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    GRE-练习十六及答案解析.doc

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    GRE-练习十六及答案解析.doc

    1、GRE-练习十六及答案解析(总分:100.00,做题时间:90 分钟)一、单项选择题(总题数:35,分数:35.00)1.If the perimeter of a triangle is 18,then the length of one of the sides CANNOT beA. 1 B. 3 C. 6D. 8 E. 9(分数:1.00)A.B.C.D.E.2.What is the ratio of the perimeter of a pentagon with each side of length 6 to the perimeter of an octagon with e

    2、ach side of length 6?(分数:1.00)A.B.C.D.E.3.If corresponding sides of AABC andABC above are proportional, what is y in terms of x?(分数:1.00)A.B.C.D.E.4.What fraction of a cubic meter is the volume of a cubic block Of stone with edge of length 10 centimeters?(1 meter=100centimeters)(分数:1.00)A.B.C.D.E.5.

    3、In the coordinate plane,points A and B are endpoints of a diameter of a circle with center(-2,1)If the coordinates of A are(-5,5),what are the coordinates of B?A. (0,0) B. (3,-2)C. (3,-1) D. (2,-2)E. (1,-3)(分数:1.00)A.B.C.D.E.6. (分数:1.00)A.B.C.D.E.7.In square PQRS aboveT is the midpoint of side RSIf

    4、PT= ,What is the length of a side of the square?(分数:1.00)A.B.C.D.E.8.If a solid pyramid has 4 vertices and4 faces,how many edges does the pyramid have?A. 2B. 3C. 4D. 6E. 8(分数:1.00)A.B.C.D.E.9. (分数:1.00)A.B.C.D.E.10.The rectangular solid above is made up of eight cubes of the same size,each of which

    5、has exactly one face painted blue What is the greatest fraction of the total surface area of the solid that could be blue?(分数:1.00)A.B.C.D.E.11.The dimensions,in centimeters,of rectangular box R are 6 by 8 by 10Which of the following CANNOT be the total surface area,in square centimeters,of two face

    6、s of R?A. 96B. 120C. 128D. 160E. 180(分数:1.00)A.B.C.D.E.12. (分数:1.00)A.B.C.D.E.13. (分数:1.00)A.B.C.D.E.14.A rectangular rug covers half of a rectangular floor that is 9 feet wide and 12feet longIf the dimensions of the rug are in the same ratio as those of the floor,how many feet long is the rug?(分数:1

    7、.00)A.B.C.D.E.15. (分数:1.00)A.B.C.D.E.16. (分数:1.00)A.B.C.D.E.17.What is the maximum number of nonover-lapping regions into which 3 lines can divide the interior of a circle?A. 4B. 6C. 7D. 8E. 9(分数:1.00)A.B.C.D.E.18. (分数:1.00)A.B.C.D.E.19.What is the area of the hexagonal region shown in the figure ab

    8、ove?(分数:1.00)A.B.C.D.E.20.In the figure above,O and P are the centers of two circlesIf each circle has radius r,what is the area of the shaded region?(分数:1.00)A.B.C.D.E.21. (分数:1.00)A.B.C.D.E.22.A certain rectangle has perimeter 54If the ratio of the length of the rectangle to the width is 5 to 4,wh

    9、at is the length of the rectangle?A. 30 B. 27 C. 24D. 18 E. 15(分数:1.00)A.B.C.D.E.23.In the figure above,what is the length of AB?(分数:1.00)A.B.C.D.E.24.If the areas of three of the faces of a rectangular solid are 6,10 and 15,what is the volume of the solid?A. 30B. 90C. 150D. 300E. 450(分数:1.00)A.B.C.

    10、D.E.25.In the figure above,if the area of the inscribed rectangular region is 32,then the circumference of the circle is(分数:1.00)A.B.C.D.E.26.In the rectangular coordinate system above,if P,not shown,is a point on AB and if the x-coordinate of P is 1,what is the y-coordinate of P?(分数:1.00)A.B.C.D.E.

    11、27. (分数:1.00)A.B.C.D.E.28.If B is the midpoint of line segment AD and C is the midpoint of line segment BD,what is the value of (分数:1.00)A.B.C.D.E.29. (分数:1.00)A.B.C.D.E.30. (分数:1.00)A.B.C.D.E.31.The figure above shows the lengths of thesides of an equiangular polygonWhat is the area of the polygon?

