PREP数学提问

Becca0223

哪位大神帮忙看下这道题为何选第一个选项？
自己一个人琢磨的时候硬是琢磨不出来呀QAQ


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.

• 
  Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  
• 
  Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  
• 
  BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  
• 
  EACH statement ALONE is sufficient.
  
• 
  Statements (1) and (2) TOGETHER are NOT sufficient.
  
  

安東尼尼

用條件1 xy+xz (even) 減掉題目的xy+z (odd)，
得到 xz-z = z*(x-1) (even-odd=odd)
--->可知 z=odd 與 x-1=odd
---> x=even
所以條件(1)充分

Becca0223

安東尼尼 发表于 2020-10-28 21:21:13

哇哦，豁然开朗，谢谢！

wendymai

安東尼尼 发表于 2020-10-28 20:21
用條件1 xy+xz (even) 減掉題目的xy+z (odd)，
得到 xz-z = z*(x-1) (even-odd=odd)
--->可知 z=odd 與 x-1 ...

同意！               

wendymai

昨天写prep也遇到了楼主这道道题，顺便问一下楼主下面这道题写对了吗？求问I为什么是对的~
是不是因为问题问的是could be true 而不是not be true?

If x  > y2 > z4 ,  which of the following statements could be true?

I. x > y > z
II. z > y > x
III.  x > z > y

A. I only

B. I and II only

C. I and III only

D. II and III only

E. I, II, and III (correct)