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

[AAPL]

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

[jbryant62]

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

This is a sequence problem. Let X represent the annual tree growth.
year 0 the tree is 4ft.

Subsequent years
1. 4+x
2. 4+2x
3. 4+3x
4. 4+4x
5. 4+5x
6. 4+6x

The amount of growth at year 6 is equal to 6/5 of the growth at year 4. Set year 6 equal to year 4

4+6x=6/5(4+4x)

multiply both sides by5

5(4+6x)=6(4+4x)

20+30x=24+24x

subtract 24x and 20 from both sides
6x=4

divide both sides by 6
x=4/6

simplify

x=2/3

[Scott@TargetTestPrep]

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