    12、A. 7 B. 8 C. 9 D. (分数:1.00)A.B.C.D.E.32.Three solid cubes of lead,each with edges10 centimeters long,are melted together in a level,rectangular shaped panThe base of the pan has inside dimensions of 20centimeters by 30 centimeters,and the pan is 15 centimeters deepIf the volume of the solid lead is

    13、approximately the same as thev olume of tile melted lead,approximately how many centimeters deep is the melted lead in the pan?A. 2.5 B. 3 C. 5D. 7.5 E. 9(分数:1.00)A.B.C.D.E.33.A rectangular tabletop consists of a piece of laminated wood bordered by a thin metals trip along its four edgesThe surface

    14、area of the tabletop is x square feet,and the total length of the strip before it was attached was x feetIf the tabletop is 3 feet wide,what is its approximate length,in feet?A. 12 B. 10 C. 9D. 8 E. 6(分数:1.00)A.B.C.D.E.34. (分数:1.00)A.B.C.D.E.35. (分数:1.00)A.B.C.D.E.二、比较题(总题数:65,分数:65.00)36. (分数:1.00)

    15、A.B.C.D.37.The altitude of a certain triangular sail is 2meters greater in length than its baseThe area of the face of the sail is 24 square meters(分数:1.00)A.B.C.D.38. (分数:1.00)A.B.C.D.39.The boundaries of regions X and y are parallelograms(分数:1.00)A.B.C.D.40. (分数:1.00)A.B.C.D.41.Points PR,and T lie

    16、 on a straight lineThe distance from P to R is 21and the distance from P to T is 9The distance(分数:1.00)A.B.C.D.42. (分数:1.00)A.B.C.D.43.The circles above,with centers O and P,each have radius r(分数:1.00)A.B.C.D.44. (分数:1.00)A.B.C.D.45.The areas of the two shaded regions of the circle are equal(分数:1.00

    17、)A.B.C.D.46.The circumference 0f a rectangle is 40(分数:1.00)A.B.C.D.47. (分数:1.00)A.B.C.D.48. (分数:1.00)A.B.C.D.49.Polygon SUVNPQ is equilateral and equiangular and TWOR is a rectangle(分数:1.00)A.B.C.D.50. (分数:1.00)A.B.C.D.51.The diameter of the circle is 10The area of the(分数:1.00)A.B.C.D.52.Board A mea

    18、sures between 2.15 feet and2.25 feet in length;board B measures between 2.20 feet and 2.30 feet in length(分数:1.00)A.B.C.D.53.2AF=AB=BD=DE=AE(分数:1.00)A.B.C.D.54.A circular flower bed is inscribed in a flat,square garden plot that measures x meters on each side(分数:1.00)A.B.C.D.55. (分数:1.00)A.B.C.D.56.

    19、The map showsthe only roads that connect the four towns and shows the distance along each road(分数:1.00)A.B.C.D.57. (分数:1.00)A.B.C.D.58.A rectangular label is attached to a right circular cylinder with radius rThe label,which encircles the cylinder without overlap,has width w and an area equal to the

    20、 area of the base of the cylinder(分数:1.00)A.B.C.D.59.In the xy-coordinate system,the point(x,y)lies on the circle with equation(分数:1.00)A.B.C.D.60. (分数:1.00)A.B.C.D.61. (分数:1.00)A.B.C.D.62.A rectangular floor with an area of 12square meters is drawn to scale with 2centimeters representing,meter(分数:1

    21、.00)A.B.C.D.63.The figure above shows a cylindrical can that has been cut open and flattened(分数:1.00)A.B.C.D.64. (分数:1.00)A.B.C.D.65. (分数:1.00)A.B.C.D.66. (分数:1.00)A.B.C.D.67.If the sum of the measures of two angles is180, each angle is a supplement of the other,whereasif the sum of their measures i

    22、s 90,each is a complement of the other(分数:1.00)A.B.C.D.68.Point S(not shown)lies above the x-axis such that RST has area equal to 6(分数:1.00)A.B.C.D.69. (分数:1.00)A.B.C.D.70.The area of square region S is 36(分数:1.00)A.B.C.D.71.RST lies in the XY-plane and points Rand T have(x,y)coordinates(0,0)and(分数:

    23、1.00)A.B.C.D.72.In the rectangular coordinate system,line k passes through the points(0,0)and(4,8);line,m passes through the points(0,1)and(4,9)(分数:1.00)A.B.C.D.73.In a rectangular coordinate system,line k hasx-intercept 4 and slope-2(分数:1.00)A.B.C.D.74. segment OP is rotated counterclockwisethrough

