请问2006年5月机经32题

MichelleZhang · 发表于 2006-5-23 04:28:00

32.有由2－30里面所有质数组成的集合，P是这个集合里面所有数的乘积再加1,问哪个是must be true
有i（忘了）ii，p有大于30的质数因子，iii，p可以被30整除；这个我不会做

是不是所有质数相乘，如果没有2，就是单数，那样+1就是复数。这题里面有2，所以相乘的积就是复数，那样+1以后就是单数，所以III一定不对。 II呢？怎样确定呢？

请教教我。谢谢！！！

yaoyao99 · 发表于 2006-5-23 04:31:00

Bad answer.. deleting it as it's extremely misleading...

[此贴子已经被作者于2006-5-23 13:09:30编辑过]

MichelleZhang · 发表于 2006-5-23 12:01:00

Oh..soga..原来是这样，那就是说， 2-30所有prime number相乘的积也不会有大于30的prime factor了。那样，+1会对这个结果有影响吗？谢谢yaoyao99~!!!

sesky · 发表于 2006-5-23 12:28:00

感觉是由得 +{2 .3 .5} 2x3X5+1=31

yaoyao99 · 发表于 2006-5-23 13:09:00

Oh oops, you're right. +1 can make all the difference in the world. For example 2*3 + 1 will have a prime factor of 7. and 2*5 +1 will have a prime factor of 11.

Ok after a quick google search, it's actually Euclid's theorems..

http://mathworld.wolfram.com/EuclidsTheorems.html

Let me read it and come back to summarize, heehee...

sesky · 发表于 2006-5-23 13:11:00

waiting for you

yaoyao99 · 发表于 2006-5-23 13:24:00

Ok here's a quick summary

If P is a prime number then of course P is greater than 30.

If P is a product of prime numbers and has no prime factor greater than 30, then one of its prime factors, say x, must be a prime between 2 and 30, and is also a factor of P-1 (product of 2, 3... 29).

Here's the tricky part. Any number that's a factor of Y and Z is also a factor of Z - Y.

That means x is a factor of 1 => impossible => x has to be greater than 30.

I think it's time for a drink, haha

MichelleZhang · 发表于 2006-5-23 13:56:00

wow~!太谢谢了。。。不过看了有点晕，。特别是最后两句：

Here's the tricky part. Any number that's a factor of Y and Z is also a factor of Z - Y.

That means x is a factor of 1 => impossible => x has to be greater than 30.

我再看看明白。反正答案是II 对 III不对，是吧？先把答案记住了。

谢谢yaoyao99!

yaoyao99 · 发表于 2006-5-23 14:07:00

Let P = 2*3*5...*29 + 1 and Q = P - 1
the earlier part explains that x has to be a prime factor of both P and Q

the tricky part is "x is also a prime factor of P - Q" (just remember this rule) => x is a factor of 1 => the assumption that P has no prime factor > 30 is wrong => II is wrong

水色 · 发表于 2006-5-23 18:29:00

“http://forum.chasedream.com/dispbbs.asp?BoardID=22&ID=170599&replyID=&skin=1

32. 有由2－30里面所有质数组成的集合，P是这个集合里面所有数的乘积再加1,问哪个是must be true有i（忘了）ii，p有大于30的质数因子，iii，p可以被30整除；这个我不会做

【讨论】P＝{2,3,5,7,11,13,17,19,23,29}

因为2*3*5=30因此所有因子相乘可以被30整除，但是＋1后不能被30整除，所以iii可以排除。

记得好像是质因子的乘积为偶数时+1=质数，因此ii是正确的。”

再次确认一些II和III都是错误的？？？（不好意思，偶还是不大懂。明天上考场，打算先背了再说）

[此贴子已经被作者于2006-5-23 18:29:11编辑过]

请问2006年5月机经32题

请问2006年5月机经32题

所属分类: GMAT考试

正在浏览此版块的会员 ()

浏览过的版块