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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- Brent@GMATPrepNow
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Height of tree day 0 = 4relaxin99 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
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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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.
[4 + 6 x - (4 + 4 x)]/(4 + 4 x) = 1/5
10 x = 4 + 4 x
x = 2/3.
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Sanjeev K Saxena
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The Princeton Review - Manya Abroad
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