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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]

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28 Jan 2008, 15:29
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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?
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Re: GMATprep : Height of the tree [#permalink]

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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?

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]

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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?

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]

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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?

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]

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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?

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]

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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?

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]

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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?

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]

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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?

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

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