swerve 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
The OA is D
Source: GMAT Prep
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. Since we know that the growth is by a constant amount, we have a linear growth problem. Thus, we can let x = the yearly growth amount in feet:
Starting height = 4
Height after year one = 4 + x
Height after year two = 4 + 2x
Height after year three = 4 + 3x
Height after year four = 4 + 4x
Height after year five = 4 + 5x
Height after year six = 4 + 6x
We are also given that at the end of the 6th year the tree was 1/5 taller than it was at the end of the 4th year. This means the height of the tree at the end of the 6th year is 6/5 times as tall as its height at the end of the 4th year. Thus, we can create the following equation:
(6/5)(4 + 4x) = 4 + 6x
To eliminate the fraction 6/5, we multiply the entire equation by 5:
6(4 + 4x) = 20 + 30x
24 + 24x = 20 + 30x
6x = 4
x = 4/6 = 2/3 feet
Answer: D
