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.

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)