一道数学题~~求分析~~~谢谢

wainilz520

Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers
in set S equal to the median of the numbers in set T ?
(1) The median of the numbers in set S is 0.
(2) The sum of the numbers in set S is equal to the sum of the numbers in set T.
答案是C

promiselu

S有5个连续整数， T有7个连续整数
（1） 中数是0，S{-2.-1.0.1.2}
(2)S的和是0，T的和也是0的话，T又有七个连续整数，易得T是-3到3

问两个中数是否相等，当然要两个条件啦 哈哈

uwants

Another way of solving this::==>

Let S consist of x,x+1,x+2,x+3 & x+4 integers
& T consist of y,y+1,y+2,y+3, y+4, y+5 & y+6 integers.

Now median for S = x+2
& for T = y+3.

Ques asked is :=> are they equal i.e is x+2 = y+3 ?
in other words is x-y = 1 ??

1.
Now St 1 tells us:
x+2 = 0 or x = -2.
So, nos are -2,-1,0,1 & 2.

But it tells nothing about y. So cant say if x-y = 1.
Hence Insufficient.

2.
Now St 2 says that
5x + 10 = 7y + 21
=> 5x-7y = 11
Hence cant say if x-y = 1.

3.
Now when both the statements are combined we get:
5x + 10 = 7y + 21
=> 5(x+2) = 7(y+3)
but x+2 =0
=> 0 = 7(y+3)
=> y=-3.
So now x-y = -2-(-3) = 1

hence option C is the right one!!

哈哈柚

（1）only肯定insufficient的
（2）的话设S的median为x，T的median为y，因为S、T数列为连续整数数列，所以S的sum可以表示为5x，T的sum可以表示为7y，由（2）可知，5x=7y，那么xy有无穷多组解，例如x=7 y=5， x=0 y=0
（1）+（2），由（1）可知x=0，那么由5x=7y可知，y=0
所以x=y sufficient

wainilz520

非常感谢~~~