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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 02 Nov 2010, 06:16
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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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Re: when a certain tree was first planted [#permalink] New post 02 Nov 2010, 06:27
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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: Height of a tree [#permalink] 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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Re: When a certain tree was first planted, it was 4 feet tall [#permalink] New post 11 Aug 2013, 22:59
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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] 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] 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: 6 + 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 [#permalink] New post 12 Aug 2013, 12:51
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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] 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] 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] New post 15 Jun 2014, 01:46
Expert's post
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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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: When a certain tree was first planted, it was 4 feet tall [#permalink] New post 28 Jun 2015, 08:05
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Re: When a certain tree was first planted, it was 4 feet tall   [#permalink] 28 Jun 2015, 08:05
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