弱弱的问一下 求助？

亦优

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

 

【答案】C

【思路】：40=2^3 *5,  2的幂最多

 

实在是没明白这题是什么意思？恳请路过的各位亲们帮忙，不胜感激

亦优

都没有人理我

结果自力更生了一下

原来CD里有解答

那我就自己解吧

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.




原文引自：http://www.chasedream.com/show.aspx?id=94&cid=40

切尔西

LZ一般在晚上发帖回复会快些的，大家白天都有事的，上来的不多

bearwinnie

翻成中文后蛮容易做的，关键是看原版还是理解不了意思