Bunuel wrote:
Five logs of wood have an average length of 100 cm and a median length of 116 cm. What is the maximum possible length, in cm, of the shortest piece of wood?
(A) 50
(B) 76
(C) 84
(D) 96
(E) 100
Kudos for a correct solution.
in order to maximize the shortest piece of wood, we need to minimize the longest ones.
suppose we have 3 logs with a length of 116. in this case, the median is 116 too.
116 * 3 = 348.
since average of 5 is 100, the sum of the five must be 500.
500-348 = 152.
to have the maximum value for first one, we need to have first two of the same length...152/2=76.
maximum possible value for the shortest log is 76. B