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关于质数的几个问题,看似简单no,no,no。they don't look as they look like.

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楼主
发表于 2008-12-2 23:46:00 | 只看该作者

关于质数的几个问题,看似简单no,no,no。they don't look as they look like.

这几个都是题库里的。知道的帮忙解释一下。先谢了。

1。for  every positive integer n,the function h(n) is defined to the product of all the even integers from 2 to n,inclusive.If p is the smallest prime factor of h(100)+1,the p is

the right answer is :Greater than 40.I don't know why.

2.If n is  a multiple of 5 and n=p*p*q,where p and q are prime numbers ,which of the following must be a multiple of 25?

the right answer is :p*p*q*q.?????????????

3.On a certain sight-seeing tour,the ratio of the number of women to thenumber of children was 5 to 2,what was the number of men on the sight-seeing tour ?

(1) On the sight-seeing tour ,the ratio of the number of children to the number of men was 5 to 11.

(2) the number of women on the sight-seeing tour was less than 30.

the right answer is c:both.. together are sufficient......I think it should be e:both.... are not sufficient.

4.If $1000 is deposited in a  certain bank account and remains in the account with any interest ,the dollar amount of interest ,I ,carned by the deposit in the first  n years is given by the formula I= 1000((1+r/100)的n次方-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 fo $210 in interest in the first 2 years.

2)(1+r/100)*(1+r/100)>1.15

the right answer is a 1 sufficient 2 not . I think each sufficient.

沙发
发表于 2008-12-3 23:38:00 | 只看该作者

Q1.首先要知道m和m+1一定没有公因数,也就是互质。然后GMAT考察偶数的一个性质就是偶数实际是2^n与一奇数的乘积。因此h(100)=2(1x2x3……50),而h(100)与h(100)+1没有公因数,就是1-50都不是h(100)+1的因子。则p>50。即选项的>40

板凳
发表于 2008-12-4 12:35:00 | 只看该作者

Q2 这道题不难,主要是题目里的must be,决定了答案的唯一性。p,q都是质数,所以要想是25的倍数的,至少有2个25,即

p=5,q非5的任意质数,则p*p*q满足,但是不是仍然有

q=5,p非5的任意质数的可能,而q在原式中只有一个,

这点恰恰是题目考点,就是你是否考虑周全。

这时需要将q补一个到式子里面, p*p*q*q。这样能够保证一定是5*5的倍数。

地板
发表于 2008-12-4 12:53:00 | 只看该作者

Q3

简单的比例题

由题目:W/C=5/2

由1,C/M=5/11,将上式用C来表示带入,得到W/M=25/22即知道女比男是25比22,不知道女是多少不能求

由2,知道女小于30,不知道男任何信息,不可求

1+2,因为W/M=25/22所以,女的人数是25的倍数,即25,50,75……,而女小于30只可能是25,因为人数是正整数。所以男可以确定是22.

5#
发表于 2008-12-4 13:32:00 | 只看该作者
Q4: 1.08^2=1.116 so r could be smaller than 8 percent
6#
 楼主| 发表于 2008-12-5 00:48:00 | 只看该作者

Thanks to zhyyy/

And hh7920,I don't know what you mean.according to you,the right answer should be 2 is sufficient/Butthis is not the truth.Can you explain it more?

7#
发表于 2008-12-5 09:27:00 | 只看该作者

hh7920,useless,careless. Just a code of the system, where I happend to touch the percetage button.

Why B? the key is C. 1 combine 2 can solve the problem. please check. 

8#
发表于 2008-12-5 14:56:00 | 只看该作者

Q4:1.0724^2=1.15

r>1.0724并不意味着r>1.08

因此B is NOT sufficient

210/2=105

105/1000=10.5%>8%

因此A is SUFFICIENT


[此贴子已经被作者于2008-12-5 14:56:14编辑过]
9#
 楼主| 发表于 2008-12-16 00:55:00 | 只看该作者
Thank you all
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