题目信息
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 ?
A:6
B:7
C:8
D:9
E:10
参考答案及共享解析
共享解析来源为网络权威资源、GMAT高分考生等； 如有疑问，欢迎在评论区提问与讨论
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已选答案：
正确答案：
D:9
Algebra Inequalities
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.
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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