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Ratios

by relaxin99 » Thu Feb 26, 2009 5:21 pm
When a certain tree was first planted, it was 4 feet tall, and the height of th etree increased by a constant amount each year for the next 6 years. 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 feet did the height of the tree increase each year?

3/10
2/5
1/2
2/3
6/5

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Re: Ratios

by Brent@GMATPrepNow » Thu Feb 26, 2009 6:38 pm
relaxin99 wrote:When a certain tree was first planted, it was 4 feet tall, and the height of th etree increased by a constant amount each year for the next 6 years. 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 feet did the height of the tree increase each year?

3/10
2/5
1/2
2/3
6/5
Height of tree day 0 = 4
Let d be the increased height each year
Height of tree at the end of the 1st year = 4+d
Height of tree at the end of the 2nd year = 4+d+d = 4+2d
Height of tree at the end of the 3rd year = 4+d+d+d = 4+3d
Height of tree at the end of the 4th year = 4+d+d+d+d = 4+4d
Height of tree at the end of the 5th year = 4+d+d+d+d+d = 4+5d
Height of tree at the end of the 6th year = 4+d+d+d+d+d+d = 4+6d

We are told that 4+6d is 1/5 greater than 4+4d
In other words 4+6d = (4+4d) + 1/5(4+4d)
or 4+6d = 6/5(4+4d)
Multiply both sides by 5 and (to eliminate fractions) and solve for d to get d=2/3

The answer is D
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by krisraam » Thu Feb 26, 2009 7:44 pm
The difference in heights when it was 6 yrs and when it was 4yrs is 1/5 the height when it was 4 yrs.

let x be the growth per year.

6x -4x = 4+4x/5
x = 2/3

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by sanju09 » Wed Apr 08, 2009 5:41 am
Let x be the height of the tree increase each year, then:

[4 + 6 x - (4 + 4 x)]/(4 + 4 x) = 1/5

10 x = 4 + 4 x

x = 2/3.
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