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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]  07 Nov 2008, 10:12
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69% (02:11) correct 30% (01:43) wrong based on 2 sessions
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
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Oct 2012, 02:10, edited 1 time in total.
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Re: 4 feet tall tree ? [#permalink]  07 Nov 2008, 11:34
D. 2/3

Say, the tree grows by x feet every year.

Then, 4 + 6x = (1+1/5)(4+4x)
or, x = 2/3
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Re: 4 feet tall tree ? [#permalink]  07 Nov 2008, 11:54
scthakur wrote:
D. 2/3

Say, the tree grows by x feet every year.

Then, 4 + 6x = (1+1/5)(4+4x)
or, x = 2/3

Agree with scthakur. D is the answer.
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Re: 4 feet tall tree ? [#permalink]  07 Nov 2008, 12:05
gameCode 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

There's something particular with the answer of this one which i don't understand, hence the posting.

height at the end of 6th yr = 4 + x + x + x + x + x + x = 4 + 6x
height at the end of 4th yr = 4 + x + x + x + x = 4 + 4x

2x/4 + 4x = 1/5
x/2 + 2x = 1/5
5x = 2 + 2x
x = 2/3
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Re: 4 feet tall tree ? [#permalink]  07 Nov 2008, 13:48
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We have to read the question carefully to make sure we see that the end of the 6th year is being compared to the end of the 4th year. Also note that the tree grows by a constant amount each year. This is different than the same % each year.

Let x = the constant annual growth in feet.

4ft is the original height of the tree, so after the 6th year, we have

4 + x + x + x + x + x + x….aslo 4 + 6x

After the 4th year we have 4 + x + x + x+ x or 4 + 4x

Lets compare the two values algebraically as the problem does:

6th year is 1/5 taller than the 4th year.

The difference in growth from the 4th to the 6th year will be 1/5 (or 0.2) of the height after the 4th year.

So…(4+6x)-(4+4x) = 1/5(4+4x)…now solve for x

4 + 6x -4 – 4x = 4/5 + 4/5x
2x = 4/5 + 4/5x
Subtract 4/5x from both sides. I’ve changed 2x into 10/5x to easily do the subtraction of fractions.

10/5x – 4/5x = 4/5

6/5x = 4/5

Divide both sides by 6/5, which is the same as multiplying by 5/6

X = 4/5 * 5/6. (Reduce the 5’s or multiply out and) you have 20 / 30 or x = 2/3.

Hope a different approach may help someone else.

gameCode 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

There's something particular with the answer of this one which i don't understand, hence the posting.

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Re: 4 feet tall tree ? [#permalink]  07 Nov 2008, 15:55
Thanks Jallen. Its a bit clear now. I was wondering how 1/5 taller led to 1+1/5 . The wordings are very difficult for this one. I would have thought its either 1/5th or addition of 1/5. I knew the height after 6 years could not be 1/5th of height after 4 years. So i thought it might be addition. But i could not really understand why its so peculiar with this qs, i have not seen any other qs of this type. Is there any other similar example anyone has seen so far ?
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Re: 4 feet tall tree ? [#permalink]  07 Nov 2008, 19:01
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x be the height increase every year

at end of 6 yrs it is 4+6x

4 yrs it is 4+4x

4+6x = 4+4x + 1/5 (4+4x) -> 2x = 1/5 (4+4x) -> 10x = 4+4x -> 6x=4 -> x=2/3
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Re: 4 feet tall tree ? [#permalink]  01 Dec 2009, 23:36
Let the tree increase by a constant amount of x
Height after 6 yrs = 4 + 6x
Height after 4 years = 4 + 4x
Therefore, from statements

4+6x = 1/5 (4+4x) + 4+4x
X=2/3
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Re: 4 feet tall tree ? [#permalink]  23 Sep 2010, 17:27
1/5th taller than 4th year....i missed taking difference while taking the exam. Nice question
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Re: 4 feet tall tree ? [#permalink]  23 Sep 2010, 22:13
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gameCode 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

There's something particular with the answer of this one which i don't understand, hence the posting.

Let the rate of increase be x feet per year.

At the end of the 4th year the height was 4+4x and at the of the 6th year the height was 4+6x, which was "1/5 taller than it was at the end of the 4th year" --> (4+4x)+\frac{1}{5}(4+4x)=4+6x --> \frac{1}{5}(4+4x)=2x --> x=\frac{2}{3}.

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Re: 4 feet tall tree ? [#permalink]  10 Oct 2010, 06:39
I fell in the trap yesterday. I read that it was 1/5" taller than at the end of year 4.

Therefore I wrote: 4+6x = 4+4x+1/5 and couldn't figure out the answer nor my error.
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Re: 4 feet tall tree ? [#permalink]  31 Aug 2011, 23:50
Lets concise equation a bit more.
if x is the constant growth then difference between end of 6th year and end of 4th year
is 2x. So
2x=(4+4x)/5
10x=4+4x
6x=4
x=2/3
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Re: When a certain tree was first planted, it was 4 feet tall, [#permalink]  13 Oct 2012, 20:08
In the question stem it is 1/5.So how does one know that they are trying to say 1/5th.Or is this a frequent trap?
Re: When a certain tree was first planted, it was 4 feet tall,   [#permalink] 13 Oct 2012, 20:08
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