Problem Solving

A step by step approach for this please :

Five 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

Ans b

five pieces of wood with an average make up the total wood length --> w1+w2+w3+w4+w5=124*5
the median length is w3 in the set {w1+w2+w3+w4+w5} and w3=140, find the shortest piece of wood-?
if we take three values from the right side, namely w5,w4,w3 and keep them equal to 140 median length, then we are left with w1 and w2 of which total length should be equal to (124*5 -140*3)=200. Now we can calculate w1 and w2 as being equal to 100. This must be an official answer, BUT I certainly would prefer choice A to make distinction between two short pieces and make the ONE shortest as 90

IOM B

tito1545 wrote:A step by step approach for this please :

Five 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

Ans b

tito1545 wrote:A step by step approach for this please :

Five 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

Ans b

Whenever you're given an average, determine the sum.

Sum = (number of things) * (average) = 5 * 124 = 620.
Median = 140 centimeters.

Let's call the 5 pieces, from shortest to longest: w, x, 140, y, z.

Since we want to maximize w, we need to minimize y and z. Let y=140 and z=140.

Thus, the 5 pieces are: w, x, 140, 140, 140.

Thus, w+x = 620 - 3*140 = 200.

Now we can plug in the answer choices for w (the shortest piece of wood). Since the median is 140, and the average is 124, w and x must each be less than 124. Eliminate D and E.

Answer choice C: w=110
If w =110, then x = 200-110 = 90. Doesn't work because x cannot be less than w.
Eliminate C.

Answer choice B: w=100
If w=100, then x = 200-100 = 100. This works. The 5 pieces will be 100, 100, 140, 140, 140.

The correct answer is B.