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by B166418 » Sun Nov 25, 2012 8:42 am
When a tree was first planted ,it was 4 feet tall ,and the height of the tree increased by a constant amount each year for the next 6 years .At the end of 6th year ,the tree was 1/5 taller than it was end of the 4th year .By how many feet did the height of tree increase each year

3/10
2/5
1/2
2/3
6/5
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by Brent@GMATPrepNow » Sun Nov 25, 2012 9:08 am
B166418 wrote:When a tree was first planted ,it was 4 feet tall ,and the height of the tree increased by a constant amount each year for the next 6 years .At the end of 6th year ,the tree was 1/5 taller than it was end of the 4th year .By how many feet did the height of tree increase each year

A) 3/10
B) 2/5
C) 1/2
D) 2/3
E) 6/5
Height of tree on day 0 = 4
Let d = the height increase 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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Brent
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by GMATGuruNY » Mon Nov 26, 2012 4:13 am
B166418 wrote:When a tree was first planted ,it was 4 feet tall ,and the height of the tree increased by a constant amount each year for the next 6 years .At the end of 6th year ,the tree was 1/5 taller than it was end of the 4th year .By how many feet did the height of tree increase each year

3/10
2/5
1/2
2/3
6/5
An alternate approach is to plug in the answer choices, which represent the yearly height increase.

Answer choice C: 1/2
Height after 4 years = 4 + 4(1/2) = 6.
Height after 6 years = 6 + 2(1/2) = 7.
(difference between the two heights)/(height after 4 years) = (7-6)/6 = 1/6.
Since the height must increase by 1/5 -- a value GREATER than 1/6 -- a greater answer choice is needed.

Answer choice D: 2/3
Height after 4 years = 4 + 4(2/3) = 20/3.
Height after 6 years = 20/3 + 2(2/3) = 24/3.
Since the two fractions have the same denominator, we can use the numerators to determine by what fraction the height here has increased:
(difference between the two heights)/(height after 4 years) = (24-20)/20 = 4/20 = 1/5.
Success!

The correct answer is D.
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