GRE数学难题(3)

　　1. A,B,C,D,E,F排在1,2,3,4,5,6六个位置上,问A不在1, B不在2, C不在3的情况下,共有多少种排法?

　　(A) 720

　　(B) 450

　　(C) 180

　　(D) 216

　　(E) 320

　　2. 一直线L过点A(5,0), B(0,2), 坐标原点为O, 点P(X,Y)为三角形OAB中一点, 问:Y<X的概率是多少?

　　(A) 1/4

　　(B) 3/8

　　(C) 1/2

　　(D) 5/8

　　(E) 3/4

　　3. If Bob can do a job in 20 days and Jane can do the job in 30 days, they work together to do this job and in this period, Bob stop work for 2.5 days and Jane stop work for x days, and the job be finished for 14 days, what is x?

　　(A) 1.6

　　(B) 3.2

　　(C) 1.5

　　(D) 1.25

　　(E) 1.15

　　4. The probability of A is 60% and the probability of B is 50%, what is the most possible probability that neither A nor B would happen?

　　(A) 0.80

　　(B) 0.40

　　(C) 0.75

　　(D) 0.55

　　(E) 0.68

　　5. In an insurance company, each policy has a paper record and an electric record. For those policies having incorrect paper record, 60% also having incorrect electric record; For policies having incorrect electric record, 75% also having incorrect paper record. 3% of all policies have both incorrect paper and incorrect electric records. If we randomly pick out one policy,what’s the probability that the one having both correct paper and correct electric records?

　　(A) 0.80

　　(B) 0.94

　　(C) 0.75

　　(D) 0.88

　　(E) 0.92

　　6. There are 1200 respondents to a poll, each favoring their preference for candidates A,B, and C. 54% favored A, 48% favored B, and 42% favored C, and there is 30% favored both A and B. what’s the largest possible number of respondents favoring C, but not C&B, nor C&A?

　　(A) 25%

　　(B) 30%

　　(C) 28%

　　(D) 38%

　　(E) 40%

　　参考答案：

　　1.解：首先考虑总的可能性为，再考虑A在1，B在2，C在3的可能性分别为，中重复计算了三者交集，分别为AB在1，2，AC在1，3，BC在2，3，所需将三种情况加回，即，但考虑这三种加回的交集又重复计算了ABC在1，2，3的情况，所以应减去P33

　　2.解：在平面直角坐标系中，T<X在第一象限是在通过原点的45°线以下，则三角形OAB中Y<X的概率应为45°线以下部分除以三角形总面积，所以概率为5/7.

　　3.解：1/20（14-2.5）+1/30（14-x）=1，得出x=1.25

　　4.解：划出图表来可以一目了然：A， B均不发生的最大概率为40％，最小概率为0.

　　5.解：设总数为x，设incorrect paper record有y, incorrect electric record有z，则：

　　x?y?60%=3％?x y=5%

　　x?z?75％=3％?x z=4%

　　则，两者至少有一个错误的百分比为5％+4％-3％=6％，所正确答案为94％

　　6.解：A和B的并集为：54％+48％-30％=72％，所C为28％.