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When a certain tree was first planted, it was 4 feet tall,

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When a certain tree was first planted, it was 4 feet tall, [#permalink] New post 28 Jan 2008, 15:29
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 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?


Could you please explain in detail?
:P
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Re: GMATprep : Height of the tree [#permalink] New post 28 Jan 2008, 18:03
GHIBI 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 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?


Could you please explain in detail?
:P


Detailed answer.

annual fixed length: x
length when planted: 4

year 1: 4+x
year 2: 4+2x
year 3: 4+3x
year 4: 4+4x
year 5: 4+5x
year 6: 4+6x

so (4+6x)=4+4x+(4+4x)/5
(4+6x)*5=24+24x
20+30x=24+24x
6x=4
x=2/3
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Re: GMATprep : Height of the tree [#permalink] New post 28 Jan 2008, 18:15
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GHIBI 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 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?


Could you please explain in detail?
:P


The tree's growth is an arithmetic sequence since the growth is constant.

a(n) = a0 + nd, where d is the difference we are looking for and a0 = 4

a(6) = 4 + 6d and a(4) = 4 + 4d, and we know that a(6) = 1.2a(4)

4 + 6d = 1.2(4 + 4d) ---> 1.2d = 0.8 ---> d = 2/3 ft or 8 inches growth per year
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Re: GMATprep : Height of the tree [#permalink] New post 28 Jan 2008, 18:23
GHIBI 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 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?


Could you please explain in detail?
:P


original height of tree = 4 feet
height gained in the past 6 years = 1/5th of the original height
= (1/5) * 4 feet
= 0.8 feet
height gained EACH YEAR = 0.8 / 6 = 0.133 feet
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Re: GMATprep : Height of the tree [#permalink] New post 28 Jan 2008, 19:44
incognito1 wrote:
GHIBI 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 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?


Could you please explain in detail?
:P


original height of tree = 4 feet
height gained in the past 6 years = 1/5th of the original height
= (1/5) * 4 feet
= 0.8 feet
height gained EACH YEAR = 0.8 / 6 = 0.133 feet


It's gained 1/5 of the height from year 4 to year 6, not from year 0 to year 6.
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Re: GMATprep : Height of the tree [#permalink] New post 28 Jan 2008, 20:32
sonibubu wrote:
incognito1 wrote:
GHIBI 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 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?


Could you please explain in detail?
:P


original height of tree = 4 feet
height gained in the past 6 years = 1/5th of the original height
= (1/5) * 4 feet
= 0.8 feet
height gained EACH YEAR = 0.8 / 6 = 0.133 feet


It's gained 1/5 of the height from year 4 to year 6, not from year 0 to year 6.


sonibubu, you're right -- it's comparing 6th year to 4th year, so an arithmetic sequence was required
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Re: GMATprep : Height of the tree [#permalink] New post 29 Jan 2008, 19:05
Agree with Ravshonbek. 2/3 is the answer.

Starts at 4ft
year 1 4+n
year 2 4+n+n
year...

Two equations...
4+4n =x
4+6n = 1/5x + x

Solve for n. n = 2/3
Ravshonbek wrote:
GHIBI 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 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?


Could you please explain in detail?
:P


Detailed answer.

annual fixed length: x
length when planted: 4

year 1: 4+x
year 2: 4+2x
year 3: 4+3x
year 4: 4+4x
year 5: 4+5x
year 6: 4+6x

so (4+6x)=4+4x+(4+4x)/5
(4+6x)*5=24+24x
20+30x=24+24x
6x=4
x=2/3
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Re: GMATprep : Height of the tree [#permalink] New post 30 Jan 2008, 10:13
GHIBI 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 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?


Could you please explain in detail?
:P



4+6x=1.2(4+4x) --> 1.2 --> 12/10 --> 6/5

4+6x=24/5+24/5x --> 20+30x=24+24x --> 6x=4 ---> x=2/3
Re: GMATprep : Height of the tree   [#permalink] 30 Jan 2008, 10:13
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