Median of their weights

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kulksnikhil: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Tue May 23, 2006 3:35 pm; Location: Seoul, Korea; Thanked: 2 times

Median of their weights

by kulksnikhil » Mon Nov 27, 2006 3:47 am

Question is not gramatically correct... but it is understandable..

500 birds, 75% is lighter than 134g. 60% of the birds heavier than 100g is heavier than 134g. What is the median of their weights?

Can anybody help me solve this?

Answer could be 92

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Source: Beat The GMAT — Problem Solving | Mon Nov 27, 2006 3:47 am

gmat_enthus: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed Oct 18, 2006 1:49 pm; Thanked: 1 times

Re: Median of their weights

by gmat_enthus » Mon Nov 27, 2006 7:12 am

kulksnikhil wrote:Question is not gramatically correct... but it is understandable..

500 birds, 75% is lighter than 134g. 60% of the birds heavier than 100g is heavier than 134g. What is the median of their weights?

Can anybody help me solve this?

Answer could be 92

Let there be three ranges:
w<100
100<w<134
134<w

Let the total greater than 100 be x

Given for greater than 100, 60% of them are greater than 134 =>
100<w<134 = 0.4x
w>134 = 0.6x

Let the total weights be T.
Given that 0.75% of T is less than 134 => 25% of T is > 134
=> 0.6x=0.25T => T=2.4x

In terms of x total weights = 2.4x. so the median will the weight at at 1.2x [approaximately]

In terms of x, the distribution is:
w<100 -> 1.4x
100<w<134 -> 0.4x
134<w -> 0.6x

So the median will lie in the range x<100

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