    24、 an angle of 90 to position OQ(not shown)(分数:1.00)A.B.C.D.75. (分数:1.00)A.B.C.D.76. (分数:1.00)A.B.C.D.77.(分数:1.00)A.B.C.D.78.A,B,and C are points on a lineThe distance between A and B is twice the distance between A and CThe distance between C and B is 10(分数:1.00)A.B.C.D.79.RST is isosceles and RST=40

    25、(分数:1.00)A.B.C.D.80.The sum of the lengths of two sides of isosceles triangle K is 7K has a side of length 4(分数:1.00)A.B.C.D.81. (分数:1.00)A.B.C.D.82. (分数:1.00)A.B.C.D.83.The vertices of an equilateral triangle are on a circle(分数:1.00)A.B.C.D.84.Exactly four faces of a rectangular solid a repainted(分

    26、数:1.00)A.B.C.D.85. (分数:1.00)A.B.C.D.86. (分数:1.00)A.B.C.D.87.All faces of the solid above are rectangular(分数:1.00)A.B.C.D.88. (分数:1.00)A.B.C.D.89.A size S soup can is 10 centimeters high and a size T soup can is 125 centimeters high(分数:1.00)A.B.C.D.90. (分数:1.00)A.B.C.D.91.Triangular garden ABC is red

    27、esigned by increasing the length of AC by 20 percent to point Cand decreasing the length of AB by20 percent to point B(分数:1.00)A.B.C.D.92. (分数:1.00)A.B.C.D.93. (分数:1.00)A.B.C.D.94.Fields X and Y are to be enclosed with fencing that costs$24 per meter(分数:1.00)A.B.C.D.95.The area of the circular regio

    28、n with center O is 16,and v,wx,y and z represent the lengths Of the line segments(分数:1.00)A.B.C.D.96.The diagram represents a rectangular gardenThe shaded regions arc planted in flowers,and the unshaded region is a walk 2 feet wideAll angles are right angles(分数:1.00)A.B.C.D.97. (分数:1.00)A.B.C.D.98.A

    29、 20-foot ladder leaning against a vertical wall with the base of the ladder 10 feet from the wall is pulled 2 feet farther out from the wall,causing the top of the ladder to drop X feet(分数:1.00)A.B.C.D.99.The three small rectangles have the same dimensions(分数:1.00)A.B.C.D.100.The point (not shown) w

    30、ith rectangular coordinates (m,n) is above line k(分数:1.00)A.B.C.D.GRE-练习十六答案解析(总分:100.00,做题时间:90 分钟)一、单项选择题(总题数:35,分数:35.00)1.If the perimeter of a triangle is 18,then the length of one of the sides CANNOT beA. 1 B. 3 C. 6D. 8 E. 9(分数:1.00)A.B.C.D.E. 解析:若三角形的周长等于 18,那么其边长不可能是:三角形中任一边的长都小于其他两边的和,也即任意

    31、一边的长都小于三角形周长的一半。2.What is the ratio of the perimeter of a pentagon with each side of length 6 to the perimeter of an octagon with each side of length 6?(分数:1.00)A.B.C.D.E. 解析:每条边长都等于 6 的五边形(pentagon)的周长与每条边长都等于 6 的八边形(octagon)周长的比率是多少?能否解对本题的关键在于考生是否认得“pentagon”(五边形)和“octagon”(八边形)这两个词,由题意可得:*3.If c

    32、orresponding sides of AABC andABC above are proportional, what is y in terms of x?(分数:1.00)A.B.C.D. E.解析:如果 AABC 与ABC的对应边成比例,那么 y 用 x 来表示是多少?因为ABC 和ABC的对应边成比例,所以有:*4.What fraction of a cubic meter is the volume of a cubic block Of stone with edge of length 10 centimeters?(1 meter=100centimeters)(分数:

    33、1.00)A.B.C.D.E. 解析:边长为 10cm 的立方体(cubic block)石块的体积是 1 立方米(cubic meter)的几分之几?由 1 米=100 厘米可得 10 厘米等于 0.1 米,所以边长为 10cm 的立方体石块的体积为:0.10.10.1=110-3立方米5.In the coordinate plane,points A and B are endpoints of a diameter of a circle with center(-2,1)If the coordinates of A are(-5,5),what are the coordinate

    34、s of B?A. (0,0) B. (3,-2)C. (3,-1) D. (2,-2)E. (1,-3)(分数:1.00)A.B.C.D.E. 解析:在坐标平面上,A 和 B 两点是以(-2,1)为圆心的直径的端点(endpoint)。若 A 点坐标为(-5,5),那么 B 点的坐标是多少?设圆心坐标(x 0,y 0),因为圆心是 A 和 B 中点,所以由平面内任两点中点的坐标公式可得:xA+xB=2x0,y A+yB=2y0。代入圆心与 B 点坐标,可求得 B 点坐标为(1,-3)。6. (分数:1.00)A.B. C.D.E.解析:若上图中长方形的周长等于 36,则 l=长方形周长(l+

