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# When a certain tree was planted, it was 4ft tall, and the

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When a certain tree was planted, it was 4ft tall, and the [#permalink]  18 Dec 2005, 18:06
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When a certain tree was planted, it was 4ft tall, and the height of the tree increased by a constant amount each year for 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

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Re: GMATPREP - PS Question [#permalink]  18 Dec 2005, 19:22
novase101 wrote:
When a certain tree was planted, it was 4ft tall, and the height of the tree increased by a constant amount each year for 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

Planted ==> 4 ft
1st year ==> 4 + x
2nd year ==> 4 + x +x ==> 4 + 2x
..
...
4th year ==> 4 + 4x
6th year ==> 4 + 6x

(6/5)(4+4x) = (4+6x)
x = 2/3
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Re: GMATPREP - PS Question [#permalink]  18 Dec 2005, 19:33
[quote="TeHCM

Planted ==> 4 ft
1st year ==> 4 + x
2nd year ==> 4 + x +x ==> 4 + 2x
..
...
4th year ==> 4 + 4x
6th year ==> 4 + 6x

(6/5)(4+4x) = (4+6x)
x = 2/3[/quote]

how do you get the 6/5? I'm confused here..
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Re: GMATPREP - PS Question [#permalink]  18 Dec 2005, 19:54
strange wrote:
TeHCM wrote:

Planted ==> 4 ft
1st year ==> 4 + x
2nd year ==> 4 + x +x ==> 4 + 2x
..
...
4th year ==> 4 + 4x
6th year ==> 4 + 6x

(6/5)(4+4x) = (4+6x)
x = 2/3

how do you get the 6/5? I'm confused here..

1/5 taller does not mean 1/5 feet taller

I'm twice as tall as you does not mean I'm 2 feet taller than you.

6/5 means 1/5 more than x
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Re: GMATPREP - PS Question [#permalink]  18 Dec 2005, 22:56
novase101 wrote:
When a certain tree was planted, it was 4ft tall, and the height of the tree increased by a constant amount each year for 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

The sequence is {4,4+x,4+2x,4+3x,4+4x,4+5x,4+6x}
Given that ht in 6th year = ht in 4th year + 1/5(ht in 4th year),
=>(4 + 6x) = (4+4x) + (4+4x)/5 (4th year height
Solving we get x = 2/3
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thanks for the explanation TeHCM, krisrini!
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Start: 4ft
1sr yr: 4+x ft
2nd yr: 4+2x ft
3rd yr: 4+3x ft
4th yr: 4+4x ft
5th yr: 4+5x ft
6th yr = 4+6x

4+6x = 6/5(4+4x)
20+30x=24+24x
6x = 4
x = 4/6 = 2/3
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Start = 4
4th Year = 4+4x
6th Year = 4+6x

end of sixth year, the tree was 1/5 taller than the end of fourth year:

4+6x - (4+4x) = 1/5(4+4x)
2x = 4/5 + 4/5x
6/5x = 4/5
x = 2/3
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First planted: 4 ft
First year = increase by x ft
Second year = increase by x ft
... and so on...
So by end of 6 years, the tree would be 4 + 6x ft tall

Equating:

4+6x = (6/5)(4+4x)
4+6x = 24/5 + 24x/5
6x/5 = 4/6
x = 4/6 = 2/3
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