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
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)
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