gwd 19-29

longxiaomeim

Q29:

Is the integer n odd?

(1) n is divisible by 3.

(2) 2n is divisible by twice as many positive integers as n.

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

B. Statement (2) ALONE is sufficient, 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

答案是 B, 但, 我觉的是 E

no matter n is odd or even, 2n should always have twice as many as many factors as n.

daoying

条件2是什么意思，lz能解释一下么？看不懂

luoye1

可以整除2n的正整数的个数是可以整除n的正整数的个数的2倍。

可能是这样的。

himba

应该是选B。

思路：如果整除n的正整数是k个，那么整除2n的正整数其实就是多了k个数（原来整除n的那些正整数分别乘以2）。但由于当n是偶数时，可以整除n的k个数里包括2，而2n的时候，那么整除2n的2k个数里就有两个2（把整除n的数都乘以2，得到可以整除2n的另外k个数），所以，计数时要去掉一个2，所以偶数时是不满足条件2的。反过来说，满足条件2的就是奇数。

此题要注意的是 1 也是可以整除n的一个正整数，不要忽略了这个数字。自己举几个例子，就明白了。