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
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