Five pieces of wood have an average arithmatic mean length

[Shib]

Source:PowerPrep

Five pieces of wood have an average arithmatic mean length of 124 cms and a median length of 140 cms.What can be the maximum possible length in cms of the shortest piece of wood?

a.90
b.100
c.110
d.130
e.140

[GMAT 2007]

Mean of the length of five pieces = 124 So total length = 124*5 = 620.

Median = 140, so the length of rest of the 4 pieces = 620 - 140 = 480

Assume the 5 pieces in ascending order be X1 X2 140 X3 X4 where X1 is the shortest.

For X1 to be maximum, X3 and X4 has to be minimum but keep in mind the median has to be 140.

The minimum possible values of X3 and X4 could be 140, hence the X1+X2 = 620 - 420 = 200. Distribute 200 among X1 and X2, the maximum possible value of X1 = 100 So the length of five pieces would be

100, 100, 140, 140, 140. The answer is (B)

GMAT 2007

[StaceyKoprince]

Very nice, both logic and explanation, GMAT 2007

[raman2072]

How can 2 pieces of wood have the "shortest" length?
--Ramesh

[gokul_nair1984]

How can 2 pieces of wood have the "shortest" length?

In a test 3 students got the following marks :10,10,20.
what is the lowest score awarded?- 10
How many students got the lowest score?- 2

Unless and until you are mentioned that the numbers are distinct, never assume them to be so.

[tim]

thanks, Gokul..