2. 外语
  3. If x＜y＜z and y-x＞5．where x is an even integer and y and z are odd integers，what is the least possible value of z-x?

If x＜y＜z and y-x＞5．where x is an even integer and y and z are odd integers，what is the least possible value of z-x?

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问题 If x＜y＜z and y-x＞5．where x is an even integer and y and z are odd integers，what is the least possible value of z-x?
选项 A、6
B、7
C、8
D、9
E、10
答案D
解析 Since y - x > 5, it follows that y must be one of the integers
x + 6, x + 7, x + 8, x + 9,...
Also, because x is even and y is odd, y cannot be an even integer added to x, and thus y must be one of the integers
x + 7，x + 9，x+ 11,，x+13,...
Since z > y and both y and z are odd integers, it follows that z must be one of the integers
y + 2, y + 4, y + 6, y+8, ...
Therefore, the least possible value of z - x occurs when y is 7 greater than x and z is 2 greater than y, which implies that z is 7 + 2 = 9 greater than x.
The correct answer is D.
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