It is currently 27 Jun 2017, 15:50

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 07 Feb 2010
Posts: 158
When a certain tree was first planted, it was 4 feet tall [#permalink]

### Show Tags

02 Nov 2010, 07:16
8
KUDOS
50
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

65% (02:17) correct 35% (01:35) wrong based on 912 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 39723
Re: when a certain tree was first planted [#permalink]

### Show Tags

02 Nov 2010, 07:27
39
KUDOS
Expert's post
36
This post was
BOOKMARKED
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" --> $$4+4x+\frac{1}{5}(4+4x)=4+6x$$ --> $$\frac{1}{5}(4+4x)=2x$$ --> $$x=\frac{2}{3}$$.

_________________
Manager
Joined: 21 Aug 2010
Posts: 188
Location: United States
GMAT 1: 700 Q49 V35
Re: Height of a tree [#permalink]

### Show Tags

26 Oct 2011, 03:25
8
KUDOS
1
This post was
BOOKMARKED
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

Posted from my mobile device
_________________

-------------------------------------

Director
Joined: 29 Nov 2012
Posts: 878
Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

### Show Tags

11 Aug 2013, 23:59
5
KUDOS
1
This post was
BOOKMARKED
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
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1158
Location: United States (CA)
Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

### Show Tags

02 Dec 2016, 10:35
3
KUDOS
Expert's post
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

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Senior Manager
Joined: 10 Jul 2013
Posts: 334
Re: when a certain tree was first planted [#permalink]

### Show Tags

12 Aug 2013, 13:51
1
KUDOS
1
This post was
BOOKMARKED
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" --> $$4+4x+\frac{1}{5}(4+4x)=4+6x$$ --> $$\frac{1}{5}(4+4x)=2x$$ --> $$x=\frac{2}{3}$$.

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
_________________

Asif vai.....

Senior Manager
Joined: 29 Jan 2011
Posts: 358
Re: when a certain tree was first planted [#permalink]

### Show Tags

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

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"
Manager
Joined: 27 Jul 2011
Posts: 61
Re: Height of a tree [#permalink]

### Show Tags

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: 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
Intern
Joined: 29 Jul 2013
Posts: 9
Re: when a certain tree was first planted [#permalink]

### Show Tags

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

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 $$\frac{6}{5}(4+4x)=4+6x$$
Intern
Joined: 26 Mar 2014
Posts: 11
Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

### Show Tags

14 Jun 2014, 21:40
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?!
Math Expert
Joined: 02 Sep 2009
Posts: 39723
Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

### Show Tags

15 Jun 2014, 02:46
Expert's post
1
This post was
BOOKMARKED
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16009
Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

### Show Tags

28 Jun 2015, 09:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 23 May 2016
Posts: 12
Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

### Show Tags

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?)
Manager
Joined: 07 Mar 2016
Posts: 77
Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

### Show Tags

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
$$4+5x = 4+3x ( \frac{1}{5} + 1)$$
Manager
Joined: 17 Sep 2016
Posts: 185
Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

### Show Tags

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.

https://www.manhattanprep.com/gmat/foru ... -t646.html
Manager
Joined: 26 Dec 2015
Posts: 125
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)
Re: When a certain tree was first planted, it was 4 feet tall [#permalink]

### Show Tags

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
Re: When a certain tree was first planted, it was 4 feet tall   [#permalink] 06 Feb 2017, 19:58
Similar topics Replies Last post
Similar
Topics:
4 A snail, climbing a 20 feet high wall, climbs up 4 feet on the first 4 14 Jun 2016, 07:37
3 A farmer is planting a row consisting of 4 unique apple trees and 4 un 3 22 Jul 2016, 00:21
1 When a certain tree was first planted, it was 4 feet tall 3 30 Nov 2012, 03:26
10 A certain kudzu plant was 11 feet long on the day it was 10 24 Oct 2016, 06:33
53 When a certain tree was first planted, it was 4 feet tall, 26 10 Apr 2017, 08:56
Display posts from previous: Sort by