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OG19-数学分册
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A total of 20 amounts are entered on a spreadsheet that has 5 rows and 4 columns; each of the 20 positions in the spreadsheet contains one amount. The average (arithmetic mean) of the amounts in row i is $$R_i$$ ($$1 \leq i \leq 5$$). The average of the amounts in column j is $$C_j$$ ($$ 1\leq j \leq 4$$). What is the average of all 20 amounts on the spreadsheet?
(1) $$R_1 + R_2 + R_3 + R_4 + R_5 = 550$$
(2) $$C_1 + C_2 +.C_3 + C_4 = 440$$
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OG19-数学分册
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If a, b, c, and dare numbers on the number line shown and if the tick marks are equally spaced, what is the value of a + c ?
(1) $$a+b=-8$$
(2) $$a+ d= 0$$
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OG19-数学分册
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What is the probability that Lee will make exactly 5 errors on a certain typing test?
(1) The probability that Lee will make 5 or more errors on the test is 0.27.
(2) The probability that Lee will make 5 or fewer errors on the test is 0.85.
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OG19-数学分册
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If pis a positive integer, is $$2^{p} + 1$$ a prime number?
(1) p is a prime number.
(2) p is an even number.
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OG19-数学分册
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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-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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OG19-数学分册
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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-数学分册
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What is the number of 360-degree rotations that a bicycle wheel made while rolling 100 meters in a straight line without slipping?
(1) The diameter of the bicycle wheel, including the tire, was 0.5 meter.
(2) The wheel made twenty 360-degree rotations per minute.
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OG19-数学分册
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In the equation $$x^{2} +bx+ 12 = 0$$, xis 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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OG19-数学分册
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In the figure above, line segment OP has slope $$\frac{1}{2}$$ and line segment PQ has slope 2. What is the slope of line segment OQ?
(1) Line segment OP has length $$2\sqrt{5}$$.
(2) The coordinates of point Q are (5,4).
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OG19-数学分册
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In △XYZ, what is the length of YZ?
(1) The length of XY is 3.
(2) The length of XZ is 5.
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OG19-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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OG19-数学分册
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What is the value of xy?
(1) $$x+y=10$$
(2) $$x-y= 6$$
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OG19-数学分册
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Michael arranged all his books in a bookcase with 10 books on each shelf and no books left over. After Michael acquired 10 additional books, he arranged all his books in a new bookcase with 12 books on each shelf and no books left over. How many books did Michael have before he acquired the 10 additional books?
(1) Before Michael acquired the 10 additional books, he had fewer than 96 books.
(2) Before Michael acquired the 10 additional books, he had more than 24 books.
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OG19-数学分册
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If xy> 0, does $$(x- 1)(y-1) = 1$$?
(1) $$x + x= xy$$
(2) $$x=y$$
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OG19-数学分册
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If $$x + y + z > 0$$, is $$z > 1$$ ?
(1) $$z>x+y+1$$
(2) $$x + y+ 1 < 0$$
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OG19-数学分册
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The circular base of an above-ground swimming pool lies in a level yard and just touches two straight sides of a fence at points A and 8, as shown in the figure above. Point C is on the ground where the two sides of the fence meet. How far from the center of the pool's base is point A ?
(1) The base has area 250 square feet.
(2) The center of the base is 20 feet from point C.
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OG19-数学分册
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[y] denotes the greatest integer less than or equal toy. Is d < 1 ?
(1) $$d=y-[y]$$
(2) $$[d] = 0$$
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OG19-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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OG19-数学分册
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What is the value of $$x^{2} - y^{2}$$ ?
(1 ) $$(x-y)^{2} = 9$$
(2) $$x+ y=6$$
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