即将裸考~请教prep数学～～

FairyFox

26号就要杀G了。。。麻烦各位教教我prep这几道题～～

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   （为什么是这个啊）

2.DS题

If $1,000 is deposited in a certain bank account and remains in the account with any accumulated interest , the dollar amount of interset I , earned by the deposit in the first n years in given by the formula I=1,000【（1+r/100)^n - 1】， where r percent is the annual interest rate paid by the bank , Is the annual interest rate paid by the bank greater than 8 percent ?

(1). The deposit earns a total of $210 interest in the first two years .

(2). （1+r/100)^2 > 1.15  （这个为什么不行啊？）

3.也是DS题

Did one of the 3 members of a certain team sell at least 2 raffle tickets yesterday?

(1). The 3 members sold a total of 6 raffle tickets yesterday.

(2).No 2 of the members sold the same number of raffle tickets yesterday.

为什么这里两个都行啊？

谢哦谢哦～～

lucy8762

第2题

(2)把（1+r/100)^2 > 1.15带入 I=1,000【（1+r/100)^n - 1】,可以算出I>150,这是2年的利息. 由此可知年利率>150/(1000*2)=7.5%,不能推出年利率>8

第三题

(1)3个人卖6张票,必然有一个人要卖>=2张票才行

(2)没有2个人卖一样数量的票,当然也就说明至少有2个人卖>=2张票的,否则不都为1了??

lambbuffalo

I did some search: found the below answer: (hope that it helps)

the question says that h(n) = 2*4*6*8* ... *n ...

.. so for example .. h(4) = 2*4 = 2^2(1*2)

h(12) = 2*4*6*8*10*12 = 2^6( 1*2*3*4*5*6)

So h(100)= 2*4*6*8*....*100 = 2^50(1*2*3*4*5*6* ... *50) ...

Now, what are the prime factors for h(100) .. that is what are the prime numbers that divide the expression h(100)=2^50(1*2*3*4*....*50) .. the prime factors would be 2,3,5,7 and so on .. that is all the prime numbers between 1 and 50 would be a factor of the expression h(100) = 2^50(1*2*3*4 ....*50) ..

.. so now consider the expression h(100)+1 = 2^50(1*2*3*4*....*50) + 1 .. since 1 is not exactly divisible by any of the prime numbers, none of the prime factors between 1 and 50 will be able to exactly divide h(100) + 1 .. so the answer is > 40 .. that is E ..

FairyFox

这样的啊～～谢谢两位啊～～谢哦谢哦～～

FairyFox

第2题，我还是不懂。。。

如果条件2能给出NO的答案，应该是充分的啊，DS题不是指的是，不确定的情况下条件才不充分才要排除的么？如果回答问题的话，不论是YES/NO， 条件都是充分的啊。不是这样的么？

zacharyzhang

以下是引用FairyFox在2008-4-24 13:27:00的发言：

第2题，我还是不懂。。。

如果条件2能给出NO的答案，应该是充分的啊，DS题不是指的是，不确定的情况下条件才不充分才要排除的么？如果回答问题的话，不论是YES/NO， 条件都是充分的啊。不是这样的么？

2年大于1.15，可以是1.151，也可以是1.17啊。因此可以算出r一定大于7.5(当然存在大于8的可能性) ，但不能确定r是不是大于8。

FairyFox

我太笨了。。。谢谢啊～～茅塞顿开～～