请教八月机经 78

lindading

2.4.8.10.  x
   1.the average =median
   2. x 不於16
参考答案：A

calista5133:答案为E,因为符合条件的X取值可以是-4,6,16,

在这种情况下， 用什么方法对x 取值呢？ 感觉无从下手...  

horsefish

以下是引用lindading在2004-9-13 10:12:00的发言：

2.4.8.10.  x
   1.the average =median
   2. x 不於16
参考答案：A

calista5133:答案为E,因为符合条件的X取值可以是-4,6,16,

在这种情况下， 用什么方法对x 取值呢？ 感觉无从下手...  

从median入手

tiger1234

2.4.8.10.  x
   1.the average =median
   2. x 不於16
1) the average = median => ( 2 + 4 + 8 + 10 + x) / 5 = the median => (24 + x) / 5 = the median

okay, now, let's take a look at which numbers can be the median:

1) if x >= 8, then 8 is the median, if this is the case, then 24 + x = 40 => x = 16

2) if 4 < x < 8, then x is the median, if this is the case, then 24 + x = 30 => x = 6

3) if x <= 4, then 4 is th emedian, if this is the case, then 24 + x = 20 => x = -4

thus 1) by iself is not sufficient to know what x is;

2) x is not 16

of course, this by itself is not sufficient

1) and 2) together: since x could be -4, 6, or 16, by knowing x != 16 is still not sufficient to know x is -4 or 6, thus 1) and 2) together are not sufficient

thus the answer is E

lindading

多谢tiger 这么 详尽的解释， 对我这种数学菜鸟特别有帮助。