gmatprep ps

[maolivie]

5 pieces of wood with an average of 124 cetimeters and a medium length of 140 centimeters.What is the maximum possible length of the shortest piece of wood?
1- 90
2- 100
3- 110
4- 130
5- 140

OA is B

[jayhawk2001]

I'm guessing it is "median" and not "medium" that is 140.

Let the sizes of the 5 pieces of wood be as below in increasing length

a b 140 c d

For max value of a : c = d = median = 140 and a=b

a+b+c+d+140 = 124*5

a+b = 200
2a = 200, a = 100

Hence B

[maolivie]

that is what confused me, why would c and d have to equal 140 as well? Can't C equal 150, and D equal 160 thus making a even smaller?

[jayhawk2001]

that is what confused me, why would c and d have to equal 140 as well? Can't C equal 150, and D equal 160 thus making a even smaller?

We are asked to find the "maximum possible" length of the shortest piece
of wood i.e. maximum value of a. If c and d are > 140, a will reduce and
hence will not be the max value.

[maolivie]

ahhh, thanks for clarifying. I read the problem like an idiot since I saw "shortest" next to maximum...

Thanks again Jay