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标题: 各位大虾,快来挑战七月数学JJ难题! [打印本页]

作者: joy 时间: 2002-7-27 06:13 标题: 各位大虾,快来挑战七月数学JJ难题!

由于本人万分火急,只好求救于各位大虾,谢谢您老人家了!!!

1, m, n are non-zero integers, is m^n integer?
a) n^m is positive
b) n^m is an integer

2, 3个人分两个办公室，可以有一个办公室空着,有几种分法?如果无这个空的条件是几种?思路是什么?

3, 对于整数x, @n表示4x除以3的余数，下面哪个等于0
1）,@(3x+3), 2),@3x, 3),@(x+1) (大概如此)

4、the vertices of A square are the midpoints of B square,what is the area of A?
(A)the length of B is 4
(B)one of the diagonals of B is 8

5， [X] 为小于或等于X的最大整数，[X]=-1？ 1）X= -1 2）-2〈X〈-1 3〉 -2 〈=X〈-1 4〉 -1〈X〈0 5〉 -1 〈=X〈0

6,For all x , x is positive interger, “2-height” is defined to be the greatest nonnegative n of x, the greatest number of 2-height when 2^n is the factor of x? A. 2 B.12 C.40 D.70 E. 36 ©

7、 Does class A have the same range as class B, if size A = size B = 26 and max A = max B = 70?
(1) min A = min B =10;
(2) mean A = mean B = 50. （E）为什么？

8,.Stock price increased k%, earning increased M%, K>M. What is the proporation of increase in price to increase to earning?

9, two companies, from Jan. 1996 to Dec, 1996, x increased its inventory by 25%, y increased its inventory by 10%. The ending inventory balance as of Dec. 1996 for x is 4000, for y is 5500, how many x’s inventory at Jan. was less than y’s inventory at Jan.

10. $ 65million endowment,simple interest 12%, if want to get $10 million, How much approxmately must be added?
A 8 million B 18 million C 21million ...(B) 怎么得来得?

11, a store, sell 500desks and 300chair was saled in reduced price, final combined profit 1400, profits of per desk is 10$, loss of per chair ?
an: 12 (500*10-1400)/300(其实desk没有reduce price) 为什么?

12. integer number n, in o~100, n/3 is square of one prime number. how many n satify such condition.
as: 3 (2*2*3,3*3*3,5*5*3) 不懂??

作者: tongxun 时间: 2002-7-27 10:54

1, m, n are non-zero integers, is m^n integer?
a) n^m is positive
b) n^m is an integer
-----------------------
A，只能推出M是偶数，或N》0；则m^n 不能确定是否是整数。
B，可推出（N》1，M》1；或N《1，M〈1），则m^n 必为整数
因此，选B
======================
2, 3个人分两个办公室，可以有一个办公室空着,有几种分法?如果无这个空的条件是几种?思路是什么?
----------------
[2（空一间）]+[3*2（不空时）]=8

作者: tongxun 时间: 2002-7-27 10:58

12. integer number n, in o~100, n/3 is square of one prime number. how many n satify such condition.
as: 3 (2*2*3,3*3*3,5*5*3) 不懂??
---------------
这题我在“机警讨论”版primefang发的数学讨论中有说。

作者: vancouver 时间: 2002-7-28 15:02 标题: [讨论]

以下是引用tongxun在2002-7-27 10:54:15的发言：
1, m, n are non-zero integers, is m^n integer? 
a) n^m is positive 
b) n^m is an integer 
-----------------------
A，只能推出M是偶数，或N》0；则m^n 不能确定是否是整数。
B，可推出（N》1，M》1；或N《1，M〈1），则m^n 必为整数
因此，选B

If n=-2 and m=2, n^m=4 while m^n=1/4, so my choice is E.

作者: tongxun 时间: 2002-7-28 21:01

脑子进水了，没想到负数！同意vancouver！

3, 对于整数x, @n表示4x除以3的余数，下面哪个等于0
1）,@(3x+3), 2),@3x, 3),@(x+1) (大概如此)
-----------------
没看懂。我下载了，容我再想想。
=================
4、the vertices of A square are the midpoints of B square,what is the area of A?
(A)the length of B is 4
(B)one of the diagonals of B is 8
----------
选D
===========
6,For all x , x is positive interger, “2-height” is defined to be the greatest nonnegative n of x, the greatest number of 2-height when 2^n is the factor of x? A. 2 B.12 C.40 D.70 E. 36 ©
-------
2height提基本选40
===============

7、 Does class A have the same range as class B, if size A = size B = 26 and max A = max B = 70?
(1) min A = min B =10;
(2) mean A = mean B = 50. （E）为什么？
------------
应该选A。range只与大小只有关。
===========
9, two companies, from Jan. 1996 to Dec, 1996, x increased its inventory by 25%, y increased its inventory by 10%. The ending inventory balance as of Dec. 1996 for x is 4000, for y is 5500, how many x’s inventory at Jan. was less than y’s inventory at Jan.
---------------
5500=Y*1.1; 4000=x*1.25;Y-X
=========
其他不会。

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