    35、4)2=36,因而解出 l=147.In square PQRS aboveT is the midpoint of side RSIf PT= ,What is the length of a side of the square?(分数:1.00)A. B.C.D.E.解析:在上面的正方形 PQRS 中,T 是 RS 的中点(midpoint),若 PT=*,那么正方形的边长是多少?设正方形边长是 2a,则|TS|=a,PST 是直角三角形,由勾股定理可知:*正方形的边长为 16。8.If a solid pyramid has 4 vertices and4 faces,how many

    36、 edges does the pyramid have?A. 2B. 3C. 4D. 6E. 8(分数:1.00)A.B.C.D. E.解析:假如一个立体四角锥有 4 个顶点和 4 个面,该四角锥有多少条边?*解答这道题的关键是对 solid pyramid 的理解。根据题中对 solidpyramid 的描述可知,所谓 solid pyramid 就是立体几何中常见的四面体如下图所示。四面体有四个面,四个顶点,六条边。*注:Solid n固体,立体(几何);Pyramid n锥体(四角锥);Vertices n顶点(pl)9. (分数:1.00)A. B.C.D.E.解析:如上图所示,AB

    37、CD 是一个平行四边形,A 在原点,问 C 点坐标是多少?因这平行四边形的对角线互相平分,也即*具有相同的中点,所以位于直角坐标系中的平行四边形具有如下性质*10.The rectangular solid above is made up of eight cubes of the same size,each of which has exactly one face painted blue What is the greatest fraction of the total surface area of the solid that could be blue?(分数:1.00)A.

    38、B.C.D. E.解析:上图所示的长方体由 8 块同样大小的立方体构成,每个立方体仅有一个面被涂成蓝色。问该长方体的表面是蓝色的部分占其总表面积的最大比例是多少?蓝色部分占表面最大比例的情况是 8 个立方体的蓝色表面均露在外面,共有 8 个平方单位,而长方体的表面共有 28 个平方单位,因而蓝色部分占长方体表面积的最大比值为*11.The dimensions,in centimeters,of rectangular box R are 6 by 8 by 10Which of the following CANNOT be the total surface area,in square

    39、centimeters,of two faces of R?A. 96B. 120C. 128D. 160E. 180(分数:1.00)A.B.C.D.E. 解析:以厘米为单位,长方体盒子 R 的尺寸为 6810,请问下列哪项不能是 R 的两个面的面积的和(以平方厘米为单位)?长方体盒子有六面,且对面两两相等,共有三个面积不同的面,分别是 68=48,610=60 和810=80,这些面两两相加,包括与自身相加,共有 6 个不同的取值:分别是:96,120,160,108,128,140。把这些值与题目的选项对照,发现(E)不等于长方体盒子两个面的面积的和。考生也可用另一种方法来解此题,在长方

    40、体中面积最大的一面为 810=80,所以两个最大面的面积和最大为 160,因此 180 显然不能是长方体两个面的面积的和。12. (分数:1.00)A.B.C.D. E.解析:在上面的圆周上有 6 个标出的点。问能画出多少条含两个标识点的不同直线?由图可知由这六个点中的任意三点都不在同一条直线上,由两个点确定一条直线可和这 6 个点能确定的不同直线数是其任 2 个点的组合数*=*13. (分数:1.00)A.B.C. D.E.解析:在左侧的图形中,若 x,y 和 z 都是整数,且满足 xyz,那么 x+z 的最小值和最大值是多少?由三角形的内角和等于 180可得:x+z=180-y,而 xyz

    41、,且 x,y,z 为整数,则 y 最小值等于 2,最大值为 89,那么 180-y 一定大于等于 91,而小于等于 178。14.A rectangular rug covers half of a rectangular floor that is 9 feet wide and 12feet longIf the dimensions of the rug are in the same ratio as those of the floor,how many feet long is the rug?(分数:1.00)A.B.C.D. E.解析:一个长方形地毯盖住 9 英尺长 12 英尺

