.
Which of the following, if true, most helps to explain why not all office buildings designed to preven't outside air from entering have air that contains elevated levels of toxic substances?
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OG19-语文分册 OG20-语文分册
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Premature babies who receive regular massages are more active than premature babies who do not. Even when all the babies drink the same amount of milk, the massaged babies gain more weight than do the unmassaged babies. This is puzzling because a more active person generally requires a greater food intake to maintain or gain weight.
Which of the following, if true, best reconciles the apparent discrepancy described above?
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OG19-语文分册 OG20-语文分册
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Which of the following, if true, most logically completes the politician's argument?
United States politician: Although the amount of United States goods shipped to Mexico doubled in the year after tariffs on trade between the two countries were reduced, it does not follow that the reduction in tariffs caused the sales of United States goods to companies and consumers in Mexico to double that year, because ___
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OG19-语文分册 OG20-语文分册
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While the total enrollment of public elementary and secondary schools in Sondland is one percent higher this academic year than last academic year, the number of teachers there increased by three percent. Thus, the Sondland Education Commission's prediction of a teacher shortage as early as next academic year is unfounded.
Which of the following, if true, most seriously weakens the claim that the prediction of a teacher shortage as early as next academic year is unfounded?
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OG19-语文分册 OG20-语文分册
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Art restorers who have been studying the factors that cause Renaissance oil paintings to deteriorate physically when subject to climatic changes have found that the oil paint used in these paintings actually adjusts to these changes well. The restorers therefore hypothesize that it is a layer of material called gesso, which is under the paint, that causes the deterioration.
Which of the following, if true, most strongly supports the restorers' hypothesis?
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OG19-语文分册 OG20-语文分册
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Rats injected with morphine exhibit decreased activity of the immune system, the bodily system that fights off infections. These same rats exhibited heightened blood levels of corticosteroids, chemicals secreted by the adrenal glands. Since corticosteroids can interfere with immune-system activity, scientists hypothesized that the way morphine reduces immune responses in rats is by stimulating the adrenal glands to secrete additional corticosteroids into the bloodstream.
Which of the following experiments would yield the most useful results for evaluating the scientists' hypothesis?
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OG19-语文分册
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It can be inferred from the passage that the author would be most likely to agree with which of the following statements about corporate acquisitions?
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OG19-数学分册
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If S is a set of four numbers w, x, y, and z, is the range of the numbers in S greater than 2 ?
(1) $$w-z>2$$
(2) z is the least number in S.
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OG19-数学分册
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If a, b, and c are consecutive integers and 0 < a < b < c, is the product abc a multiple of 8 ?
(1) The product ac is even.
(2) The product be is a multiple of 4.
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OG19-数学分册
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Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other's point of departure. The two trains passed each other after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?
(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
(2) Train Q averaged a speed of 55 miles per hour for the entire trip.
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OG19-数学分册
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Last week Jack worked 70 hours and earned $1,260.
If he earned his regular hourly wage for the first
40 hours worked, $$1\frac{1}{2}$$ times his regular hourly wage
for the next 20 hours worked, and 2 times his regular
hourly wage for the remaining 10 hours worked, what
was his regular hourly wage?
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OG19-数学分册
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If a and bare positive integers and$$(2^{a})^{b}=2^{3}$$, what is .
the value of $$2^{a}2^{b}$$ ?
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OG19-数学分册
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$$\frac{1}{3- \frac{1}{3- \frac{1}{3-1}}}$$=
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OG19-数学分册
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Stephanie has 2$$\frac{1}{4}$$ cups of milk on hand and makes
2 batches of cookies, using $$\frac{2}{3}$$ cup of milk for each
batch of cookies. Which of the following describes the
amount of milk remaining after she makes the cookies?
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