prep-ds2-21

[william0625]

21. 1407-!-item-!-187;#058&000929
Is the integer n odd?

(1) n is divisible by 3.

(2) 2n is divisible by twice as many positive integers as n.
--------------------------------------------------------------------------------------------------------------------------------------------------------
【答案】B

可以解釋一下(2)嗎
和怎樣推演

[leafage]

21. 1407-!-item-!-187;#058&000929
Is the integer n odd?

(1) n is divisible by 3.

(2) 2n is divisible by twice as many positive integers as n.
--------------------------------------------------------------------------------------------------------------------------------------------------------
【答案】B

可以解釋一下(2)嗎
和怎樣推演

(2) 2n is divisible by twice as many positive integers as n. -> 2n可以被比n多一倍的正整數整除
假設n=axbxc且abc為質數，則n的因數個數=(1+1)(1+1)(1+1)=8
2n=2xaxbxc(且2不等於a,b,c)，則2n的因數個數=(1+1)(1+1)(1+1)(1+1)=16
若a,b,c有一個為2的話，則2n=2x2xbxc，因數個數=(2+1)(1+1)(1+1)=12

換句話說，也就是n的因數當中不能夠有2，如果有2的話，2n的因數個數就不會是n的兩倍
所以(B)是sufficient的

可參考http://www.beatthegmat.com/is-integer-n-odd-t11618.html