GWD30-18

nolanchen

If k is a positive integer, is k the square of an integer?

(1)   k is divisible by 4.

(2)   k is divisible by exactly 4 different prime numbers.

                      

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficien

t, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: E

我觉得该选B啊?哪位NN指点迷津?

yaoyao99

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zhaoyak7

以下是引用nolanchen在2006-8-3 11:58:00的发言：

If k is a positive integer, is k the square of an integer?

(1)   k is divisible by 4.

(2)   k is divisible by exactly 4 different prime numbers.

                      

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficien

t, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: E

我觉得该选B啊?哪位NN指点迷津?

B不对，选E

比如420有2 ，3，5，7四个不同的质因子（当然用数字验证时可以倒着算，先找4个最小的质因子，算起来比较方便）符合条件（2），

也能被4整除，符合条件（1），

但不是某个数的平方

所以是E。

应该是的。偶现在做了一些题，错误较多，有时都影响自信心了。

chenguiwen

请问哪里可以下载GWD呀?多谢啦!

kaokai

How about K=44100 ?

44100= 210 * 210. only disvisible by 4 different prime numbrs (2,3,5,7)

so answer B is not sure, K is maybe a square of integer or not.

liubin1987

以下是引用zhaoyak7在2006-8-3 23:55:00的发言：

B不对，选E

比如420有2 ，3，5，7四个不同的质因子（当然用数字验证时可以倒着算，先找4个最小的质因子，算起来比较方便）符合条件（2），

也能被4整除，符合条件（1），

但不是某个数的平方

所以是E。

应该是的。偶现在做了一些题，错误较多，有时都影响自信心了。

前辈的讨论是有错误的,错误就在于弄错了题目的意思,题目是问是否为一个整数的平方,所以如果可以确定它不是或者确定它是都是正确的.

 我觉得同样用2,3,5,7

像前辈说的是证明了它不是一个数的平方.

同样,我们把420再平方下,那么得到的仍然是只能被四个质数:2,3,5,7所整除,而且又能被四除. 结果是个整数的平方.

正是这种不确定才说明选E.

chenhei

exactly.....强调了什么呢?

liubin1987

没看懂LS的意思...

djzt

用反证法

[此贴子已经被作者于2007-3-6 12:00:06编辑过]

kaijen

以下是引用kaokai在2006-11-10 13:22:00的发言：

How about K=44100 ?

44100= 210 * 210. only disvisible by 4 different prime numbrs (2,3,5,7)

so answer B is not sure, K is maybe a square of integer or not.

如果K=44100

這樣還符合題意 k is divisible by exactly 4 different prime numbers 嗎?

我以為只能是4個質數乘積 EX 2*3*5*7