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

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02 Nov 2010, 07:16

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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

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

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

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11 Aug 2013, 23:59

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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]

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21 Jul 2011, 03:48

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"

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

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

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12 Aug 2013, 13:51

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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]

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02 Sep 2013, 15:08

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

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.

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

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28 Jun 2015, 09:05

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

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25 May 2016, 15:42

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?)

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

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06 Aug 2016, 04:26

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 \(4+5x = 4+3x ( \frac{1}{5} + 1)\)

gmatclubot

Re: When a certain tree was first planted, it was 4 feet tall
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06 Aug 2016, 04:26

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