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标题: 向好心人求助一题 GWD29-Q13 [打印本页]

作者: bigdreamer 时间: 2006-8-5 00:18
标题: 向好心人求助一题 GWD29-Q13

GWD29-Q13:

For any positive integer x, the 2-height of x is defined to be the greatest nonnegative integer n such that 2ⁿ is a factor of x. If k and m are positive integers, is the 2-height of k greater than the 2-height of m ?

(1) k > m

(2) K除以mis an even integer. 答案是 B, 没看懂题意.

作者: lovetiky 时间: 2006-8-5 17:16

if k=8 and m=4, then the 2-height of k is 3, and the 2-height of m is 2.

if k=6 and m=4, then the 2-height of k is 2, the same as the m's

hence, (1) is insufficient.

if k/m is an even integer, supposing that k=m*2t,

then suppose that the 2-height of m is n, that means 2^n is the factor of m and m can be represented as 2^n*s.

we have assumed that k=m*2t, so k=2^n*s*2*t=2^(n+1)*s*t

thus, the 2-height of k is (n+1)

作者: bigdreamer 时间: 2006-8-5 23:22
Thank you very much for help, but i think you are right, but i still don't understand the question.

作者: bigdreamer 时间: 2006-8-5 23:27
Now, i understand. thank you

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