height

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Tue Feb 09, 2010 7:14 am

The height of an apple tree is given by the sum of two terms. The first term is directly proportional to the weight of the tree and the second term is directly proportional to the square of the weight of the tree. The height of the tree was 6 m and 8 m, when its weight was 40 kg and 50 kg respectively. Find the approximate weight of the tree when its height was 5 m.

a 39
b 44
c 25
d 35
e 32

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Source: Beat The GMAT — Problem Solving | Tue Feb 09, 2010 7:14 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Tue Feb 09, 2010 12:09 pm

shashank.ism wrote:The height of an apple tree is given by the sum of two terms. The first term is directly proportional to the weight of the tree and the second term is directly proportional to the square of the weight of the tree. The height of the tree was 6 m and 8 m, when its weight was 40 kg and 50 kg respectively. Find the approximate weight of the tree when its height was 5 m.

a 39
b 44
c 25
d 35
e 32

h = a*w + b*w^2
6 = 40 a + 1600 b
8 = 50a + 2500 b

30 = 200a + 8000b
32 = 200a +10000b
2= 2000b
b= .001

22 = 200a
a = 0.11

Let us try 35 now

35*.11+.001*35^2 = 5.07
close enough

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