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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 and the height of the tree increased by a constant amount each year for the next 6 years. At the end of 6 year the tree was 1/5 taller then it was at the end of 4 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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anilnandyala wrote:
when a certain tree was first planted, it was 4 feet tall & the height of the tree increased by a constant amount each year for the next 6 years. at the end of 6 year the tree was 1/5 taller then it was at the end of 4 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


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" --> \(4+4x+\frac{1}{5}(4+4x)=4+6x\) --> \(\frac{1}{5}(4+4x)=2x\) --> \(x=\frac{2}{3}\).

Answer: D.
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Re: when a certain tree was first planted [#permalink]

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New post 21 Jul 2011, 02:48
Bunuel wrote:
anilnandyala wrote:
when a certain tree was first planted, it was 4 feet tall & the height of the tree increased by a constant amount each year for the next 6 years. at the end of 6 year the tree was 1/5 taller then it was at the end of 4 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


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" --> \(4+4x+\frac{1}{5}(4+4x)=4+6x\) --> \(\frac{1}{5}(4+4x)=2x\) --> \(x=\frac{2}{3}\).

Answer: D.


Shouldnt this be 1/5 (4 + 4x) = 4 + 6x ?? why is it (4 + 4x) + 1/5 (4 + 4x) = 4 + 6x ? when the stmt says : " at the of the 6th year the height was 1/5 taller than it was at the end of the 4th year"

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Re: Height of a tree [#permalink]

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New post 26 Oct 2011, 02:25
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The tree grows by x feets per year
At d end of 4th year the height of tree =4x+4
Between 4 th and sixth year the tree grows by 2x feet=(1/5)(4+4x)

2x=1/5(4+4x)
2x=.8x+.8
1.2x=.8
X=2/3

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

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New post 26 Oct 2011, 03:30
Please help me, every time I attempt question as such I tend to do it the long way. This is my working:
Initial, 0: 4 feet
4 years: 4 + 4 x
6 years: 4 + 6 x

Given,
Increment from year 4 to 6: 1/5
Therefore, year 6: 6/5 (4 + 4X)

Equate 2 year 6 equation:
6/5 (4 + 4x) = 4 + 6 X
x = 2/3

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Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

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anilnandyala 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 6 year the tree was 1/5 taller then it was at the end of 4 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


Year 1 = 4+x
Year 2 = 4+2x
Year 3 = 4+3x
year 4 = 4+4x
Year 5 = 4+5x
year 6 = 4 + 6x

\(4+6x = 4+4x ( \frac{1}{5} + 1)\)

When we solve this we get answer D
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Re: when a certain tree was first planted [#permalink]

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siddhans wrote:
Bunuel wrote:
anilnandyala wrote:
when a certain tree was first planted, it was 4 feet tall & the height of the tree increased by a constant amount each year for the next 6 years. at the end of 6 year the tree was 1/5 taller then it was at the end of 4 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


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" --> \(4+4x+\frac{1}{5}(4+4x)=4+6x\) --> \(\frac{1}{5}(4+4x)=2x\) --> \(x=\frac{2}{3}\).

Answer: D.


Shouldnt this be 1/5 (4 + 4x) = 4 + 6x ?? why is it (4 + 4x) + 1/5 (4 + 4x) = 4 + 6x ? when the stmt says : " at the of the 6th year the height was 1/5 taller than it was at the end of the 4th year"

just like 10% increase = 100+10 here, tall=increase.
so,
1/5 taller means" original height + 1/5 of (original height) "
so, original height at 4 years = 4+4x
and at 6years = 4+6x
According to the question,
4+4x+ 1/5(4+4x) = 4+6x, or , x = 2/3
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Re: when a certain tree was first planted [#permalink]

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New post 02 Sep 2013, 14:08
siddhans wrote:
Bunuel wrote:
anilnandyala wrote:
when a certain tree was first planted, it was 4 feet tall & the height of the tree increased by a constant amount each year for the next 6 years. at the end of 6 year the tree was 1/5 taller then it was at the end of 4 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


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" --> \(4+4x+\frac{1}{5}(4+4x)=4+6x\) --> \(\frac{1}{5}(4+4x)=2x\) --> \(x=\frac{2}{3}\).

Answer: D.


Shouldnt this be 1/5 (4 + 4x) = 4 + 6x ?? why is it (4 + 4x) + 1/5 (4 + 4x) = 4 + 6x ? when the stmt says : " at the of the 6th year the height was 1/5 taller than it was at the end of the 4th year"


Since it's an increase it has to be expressed as original height + % of increase on original height.

My thought was that because it's a 1/5 increase, meaning 20% = 0.2, this also means that it increased by 1.2= 6/5, so I simply said \(\frac{6}{5}(4+4x)=4+6x\)

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Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

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New post 14 Jun 2014, 20:40
ok... English is not m native language is for this problem, i struggle is what it meant "1/5 taller than it was at the end of 4th year"

why is not the equation

a6 = a4+1/5 ??!!!!!

how is that different than saying John is 5 years old than tom?!!!! which is John = tom + 5?

