Woody

[Baldini]

Five pieces of wood have an average (arithmetic mean) length of 124 cm and a median of 140 cm. what is the maximum possible length, in cm, of the shortest piece of wood?

1. 90
2. 100
3. 110
4. 130
5. 140

OA is 100

How does one attain the answer?
Thx

[zephir21]

Answer 2 : 100

a<b<c<d<e the 5 lengths
Asume c=d=e=140

(140-124)*3 = 48

To get the mean equal to 124 you need max(a)=b=124-48/2=100

...

[Baldini]

Thanks for the response. But why does A=B?

When I tried to work this question out, I did A + 140 + 140 + 140 + E = 620 therefore A + E = 200. But I couldn't put a limit to A or E...

Thanks in advance

[zephir21]

Other explanation :
In order to maximize A you need to have the smallest standard deviation for your list of numbers. So you get the mean equal to :
Mean = [max(A+B)+min(C+D+E)]/5
min(C+D+E)= 140+140+140 'cause E>=D>=C=140 (so you choose E=D=C=140)

A=B 'cause you want to maximize A (as B>=A, to maximize A you need A=B)
So max(A+B)=2A

Thus (2A+140*3)/5=124
Do the math and you get A=100

I don't know if it's clear, that's how it work in my head lol