大牛帮忙解释一下那道2－height题，我怎么觉得选E呢！

lzhch89

1. X is a positive integer. 2-height of X is defined as the greatest negative integer n where 2^n is a factor of X. K and M are two positive integers. Whether 2-height of K is greater than 2-height of M?
a. K is greater than M
b. K is even times of M
(Key: B)
(by rosemsem)
题义解析：说对于含2的n次方的数, 2-height 指的是n的值。问k和m谁的2-height大？
(1) K>M
(2) K除以M是偶数.
(please notice K,k; M,m; e)
K = a* 2^k;
M = b* 2^m;
(1) k>m, means nothing.
(2) k/m= (a/b) * (2^k/2^m) = 2^e;
A, b must be odd number, or you can extract at least one more 2, which gonna change k or m. So in this case, (a/b) must be 1, otherwise it would be a fraction.
In a word, k-m=e. K>m.
B is sufficient.


我觉得是不是选E呢
设

k=2⁶＊5   m＝5，则k/m为偶，符合条件B。 2－height K＝6 所以   2－height K>m

k=

2³＊5     m=5  ,    则k/m为偶，符合条件B。 2－height K＝3 所以 2－height K<m

所以我觉得 2－height k 和m的大小没法确定啊。

大家看看我设的这两个数有没有问题。

lzhch89

刚意识到，被另外一条没写全的寂静误导了一下。

sdcar2010

You are comparing apple with oranges. You need to compare 2－height k vs. 2－height m.