    42、宽的地板的一半,若该地毯的长与宽的比例和地板的长与宽比例相同,问该地毯有多长?“dimension”指图形的维,在这里指长方形地毯的长和宽。由题意可得地毯的面积=*地板面积=*912=54;而地毯长和宽比例也为 12:9。设地毯长为”,则宽为*54*15. (分数:1.00)A.B.C.D.E. 解析:上图所示长方体盒子被两条胶带捆住,每条胶带无重叠地缠绕长方体盒子一圈,且与长方体盒子的边缘相平行。问包盒子共用了多长的胶带?该题实际上是让考生求长方体盒子的两个矩形周长的和,因此带长等于:2(20+15)+2(25+15)=150cm16. (分数:1.00)A.B. C.D.E.解析:若 9

    43、棵树最初以如左图所示的圆形种植要使 9 棵树排在两条直线上问最少需移植几棵树?圆上的任意三点都不在同一条直线上,又根据在同一平面内的两点确定一条直线可知,要使这 9 棵树排在两条直线上,则至少得有 9-22=5 棵树被移植。17.What is the maximum number of nonover-lapping regions into which 3 lines can divide the interior of a circle?A. 4B. 6C. 7D. 8E. 9(分数:1.00)A.B.C. D.E.解析:3 条直线最多可以把 1 个圆的内部分成多少个非重叠的区域?其分法

    44、如下图所示:*由图可知,最多可分成 7 个区。18. (分数:1.00)A. B.C.D.E.解析:左图所示的长方形地毯在各边均有 1 英尺宽的花边。以平方英尺为单位,地毯的非花边部分的面积是多少?由花边宽 1 英尺可知,这块地毯去除花边后,长和宽分别为 7 英尺和 4 英尺,所以其面积=74=28 平方英尺。19.What is the area of the hexagonal region shown in the figure above?(分数:1.00)A. B.C.D.E.解析:左而图形中六边形(hexagonal)的面积是多少?由图可知,此六边形是正六边形(边长相等内角相等),

    45、连接正六边形的 3 条长对角线可构成 6 个全等的等边三角形,这些等边三角形的边长为 6,其面积可由勾股定理求出:*则面积为:*20.In the figure above,O and P are the centers of two circlesIf each circle has radius r,what is the area of the shaded region?(分数:1.00)A.B. C.D.E.解析:在上面的图形中,O 和 P 是两个圆的圆心。若两个圆的半径都为 r 那么阴影部分的面积是多少?阴影区所构成的四边形的四条边都等于 r,所以它可以分成两个边长为 r 的等边三

    46、角形,所以阴影区的面积*21. (分数:1.00)A.B.C.D.E. 解析:在上图所示的直角坐标系中,位于阴影区内或边界上的点坐标是整数的点有多少个?由图可知,阴影区由 y=x,y=0,x=3 这三条直线围成,其边界为这三条直线。因此阴影区内点的坐标范围为 0x3,0y3,yx。当 x 和 y 只能取整数时,所求的点为:(0,0),(0,1),(0,2),(0,3),(1,1),(1,2),(1,3),(2,2),(2,3),(33)共计十点。22.A certain rectangle has perimeter 54If the ratio of the length of the re

    47、ctangle to the width is 5 to 4,what is the length of the rectangle?A. 30 B. 27 C. 24D. 18 E. 15(分数:1.00)A.B.C.D.E. 解析:一长方形的周长等于 54,其长宽比为 5:4,问该长方形的长为多少?设该长方形的长和宽分别是 5x,4x,由题意可得:(5x+4x)2=54*x=3, 5x=1523.In the figure above,what is the length of AB?(分数:1.00)A.B.C.D. E.解析:在上面图中,AB 的长度是多少?因为CAD=45,所以ADC

    48、 为等腰直角三角形,因而 AC=CD=10sin45=10:而CBD=180-120=60*24.If the areas of three of the faces of a rectangular solid are 6,10 and 15,what is the volume of the solid?A. 30B. 90C. 150D. 300E. 450(分数:1.00)A. B.C.D.E.解析:若一个长方体 3 个面的面积为 6,10 和 15,该长方体(rectangular solid)的体积是多少?设长方体的长,宽,高分别为 l,w,h,则有:lw=6wh=10hl=15长

    49、方体体积为 lwh,上面三项相乘得(lwh)2=900,lwh=30。25.In the figure above,if the area of the inscribed rectangular region is 32,then the circumference of the circle is(分数:1.00)A.B. C.D.E.解析:在上面的图形中若圆的内接长方形的面积等于 32,那么圆的周长等于由长方形的面积公式可得:2x2=32*x=4应用勾股定理:4R2=4x2+x2=R=*圆的周长=2R=*。26.In the rectangular coordinate system above,if P,not shown,is a point on AB and if the x-coordinate of P is 1,wh


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