BTGmoderatorLU wrote:**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 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. 2/3

E. 6/5

Let x = the yearly increase.

Height after 4 years = 4 + 4x.

Height after 6 years = 4 + 6x.

At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year.

The phrase in red implies the following:

The height in the 6th year was 6/5 of the height in the 4th year.

Since the height in the 6th year was 6/5 of the height in the 4th year, we get:

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

20 + 30x = 24 + 24x

6x = 4

x = 4/6 = 2/3.

The correct answer is

D.

An alternate approach is to plug in the answers, which represent the increase each year.

When the correct answer choice is plugged in, (6th-year height)/(4th-year height) = 6/5.

Answer choice D: 2/3

Height after 4 years = 4 + 4(2/3) = 20/3.

Height after 2 more years = 20/3 + 2(2/3) = 24/3.

(6th-year height)/(4th-year height) = (24/3) / (20/3) = 24/20 = 6/5.

Success!

The correct answer is

D.

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