PREP模考一题

evelyn205205

5 pieces of wood have an average length of 124 centimeters and a median length of 140 centimeters. What is the maximum possible length, in centimeters, of the shortest piece of wood?

ANSWER: 100

怎么算啊，这道题？
求指教拉~

sdcar2010

Total length = 5* 124 = 620

If you want the shortest piece as long as possible, you need the longest piece as short as possible.  But those long pieces cannot be shorter than 140.  So let them be 140!!! What you got is 3 pieces at 140.  
620 - 3*140 = 200
That leaves 200 for the shorter two pieces.  Let each of the two shorter pieces be 100, so that we can have the maximum possible length for the shortest piece.

poseidonxiang

因为只有五个数，中间数是140，平均数124，小于中间数，所以要让最小的数最大，那么只能让最大的三个数都为140，可以保证五个数的中间数为140。
平均数124，五个数的和为620，后三个数为140×3=420，那么前两个数和为200。要让最小的数最大，那么只能让前面两个数相等，因此最小的数最大的可能性为100。