HELP?!

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Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

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bb0214 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 6 year the tree was 1/5 taller then it was at the end of 4 year. By how many feet did the height of the tree increase each year

ok... English is not m native language is for this problem, i struggle is what it meant "1/5 taller than it was at the end of 4th year"

why is not the equation

a6 = a4+1/5 ??!!!!!

how is that different than saying John is 5 years old than tom?!!!! which is John = tom + 5?

HELP?!


It would be a6 = a4+1/5, if it were "at the end of 6 year the tree was 1/5 foot taller then it was at the end of 4 year". In its current form 1/5 MUST refer to a fraction, not to the quantity.

Hope it's clear.
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Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

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New post 25 May 2016, 14:42
Can someone help explain:

1) Should we normally assume we plant in year 0, not year 1 for similar questions? (Would then get 4 + 5x and 4+3x instead)
2) Why isnt the sequence 4, 4k, 4k^2 etc? (What determines when we should see the growth as additive vs. multiplicative?)

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Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

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New post 06 Aug 2016, 03:26
fozzzy wrote:
anilnandyala 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 6 year the tree was 1/5 taller then it was at the end of 4 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


Year 1 = 4+x
Year 2 = 4+2x
Year 3 = 4+3x
year 4 = 4+4x
Year 5 = 4+5x
year 6 = 4 + 6x

\(4+6x = 4+4x ( \frac{1}{5} + 1)\)

When we solve this we get answer D


Hey thanks!
i think i took it wrong. is it wrong if i say..
Year 1 = 4
Year 2 = 4+x
Year 3 = 4+2x
year 4 = 4+3x
Year 5 = 4+4x
year 6 = 4 + 5x
\(4+5x = 4+3x ( \frac{1}{5} + 1)\)

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Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

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New post 29 Nov 2016, 00:04
Hi All,
I failed this as well.
I want to share what I search from MANHATTAN forums,
RON wrote:
Interesting question vijaykumar.kondepudi, but no. Integers work differently than either fractions or percents. Note that the particuar values used below are arbitrary.

FRACTIONS:
1/5 greater than x = x + (1/5)x=(6/5)x

PERCENTS
15% less than y=y-%15y=85%y

INTEGERS
7 more than z=z+7

And your example, "tim is 4 older than joe" doesn't mean anything, alas. If you put in a unit, though, it'll signal addition.


more details please check following link
https://www.manhattanprep.com/gmat/foru ... -t646.html

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Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

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anilnandyala 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 6 year the tree was 1/5 taller then it was at the end of 4 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


We are given that 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. Since we know that the growth is by a constant amount, we have a linear growth problem. Thus, we can define this constant amount as x = the yearly growth amount, in feet:

Starting height = 4
height after year one = 4 + x
height after year two = 4 + 2x
height after year three = 4 + 3x
height after year four = 4 + 4x
height after year five = 4 + 5x
height after year six = 4 + 6x

We are also 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. This means the height of the tree at the end of the 6th year was 6/5 times as tall as its height at the end of the 4th year. Thus, we can create the following equation:

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

To eliminate the fraction of 6/5, we can multiply the entire equation by 5.

6(4 + 4x) = 20 + 30x

24 + 24x = 20 + 30x

6x = 4

x = 4/6 = 2/3 feet

Answer: D
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Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

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New post 06 Feb 2017, 18:58
I tweaked this a bit.

I think we can all see how the setup is: 4'+x (for the # of yrs you're calculating)

End of 6th year = 4+6x
End of 4th year = 4+4x

BUT if end of 6th year is 1/5 taller than it was at end of 4th year: 4+6x = 6/5(4+4x)
> 4+6x = 24/5 + 24/5x (now you can mult each side by 5) --> 20+30x = 24+24x --> 6x = 4 --> x=2/3

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

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New post 18 Sep 2017, 10:40
Hi GMATters,

Check out my video explanation of the problem here:



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Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

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anilnandyala 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 6 year the tree was 1/5 taller then it was at the end of 4 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


Height of tree on day 0 = 4
Let d = the height increase each year
Height of tree at the end of the 1st year = 4+d
Height of tree at the end of the 2nd year = 4+d+d = 4 + 2d
Height of tree at the end of the 3rd year = 4+d+d+d = 4 + 3d
Height of tree at the end of the 4th year = 4+d+d+d+d = 4 + 4d
Height of tree at the end of the 5th year = 4+d+d+d+d+d = 4 + 5d
Height of tree at the end of the 6th year = 4+d+d+d+d+d+d = 4 + 6d

At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year
In other words, 6th year height = 4th year height + 1/5(4th year height)
Or we can write 4 + 6d = (4 + 4d) + 1/5(4 + 4d)
Simplify: 4 + 6d = 6/5(4 + 4d)
Multiply both sides by 5 to get: 5(4 + 6d) = 6(4 + 4d)
Expand: 20 + 30d = 24 + 24d
Simplify: 6d = 4
d = 4/6 = 2/3 = D

Cheers,
Brent
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