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OG19-数学分册
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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-数学分册
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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-数学分册
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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-数学分册
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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-数学分册
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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-数学分册
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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-数学分册
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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-数学分册
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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-数学分册
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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-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 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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OG19-数学分册
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If a and b are positive integers, what is the value of the product ab?
(1) The least common multiple of a and b is 48.
(2) The greatest common factor of a and b is 4.
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OG19-数学分册
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If $$x^{2} + y^{2} = 29$$, what is the value of $$(x-y)^{2}$$ ?
(1) $$xy= 10$$
(2) $$x= 5$$
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OG19-数学分册
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After winning 50 percent of the first 20 games it played, Team A won all of the remaining games it played. What was the total number of games that Team A won?
(1) Team A played 25 games altogether.
(2) Team A won 60 percent of all the games it played.
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OG19-数学分册
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Is x between 0 and 1 ?
(1) $$x^{2}$$ is less than x.
(2) $$x^{3}$$ is positive.
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OG19-数学分册
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Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year?
(1) Last year 12 of the 30 businesses reported a net profit and had investments in foreign markets.
(2) Last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.
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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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