BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

apple

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 1022
Joined: Mon Jul 20, 2009 11:49 pm
Location: Gandhinagar
Thanked: 41 times
Followed by:2 members

apple

by shashank.ism » Tue Feb 09, 2010 1:19 pm
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.


39
44
25
35
32
My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 777
Joined: Fri Jan 01, 2010 4:02 am
Location: Mumbai, India
Thanked: 117 times
Followed by:47 members

by komal » Tue Feb 16, 2010 11:59 am
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.


39
44
25
35
32
H = 8 ===> W = 50
H = 6 ===> W = 40
H = 5 ===> some quantity moderately less than 40 (39 is too close)
Hence 35 is the correct answer
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 241
Joined: Wed Jan 27, 2010 10:10 pm
Location: Chennai
Thanked: 23 times
Followed by:2 members
GMAT Score:690

by sars72 » Tue Feb 16, 2010 12:18 pm
h=a+b
a=kw
b=jw^2

h=6, w = 40
-> a+b = 6, w = 40
-> kw+jw^2 = 6 -> 40k + 1600j = 6 ............1

h=8, w = 50
-> 50k + 2500j = 8.............2

multiplying eqn 1 by 5 and eqn 2 by 4
--> 200k+8000j=30.......1
200k+10000j =32.....2

subtracting -> -2000j=-2 -> 1000j=1--> j = 1/1000

--> 50k = 8-2500/1000 = 8-2.5 = 5.5 --> k = 5.5/50 = 0.11

--> when height = 5 --> a+b = 5
-> 0.11w+(1/1000)w^2=5
-> w^2 + 110w - 5000 = 0

[-110 +- root(110^2 - 4*1*-5000)]/2

=[-110+root(12100 + 20000)]/2

root of 32100 is approx 180 since 180^2 = 32400

-> (-110+-180)/2 --> h = 35 or h=-145

since height cannot be negative, the answer is h = 35
Top
Post new topic Post Reply
• Page 1 of 1