5 pieces of wood have an average (arithmetic mean) 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?
A. 90
B. 100
C. 110
D. 130
E. 140
Answer: B
Answer: B
Shortest to Longest length ---- L1, L2, L3 = 140, L4, L5
L1 + L2 + 140 + L4 + L5 = 5 * 124
For L1 to be the maximum, L4 and L5 should be minimum
L1 + L2 + 140 + L4 + L5 = 5 * 124
For L1 to be the maximum, L4 and L5 should be minimum
L1=L2
Thus, L1 + L2 = (5*124) - (140*3) = 620 - 420 = 200
Hence L1 = L2 = 100 Thus, L1 + L2 = (5*124) - (140*3) = 620 - 420 = 200
