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标题: prep ds 2-166 [打印本页]

作者: haileywang    时间: 2010-10-22 06:51     标题: prep ds 2-166

166.


If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of p2t ?

(1) m has more than 9 positive factors.

(2) m is a multiple of p3.

【答案】B

【思路】

t are the only prime factors of the integer m,m沒有其他質因數,mt所組成,有可能為m=t,m=
t^2.................
(1) m has more than 9 positive factors 可知mt^9, 但無法知道和p的關係,NOT sufficient
(2) m is a multiple of p^3,pm的質因數,t are the only prime factors of the integer m,t=m, m is a multiple of p^3 ,可以写成m is a multiple of p2t,sufficient

无法理解上面那句话~~感觉前面是不是少了p and t。。。
作者: piacia    时间: 2010-10-22 20:38

不是nn,但回答一下

注意谓语的是are,表语是factors,故题意为p和t是m的唯一的两个质因子

提干:p, t为质数,m整数,p和t为m唯一质因子, 问m/(tp^2)是否为整数?
解:设x为余下因子乘积,即xpt=m,则m/(tp^2)=xpt/(tp^2)=x/p,看能否判断x/p是否为整数

1)m有多余9个的正数因子——不相关条件,显然不能判断x/p是否为整数,不充

2)m=p^3——计算m/(tp^2)=p^3/(tp^2)=p/t,p, t为质数,显然p/t不为整数,充分

答案B
作者: haileywang    时间: 2010-10-23 06:34

嗯嗯嗯。。。got it...thx




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