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OG18-数学分册
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If p and q are positive, is $$\frac{q}{p}$$less than 1?(1) p is less than 4.(2) q is less than 4.
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OG18-数学分册
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 In the quilting pattern shown above, a small square has its vertices on the side of a larger square. What is the side length, in centimeters, of the larger square?(1) The side length iof the smaller square is 10 cm.(2) Each vertex of the small square cuts 1 side of the larger into 2 segments with length in the ratio of 1 : 2.
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OG18-数学分册
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 In the rectangular coordinate system above, if $$\bigtriangleup$$ OPQ and $$\bigtriangleup$$ QRS have equal area, what are the coorddinates of point R?(1) The coordinates of point P are (0,12).(2) OP = OQ and QS = RS.
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OG18-数学分册
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What is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out? (Two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal.)
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OG18-数学分册
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One inlet pipe fills an empty tank in 5 hours. A second inlet pipe fills the same tank in 3 hours. If both pipes are used together, how long will it take to fill $$\frac{2}{3}$$of the tank?
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OG18-数学分册
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If x and y are integers such that $$2 < x \le 8$$ and $$2 < y \le 9$$, what is the maximum value of $$\frac{1}{x} - \frac{x}{y}$$?
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OG18-数学分册
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Company K's earnings were $12 million last year. If this year's earnings are projected to be 150 percent greater than last year's earnings, what are Company K's projected earnings this year?
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OG18-数学分册
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Items that are purchased together at a certain discount store are priced at $3 for the first item purchased and $1 for each additional item purchased. What is the maximum number of items that could be purchased together for a total price that is less than $30 ?
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OG18-数学分册
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Andrew started saving at the beginning of the year and had saved $240 by the end of the year. He continued to save and by the end of 2 years had saved a total of $540. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year?
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OG18-数学分册
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Machines A and B always operate independently and at their respective constant rates. When working alone, Machine A can fill a production lot in 5 hours, and Machine B can fill the same lot in x hours. When the two machines operate simultaneously to fill the production lot, it takes them 2 hours to complete the job. What is the value of x ?
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When asteroids collide, some collisions cause an asteroid to spin faster; others slow it down. If asteroids are all monoliths-single rocks-undergoing random collisions, a graph of their rotation rates should show a bell-shaped distribution with statistical "tails" of very fast and very slow rotators. If asteroids are rubble piles, however, the tail representing the very fast rotators would be missing, because any loose aggregate spinning faster than once every few hours (depending on the asteroid`s bulk density) would fly apart. Researchers have discovered that [line:12]all but five observed asteroids obey a strict limit on[/line:12] rate of rotation. The exceptions are all smaller than 200 meters in diameter, with an abrupt cutoff for asteroids larger than that.The evident conclusion-[line:16][hl:2]that asteroids larger than 200 meters across are multicomponent structures or rubble piles[/hl:2][/line:16]-agrees with recent computer modeling of collisions, which also finds a transition at that diameter. A collision can blast a large asteroid to bits, but after the collision those bits will usually move slower than their mutual [line:22][hl:4]escape velocity[/hl:4][/line:22]. Over several hours, gravity will reassemble all but the fastest pieces into a rubble pile. Because collisions among asteroids are relatively frequent, most large bodies have already suffered this fate. Conversely, most small asteroids should be monolithic, because impact fragments easily escape their feeble gravity.
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OG18 OG19 OG20 OG2022
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[line:12:enable]The passage implies which of the following about the five asteroids mentioned in line 12 ?
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Manhattan
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John was 27 years old when he married Betty. They just celebrated their fifth wedding anniversary, and Betty's age is now $$\frac{7}{8}$$ of John's. How old is Betty?
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Manhattan
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If $$x^{2} – 4x = 5$$, then one possible value of x – 4 =
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Manhattan
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In the figure to the right, what is the value of x?Note: Not drawn to scale.
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Manhattan
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Machine A, working alone at a constant rate, can complete a certain production lot in x hours. Machine B, working alone at a constant rate, can complete 1/5 of the same production lot in y hours. Machines A and B, working together, can complete$$ \frac{1}{2}$$ of the same production lot in z hours. What is the value of y in terms of x and z?
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Manhattan
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 Two circles share a center at point C, as shown to the right. Segment AC is broken up into two shorter segments, AB and BC, with dimensions shown. What is the ratio of the area of the large circle to the area of the small circle ?
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Manhattan
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If a, b, c, and d are integers and$$ ab^{2}c^{3}d^{4} > 0$$, which of the following must be positive? I. $$a^{2}cd $$II. $$bc^{4}d $$III.$$ a^{3}c^{3}d^{2} $$
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Manhattan
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When a is divided by b, the quotient is c and the remainder is d. Which of the following expressions is equal to d?
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Manhattan
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What is the minimal value of function f(x)?(1) $$f(0) = 16$$(2) $$f(x) = (x – 4)^2$$
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