Question

GMAT题目，求解答，解释

Answer 1

主要就是你得弄明白2-height是什么意思

2-height 题是GMAT数学部分常考的一个题型。因为题中会给出一个关于2-height的定义, 所以G友通常称之为2-height题。
举个例子吧，40=2*2*2*5，即2的三次方乘以5，3就是2-height 的值，再如12=2*2*3，即2的二次方乘以3，所以2就是2-height 的值。
总的来说，就是把一个整数分解成质数的乘积，其中2的幂就是2-height 的值。
10、For all x, x is positive integer, "2-height" is defined
to be the greatest nonnegative n of x, what is the
greatest number of 2-height when 2" is the factor of x?
A. 2
B. 12
C. 40
D. 76
E. 90
Answer: (by Anchoret)
A. 2=2^1
B. 12=2^2*3
C. 40=2^3*5
D. 76=19*2^2
E. 90=45*2^1
B is the answer.

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.

linda（2004）