prep1 两道ps，求高手解答

norlanzhang

1. For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is
A. between 2 and 10
B. between 10 and 20
C. between 20 and 30
D. between 30 and 40
E. greater than 40
为什么选的是E ?

2.Before being simplified, the insructions for computing income tax in Country R were to  add 2 percent of one's annual income to the average(arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is I ?
A. 50+I/200
B. 50+3I/100
C. 50+I/40
D. 100+I/50
E. 100+3I/100
这个第二道题目大概讲的是什么意思啊？求指点~

treewing929

1. 又看見這條題目..............!!!!!!!!!!!!!!!

h(100) = 2+4+6+...+98+100
=2(1+2+3+..+49+50)
=2*50!
h(100)+1 = 2*50!+1

h(100)+1 最少質因子比 h(100) 的大
而且, 兩個連續數除 1 外, 沒有其他公同因子.
所以, 由於 h(100) = 2*50!, 所以 h(100)+1 不含 h(100) 的因子. 即是不含 1-50 裡所有質因子.
所以, 答案是會大於 50, 即是大於 40.


其實這條真的很難....這條是其他會員教我的, 某些定理我也不清楚, 只是牢記了!!

treewing929

2. 就是說加2% of income 去 100&1% income 的平均
= 2%Income + (100+1%Income)/2
=3Income/100   +100
=E

treewing929

我的數學很差, 是其他會員教我才有點進步!

norlanzhang

呃...h(n)定义不是说的2~100的乘积吗？

treewing929

我打錯了!
2*4*6*....*98*100
=2(1*2*3*..*49*50)

多謝你!!

treewing929

所以 2*50!

norlanzhang

2. 就是說加2% of income 去 100&1% income 的平均
= 2%Income + (100+1%Income)/2
=3Income/100   +100
=E

-- by 会员 treewing929 (2012/3/4 20:38:29)

prep上给的答案是C.晕了~

norlanzhang

所以 2*50!

-- by 会员 treewing929 (2012/3/4 20:46:09)

顿悟啊，原来就是把2提出来后得到一个50的阶乘~多谢

treewing929

2. 就是說加2% of income 去 100&1% income 的平均
= 2%Income + (100+1%Income)/2
=3Income/100   +100
=E

-- by 会员 treewing929 (2012/3/4 20:38:29)

prep上给的答案是C.晕了~

-- by 会员 norlanzhang (2012/3/4 20:47:14)

因為我計錯數......
對, 是 C
數式沒有錯! 你試一試!