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

Answer: D

Source: GMAT Paper Tests

## When a certain tree was first planted, it was 4 feet tall and the height of the tree increased by a constant amount each

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Height of tree on day 0 = 4Vincen wrote: ↑Thu Apr 15, 2021 10:36 amWhen 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

Answer: D

Source: GMAT Paper Tests

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