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GMAT Prep PS Question

by queenisabella » Sun Mar 11, 2012 1:13 pm
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

OA is D
Source: GMAT Prep

I got so far as to identify that the increments increased by 1/10 each year, but couldn't figure out how to translate that to feet.
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by Mike@Magoosh » Sun Mar 11, 2012 4:06 pm
Hello. I'll help with this. :)

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.

So, at the end of the nth year (n = 1, 2, . . . 6), the height in feet of the tree was

h(n) = 4 + nd, where d is the unknown amount of growth each year.

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

h(4) * (1 + 1/5) = h(6)

(4 + 4d)*(6/5) = 4 + 6d

Multiply both sides by 5 to clear the fraction

(4 + 4d)*6 = (4 + 6d)*5
24 + 24d = 20 + 30 d
subtract 20 from both sides
4 + 24d = 30d
subtract 24d from both sides
4 = 6d
4/6 = 2/3 = d

The tree grows 2/3 of a foot each year. Answer = D

Alternate Method:
growth in two years = (1/5) of height at year 4
2d = (1/5)*(4 + 4d)
Multiply by 5
10d = 4 + 4d
6d = 4
d = 4/6 = 2/3

Here's a somewhat related PS question, for further practice.

https://gmat.magoosh.com/questions/67

When you submit an answer to that question, it will be followed by a page with a video explanation.

Does all of this make sense? Please let me know if you have any further question on what I've done here.

Mike :)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
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by Anurag@Gurome » Sun Mar 11, 2012 7:54 pm
queenisabella wrote: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

OA is D
Source: GMAT Prep

I got so far as to identify that the increments increased by 1/10 each year, but couldn't figure out how to translate that to feet.
Let the height by which the tree increased constantly each year be x ft.
At the end of the 1st year, height of tree = 4 + x
At the end of the 2nd year, height of tree = 4 + 2x
...
At the end of the 6th year, height of the tree = 4 + 6x
It is 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, so 4 + 6x = (1 + 1/5) * (4 + 4x)
Solving, we get, 20 + 30x = 24 + 24x
6x = 4
x = 2/3

The correct answer is D.
Anurag Mairal, Ph.D., MBA
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