AnkitK wrote:
5 pieces of wood have an average length of 124 cm and a median of 140 cm .what is the maximum possible length in cm of the shortest piece of wood?
A.90
B.100
C.110
D.130
E.140
It is a nice question, a GMAT type question i.e. fun to work out, can be reasoned out fairly quickly but needs you to think a little. Follow my train of thought here (which finally takes just a few seconds when you start doing it on your own)
First thing that comes to mind - Median is the 3rd term out of 5 so the lengths arranged must look like:
___ _____ 140 _______ __________
The mean is given and I need to maximize the smallest number. Basically, it should be as close to the mean as possible. Which means the greatest number should be as close to the mean as possible too.
If this doesn't make sense, think of a set with mean 20:
19, 20, 21 (smallest number very close to mean, greatest very close to mean too)
10, 20, 30 (smallest number far away, greatest far away too)
Using the same logic, lets make the greatest number as small as possible. The two greatest numbers should both be at least 140 (since 140 is the median)
___ _____ 140 140 140
Since the mean is 124, the 3 greatest numbers are already 16 each more than 124 i.e. total 16*3 = 48 more than the mean. So the two smallest numbers should be a total of 48 less than mean, 124. To make the smallest number as great as possible, both the small numbers should be 24 each less than the mean i.e. they should be 100.
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