PREP DS1 167

Julie1125

prep DS1 167

感觉求解思路非常复杂，是不是已经高出考试要求了？

167.  16626-!-item-!-187;#058&010859   ??

If x, y, and z are integers and xy + z is an odd integer, is x an even integer?

 

(1) xy + xz is an even integer.

 

(2) y + xz is an odd integer.

--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】A

 

【思路】xy + z = odd integer , xy(odd)+z(even)= odd integer , xy(even)+z(odd)=odd integer

  (1) xy + xz = even , xy(even)+xz(even)=even , so z 應該為odd , x為even , xz才為even , xy(odd)+xz(odd)=even ,

z 為even , xz不等於odd , 充份

  (2) y + xz = odd integer , y(odd)+xz(even)=odd , z=even ,x=even , y(even)+xz(odd)=odd ,z=odd,x=odd , 所以不充份