GRE数学机经试题练习一

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　　题目：

　　1. In a probability experiment, G and H are independent events. The probability that G will occur is r, and the probability that H will occur is s, where both r and s are greater than 0.

　　Quantity A：the probability that either G will occur or H will occur, but not both

　　Quantity B：r+s-r*s

　　A. Quantity A is greater.

　　B. Quantity B is greater.

　　C. The two quantities are equal.

　　D. The relationship cannot be determined from the information given.

　　正确答案：B

　　题目解析：G事件与H事件互相独立，G事件概率为r, H事件概率为s，求两事件其中之一发生的概率。

　　只发生G事件：r*(1-s)

　　只发生H事件：s*(1-r)

　　相加可得 r+s-2*r*s，小于Quantity B，因此选B。

　　2. The area of circle W is 16*π and the area of circle Z is 4*π. What is the ratio of the circumference of W to the circumference of Z?

　　A. 2 to 1

　　B. 4 to 1

　　C. 8 to 1

　　D. 16 to 1

　　E. 32 to 1

　　正确答案：A

　　题目解析：根据圆形面积公式，可知两圆的半径比例为2:1，然后根据周长公式计算，其州长比例也为2:1。所以选A。

　　3. The interior dimensions of a rectangular tank are as follows: length 110 centimeters, width 90 centimeters, and height 270 centimeters. The tank rests on level ground. Based on the assumption that the volume of water increases by 10 percent when it freezes, which of the following is closest to the maximum height, in centimeters, to which the tank can be filled with water so that when the water freezes, the ice would not rise above the top of the tank?

　　A. 230

　　B. 235

　　C. 240

　　D. 245

　　E. 250

　　正确答案：D

　　题目解析：已知水箱长宽高数据，和水结冰时会上升10%高度的推论，问水箱里可以装多少水，其结冰时也不会超过水箱高度。设为x，列出1.1x=270，x约等于245，所以选D。

　　4. In a certain sequence of numbers, each term after the first term is found by multiplying the preceding term by 2 and then subtracting 3 from the product. If the 4th term in the sequence is 19, which of the following numbers are in the sequence? Indicate all such numbers.

　　A. 5

　　B. 8

　　C. 11

　　D. 16

　　E. 35

　　正确答案：A C E

　　题目解析：第一项设为x，根据题目条件可知第二项2x-3，第三项2(2x-3)-3=4x-9，第四项依次类推为8x-21。接下来根据第四项=40算出x=5，代入前五项，分别算出5,7,11,40,35。其中符合条件的选项为ACE。

　　5.

　　The quadrants of the xy-plane are shown in the figure above. In the xy-plane, line m (not shown) has a positive slope and a positive x-intercept. Line m intersects which of the quadrants? Indicate all such quadrants

　　A. Quadrant I

　　B. Quadrant II

　　C. Quadrant III

　　D. Quadrant IV

　　正确答案：A C D

　　题目解析：本题关键在于看懂抽象描述。问直线m经过哪几个象限。条件positive slope可知m大致上是从左下往右上的斜线，那么第二和第四象限必然有一个不经过或者两个都不经过，条件positive x-intercept表明m和x轴的正数侧也就是右侧相交，那么m经过象限就是1,3,4，所以选ACD。