When a certain tree was first planted, it was 4 feet tall and the height of the tree increased by...

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Sat Feb 01, 2020 7:49 am

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. At the end of 6 years, the tree was 1/5 taller then it was at the end of 4 years. By how many feet did the height of the tree increase each year?

A. 3/10
B. 2/5
C. 1/2
D. 3/2
E. 6/5

OA D

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

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: 2/3