6月MATH机警1助

bettyofarim

6月MATH机警

value x/y? 1)x^2y=1 2)xy^2>1 答案：C

11. In box A, there are 20 purple 30 red marbles. In box B, there are 15 purple and 35 red ones. If someone randomly select the box first then select one marble from the box, what is the posiblity to select a purple one? 答案是 9/20 ，我得20/50哪？是什么地方错了？

12. Catalog A has x dresses and Catalog B has y dresses. If combine the two catalogs and one dress should only appear once, then the combined catalog has 3x dresses. How many dresses appear on both A and B? (y-2x) 请问怎么考虑呢？

13. Distribute something to 7 people, then 2 left, How many something there are?
1) something less than 20.
2) if for 8 people, then nothing left.
答案是 C 但是我算的有something有 1和2 都成立的情况，那应该是E罗

14. 一个数列,首项65,二项67,三项68,a(n)=8+a(n-3), 问一些很大的数字800, 1000,2000的哪个是数列的一项. 怎么算呢？用代入法吗？

18. (4的9次方)乘以5的17次方的结果是几位数？ 这种有什么技巧的吗？

19. X1=3，Xn+1=2Xn - 1, 求 X20 - X19 答案是20吗


22. 一数列,第三位是前两位之和(如是奇数)(如是偶数则是前两位之和除以2),以此类推,第4位是7,第5位是5,求第一位? 怎么算啊？

gsluo

1.E
11.  7/20
13.  C设SOMETHING 为X 由（1）X=7N+2  X可能是16 和9 无法判断 由（2）X=8M X 可能是   16，44， 72。。。。但（1）（2）可判断X为16
18。 4^9*5^17简化为  2乘以10的17次方就好做了
14题不明白
19、22题目有歧义吧

hexin

14. 可以想成a(1), a(4), a(7)...a(1+3k)是公差是8的等差数列，这样比如说800可以代入，如果不是再分别减去1和2看看是不是a(2),a(5),a(8)..数列， 或者a(3), a(6), a(9)...数列中的一项。也就是说把a数列看成是3个等比数列分别代入。

hz

19、2^19

tocean0222

22、第一项是2

brunhild

22题，—13

albert

19.      X(20)-X(19)=2X(19)-1-X(19)=X(19)-1
  X(n+1)=2X(n)-1
            =2[X(n-1)-1]-1
            =.......
           = X1*2^n-2^(n-1)
so X(19)=X1*.......  but the answer is quite weird..

22...I guess all the number in the set should be positive integer, otherwise we can not get a specifit a1...
suppose a1, a2, a3, 7, 5
then a3 must be 5*2-7=3 OR -2, since the number should be positive..a3=3
then suppose a3=3, a2 must be 4 or 11
suppose a3=3 a2=4  a1 must be 2 or -1, but since the number should be positive a1=2
suppose a3=3 a2=11, a1 must be -14 or -5, both of which are not the number we gonna get..
so the final answer is a1=2

hz

19、Xn+1=2Xn - 1, Xn+1 - 1=2(Xn - 1), (Xn+1 - 1)/(Xn - 1)=2,
假设Xn+1 - 1=An+1,则Xn - 1=An,X1 - 1=A1, An+1/An=2,An为等比数列,
An=A1*2^(n-1)=(X1 - 1)*2^(n-1)=2^n,Xn=An + 1=2^n + 1,
所以X20 - X19 =2^20 - 2^19=2^19。

[此贴子已经被作者于2003-7-22 11:30:38编辑过]

albert

great, HZ...thanks