GMAT Prep #2 Quant help!

[casalily]

So I did the GMAT Prep #2 yesterday and this question has been messing with my head every since. I'm not sure if I'm not seeing it right but I have no clue how they managed to get to the answer at all. I happen to be reviewing the questions before my exam (tomorrow) and I can't seem to solve this one.

So the question goes as follows:
When a certain tree was first planted, it was 4 ft 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?
The correct answer is 2/3

My logic:
each year increase: x
If the plant was 4 ft the first year, then 6th year = 4 + 5x (as 2nd year - x, 3rd year - 2x, 4th year - 3x etc.) and 4th year = 4 + 3x
The different between both years = 1/5
So 6th - 4th = 2x
Therefore, 2x =1/5
and x = 1/10

I have been thinking and re-thinking but I have no clue how else to solve it. I'm clearly missing something obvious. Any ideas where I'm going wrong?

[Brent@GMATPrepNow]

When a certain tree was first planted, it was 4 ft 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?
The correct answer is 2/3

My logic:
each year increase: x
If the plant was 4 ft the first year, then 6th year = 4 + 5x (as 2nd year - x, 3rd year - 2x, 4th year - 3x etc.) and 4th year = 4 + 3x
The different between both years = 1/5
So 6th - 4th = 2x
Therefore, 2x =1/5
and x = 1/10

I have been thinking and re-thinking but I have no clue how else to solve it. I'm clearly missing something obvious. Any ideas where I'm going wrong?

You were on the right track. Just one small problem, which I highlighted above in blue.

Height of tree day 0 = 4
Let d be the increased height 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

We are told that 4+6d is 1/5 greater than 4+4d
In other words 4+6d = (4+4d) + 1/5(4+4d)
or 4+6d = 6/5(4+4d)
Multiply both sides by 5 and (to eliminate fractions) and solve for d to get d=2/3

Cheers,
Brent

[casalily]

I can see where I went wrong - I think I was looking at the question as the difference between 6th and 4th year was equal to 1/5.
The wording of the question is throwing me off still because it says the 6th year is 1/5 greater than the 4th year and have expressed that as 6th year = (4+4d) +1/5(4+4d) so it wouldn't be right to say 6th year = (4+4d) = (1/5), yes?
So the logic behind it is that you know it's 1/5 greater but since you don't know the value of the 4th itself (namely, a number), you need to add 4th year + 1/5(4th year) - am I following it correctly?

Thanks a lot for the prompt response!