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[求助]两道GWD Math

For any positive integer x, the 2-height of x is defined to be the greatest nonnegative 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/m is an even integer.

Key: B, why? 不是很理解题意,请大家指教!

A certain company expects quarterly earnings of $0.80 per share of stock, half of which will be distributed as dividends to shareholders while the rest will be used for research and development. If earnings are greater than expected, shareholders will receive an additional $0.04 per share for each additional $0.10 of per share earnings. If quarterly earnings are $1.10 per share, what will be the dividend paid to a person who owns 200 shares of the company's stock?

A)92 B)96 C)104 D)120 E)240 Key: C

Ans: 0.80*200+0.04*3*200=104 我的思路对吗?Thanks!

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第一题,所谓2-height,是指自然数的因子中因子2的个数。例如28=2×2×7,那么28的2-height就是2。同理16的2-height是4,115的2-height是0。一般的,奇数的2-height都是0,偶数的2-height至少是1,所以条件(1)不能得到任何判断。条件(2),k/m是偶数,那么k里面的因子2的数目当然比m大,于是k的2-height至少比m大1。

第二题agree with you

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himba真是厉害,我连2-height都不知道.
把所有的困苦都看做是有意义的,是生命对你的磨练,也许,是为了让你成大事而做准备。

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