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When a certain tree was first planted, it was 4ft tall, and

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When a certain tree was first planted, it was 4ft tall, and [#permalink] New post 30 May 2008, 04:47
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When a certain tree was first planted, it was 4ft tall, and the height of the tree increased by a constant amount each year for the next 6 yrs. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many ft. did the height of the tree increase each year?
A) 3/10
B) 2/5
C) 1/2
D) 2/3
E) 6/5

OA is D, please show me how you solve this problem!
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Re: GMATPrep PS [#permalink] New post 30 May 2008, 06:28
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Re: GMATPrep PS [#permalink] New post 30 May 2008, 07:51
Initial tree height - 4 ft
It grows at constant growth rate for next 6 years, say X ft/year
At the end of 1 year, the tree height will be - 4 + X ft
2 year - 4 + 2X ft
3 year - 4 + 3X ft
4 year - 4 + 4X ft
5 year - 4 + 5X ft
6 year - 4 + 6X ft

At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year
So, the difference in height between 6th year and 4th year is 1/5 the height of 4th year (4+4X ft)
6th year height - 4th year height = 1/5(4th year height)
(4+6X) - (4+4X) = 1/5(4+4X)
2X = 1/5(4+4X)
10X = 4+4X
6X = 4
X = 2/3
So, growth per year - 2/3 ft
Re: GMATPrep PS   [#permalink] 30 May 2008, 07:51
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