1、In an insurance company, each policy has a paper record or an electric record, or both of them. 60 percent of the policies having incorrect paper record have incorrect electric record and 75 percent of the policies having incorrect electric record have incorrect paper record. 3 percent of all the policies have both incorrect paper and incorrect electric records. If we randomly pick out one policy, what is the probability that it is one having both correct paper and correct electric record?
【答案】94%
【思路】
设总数为X policies，则既有非P又有非E为3%X;60%的非P中为非E，则非P为3%X/60%;75%的非E为非P，则非E为3%/75%，那么非P与非E一共有(3%X/60%+3%X/75%-3%X) ，那么P与E一共有X-(3%X/60%+3%X/75%-3%X)，则其概率为[X-(3%X/60%+3%X/75%-3%X)]/X=94%
2、If for all x, x^2+ax+b = (x+c)^2, then a =?
(1)b=0;
(2)c=-3;
【答案】B
【思路】x^2+ax+b = (x+c)^2= x^2+2cx+c^2，则A=2C，只要知道C的值就可以知道A值了
x^2+ax+b = (x+c)^2= x^2+2cx+c^2
x^2+ax+b = x^2+2cx+c^2
化简后：(a-2c)x+(b-c^2)=0
因为对于所有的x值，上式均成立，则a-2c与b-c^2必须同时为0;
a-2c=0
b-c^2=0
只要知道了b或c中的任何一个数，a均可求。
偶选D。
3、随机抽样10个产品有N个坏的，N<5，问N=?
(1)任取两个产品，都是坏的可能性为1/15;
(2)任取两个产品，一好一坏的可能性为7/15;
【答案】D
【思路】(1)C(N 2)/C(10 2)=1/15可算出N(N-1)=6=3*2则N=3
(2)C(N 1)*C(10-N 1)/C(10 2)=7/15可算出N(10-N)=21=3*7=7*3则N=3或7，又N<5，所以N=3
4、xyz<>0, 问x(y+z)>0?
(1)|x+y|=|x|+|y|
(2)|y+z|=|y|+|z|
【答案】C
【思路】由(1)可知X、Y是同号，由(2)可知Y、Z也是同号，则X、Y、Z都是同号，所以x(y+z)>0
5、1/a+1/b+1/c+1/d+1/e=1，a…e全是不同的正整数，问：a+b+c+d+e的least possible value?
【答案】3+4+5+6+20
【思路】没有特殊的方法，最好能够记住。