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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 [#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"

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

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26 Oct 2011, 04:30

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

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

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

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29 Nov 2016, 01:04

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.

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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06 Feb 2017, 19:58

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

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

TESTing the ANSWERS is a great way to tackle this question. The "fast" way to solve a problem can still sometimes take time, but regardless of how you approach a prompt, you still need to take notes and stay organized.

From the screen capture, you chose answer C (1/2). If you jot down some quick notes, here's what you'd have:

It doesn't make much time/effort to take these notes. Now, compare Year 6 to Year 4….Is it 1/5 greater? 7 to 6 is 1/6 greater, so answer C is not what we're looking for. It also gives us a "nudge" in the right direction. We need a 1/5 increase, but we only have a 1/6 increase right now….so we need a bigger increase…..so we need a bigger absolute increase each year. The correct answer has to be D or E.

Looking at all 5 choices as a group, I'm pretty sure the answer is D, but we can certainly prove it…