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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
When a certain tree was first planted, it was 4 feet tall and the heig
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20 Sep 2021, 04:58
20 Sep 2021, 04:58
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When a certain 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 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?
A. 3/10
B. 2/5
C. 1/2
D. 2/3
E. 6/5
A. 3/10
B. 2/5
C. 1/2
D. 2/3
E. 6/5
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: When a certain tree was first planted, it was 4 feet tall and the heig
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20 Sep 2021, 05:06
20 Sep 2021, 05:06
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GeminiHeat wrote:
When a certain 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 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?
A. 3/10
B. 2/5
C. 1/2
D. 2/3
E. 6/5
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
At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year
In other words, 6th year height = 4th year height + 1/5(4th year height)
Or we can write 4 + 6d = (4 + 4d) + 1/5(4 + 4d)
Simplify: 4 + 6d = 6/5(4 + 4d)
Multiply both sides by 5 to get: 5(4 + 6d) = 6(4 + 4d)
Expand: 20 + 30d = 24 + 24d
Simplify: 6d = 4
d = 4/6 = 2/3 = D
Cheers,
Brent
gmatclubot
Re: When a certain tree was first planted, it was 4 feet tall and the heig [#permalink]
20 Sep 2021, 05:06
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