william0625 \$m[1]: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.
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【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