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OG19-定量推理
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In the xy-plane, point (r,s) lies on a circle with center at the origin. What is the value of $$r^{2} + s^{2}$$ ?
(1) The circle has radius 2.
(2) The point ($$\sqrt{2},-\sqrt{2}$$) lies on the circle.
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OG19-定量推理
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If r, s, and tare nonzero integers, is $$r^{5}s^{3}t^{4}$$ negative?
(1) rt is negative.
(2) s is negative.
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OG19-定量推理
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Each Type A machine fills 400 cans per minute, each Type B machine fills 600 cans per minute, and each Type C machine installs 2,400 lids per minute. A lid is installed on each can that is filled and on no can that is not filled. For a particular minute, what is the total number of machines working?
(1) A total of 4,800 cans are filled that minute.
(2) For that minute, there are 2 Type B machines working for every Type C machine working.
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OG19-定量推理
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If a and bare constants, what is the value of a?
(1) $$a< b$$
(2) $$(t- a)(t- b)= t^{2} + t-12$$, for all values oft.
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OG19-定量推理
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If x is a positive integer, is $$\sqrt{x}$$ an integer?
(1) $$\sqrt{4x}$$ is an integer.
(2) $$\sqrt{3x}$$ is not an integer.
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OG19-定量推理
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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
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OG19-定量推理
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If $$w + z = 28$$, what is the value of wz?
(1) wand z are positive integers.
(2) wand z are consecutive odd integers.
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OG19-定量推理
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If $$abc \neq 0$$, is $$\frac{\frac{a}{b}}{c}=\frac{a}{\frac{b}{c}}$$ ?
(1) $$a=1$$
(2) $$c= 1$$
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OG19-定量推理
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The arithmetic mean of a collection of 5 positive integers, not necessarily distinct, is 9. One additional positive integer is included in the collection and the arithmetic mean of the 6 integers is computed. Is the arithmetic mean of the 6 integers at least 10 ?
(1) The additional integer is at least 14.
(2) The additional integer is a multiple of 5.
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OG19-定量推理
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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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OG19-定量推理
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In a two-month survey of shoppers, each shopper bought one of two brands of detergent, X or Y, in the first month and again bought one of these brands in the second month. In the survey, 90 percent of the shoppers who bought Brand X in the first month bought Brand X again in the second month, while 60 percent of the shoppers who bought Brand Y in the first month bought Brand Y again in the second month. What percent of the shoppers bought Brand Y in the second month?
(1) In the first month, 50 percent of the shoppers bought Brand X.
(2) The total number of shoppers surveyed was 5,000.
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OG19-定量推理
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If m and n are positive integers, ism+ 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-定量推理
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What is the area of rectangular region R?
(1) Each diagonal of R has length 5.
(2) The perimeter of R is 14.
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OG19-定量推理
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How many integers n are there such that r < n < s?
(1) $$s - r = 5$$
(2) rand s are not integers.
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OG19-定量推理
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If the total price of n equally priced shares of a certain stock was $12,000, what was the price per share of the stock?
(1) If the price per share of the stock had been $1 more, the total price of the n shares would have been $300 more.
(2) If the price per share of the stock had been $2 less, the total price of the n shares would have been 5 percent less.
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OG19-定量推理
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If n is positive, is $$\sqrt{n}$$ > 100?
(1) $$\sqrt{(n-1)}$$> 99
(2) $$\sqrt{(n+1)}$$> 101
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OG19-定量推理
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Is xy> 5?
(1) $$1 \leq x \leq 3$$ and $$2 \leq y \leq 4$$.
(2) $$x+ y= 5$$
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OG19-定量推理
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In Year X, 8. 7 percent of the men in the labor force were unemployed in June compared with 8.4 percent in May. If the number of men in the labor force was the same for both months, how many men were unemployed in June of that year?
(1) In May of Year X, the number of unemployed men in the labor force was 3.36 million.
(2) In Year X, 120,000 more men in the labor force were unemployed in June than in May.
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OG19-定量推理
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If $$ x\neq 0$$, what is the value of $$(\frac{x^{p}}{x^{q}})^{4}$$?
(1) $$p = q$$
(2) $$x= 3$$
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OG19-定量推理
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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 began filling the order at 9:30 a.m.
(2) The machine had filled $$\frac{1}{2}$$ of the order by 5 10:30 a.m. and $$\frac{5}{6}$$ of the order by 11:10 a.m.
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