GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Nov 2019, 12:30

### 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

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 07 Feb 2010
Posts: 114
When a certain tree was first planted, it was 4 feet tall  [#permalink]

### Show Tags

02 Nov 2010, 07:16
17
170
00:00

Difficulty:

55% (hard)

Question Stats:

67% (02:23) correct 33% (02:41) wrong based on 1145 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
Math Expert
Joined: 02 Sep 2009
Posts: 59182
Re: when a certain tree was first planted  [#permalink]

### Show Tags

02 Nov 2010, 07:27
62
65
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: 163
Location: United States
GMAT 1: 700 Q49 V35
Re: Height of a tree  [#permalink]

### Show Tags

26 Oct 2011, 03:25
19
8
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
_________________
-------------------------------------
##### General Discussion
Manager
Joined: 29 Jan 2011
Posts: 238
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"
Director
Joined: 29 Nov 2012
Posts: 685
Re: When a certain tree was first planted, it was 4 feet tall  [#permalink]

### Show Tags

11 Aug 2013, 23:59
11
4
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
Senior Manager
Joined: 10 Jul 2013
Posts: 282
Re: when a certain tree was first planted  [#permalink]

### Show Tags

12 Aug 2013, 13:51
8
1
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.....
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: 59182
Re: When a certain tree was first planted, it was 4 feet tall  [#permalink]

### Show Tags

15 Jun 2014, 02:46
3
3
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.
_________________
Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 714
Location: United States (CA)
Age: 40
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GRE 1: Q168 V169
WE: Education (Education)
When a certain tree was first planted, it was 4 feet tall,  [#permalink]

### Show Tags

05 Apr 2016, 20:40
1
Attached is a visual that should help. Notice that multiplying by $$\frac{6}{5}$$ is an easier way to get to "$$\frac{1}{5}$$ greater than"
Attachments

Screen Shot 2016-04-05 at 8.34.56 PM.png [ 69.98 KiB | Viewed 5327 times ]

_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching worldwide since 2002.

One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V.

You can download my official test-taker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y7knw7bt Date of Birth: 09 December 1979.

GMAT Action Plan and Free E-Book - McElroy Tutoring

Contact: mcelroy@post.harvard.edu (I do not respond to PMs on GMAT Club) or find me on reddit: http://www.reddit.com/r/GMATpreparation
Senior Manager
Joined: 17 Sep 2016
Posts: 311
Re: When a certain tree was first planted, it was 4 feet tall  [#permalink]

### Show Tags

29 Nov 2016, 01:04
1
1
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
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8427
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
6
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

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 27 Nov 2013
Posts: 20
Location: Peru
GMAT 1: 770 Q49 V47
GPA: 3.99
Re: When a certain tree was first planted, it was 4 feet tall,  [#permalink]

### Show Tags

10 Apr 2017, 08:56
1
I was surprised to see that everyone has taken an algebraic approach. The problem isn't that complicated and can be solved with no algebra at all.

We will simply run two scenarios based on answer choices (B) and (D). If either of them turns out to be the answer, then we're golden. This will happen 40% of the time. Otherwise, we should be able to see whether the answer lies between (B) and (D) or whether it is an outlier.

To make the scenario easier, I will reclassify the original height for answer choice (B) as 20/5 and for answer choice (D) as 12/3, although I will not write the denominator each time for added speed and simplicity.

Scenario (B)

Year 0—20/5
Year 1—22
Year 2—24
Year 3—26
Year 4—28
Year 5—30
Year 6—32

Since 1/5 of 28 (year 4) is 5 and change, we can see that one fifth more will be 33 and change. So (B) is not the answer—it's too small.

Scenario (D)
Year 0—12/3
Year 1—14
Year 2—16
Year 3—18
Year 4—20
Year 5—22
Year 6—24

Since 1/5 of 20 (year 4) is 4, (D) is the answer. Had (D) not been the answer, we would have been able to determine which of the other three [(A), (C), or (E)] was the answer with no difficulty.
_________________
GMAT Instructor
ApexGMAT
http://www.apexgmat.com/
Intern
Status: London UK GMAT Consultant / Tutor
Joined: 30 Oct 2012
Posts: 49
When a certain tree was first planted, it was 4 feet tall  [#permalink]

### Show Tags

18 Sep 2017, 11:40
Hi GMATters,

Check out my video explanation of the problem here:

Enjoy!

Rowan
_________________
Is Your GMAT Score Stuck in the 600s? This FREE 8-Video, 20-Page Guide Can Help.

http://yourgmatcoach.com/gmat-score-stuck-plateau-600/

PS have you seen the new GMAT Work and Rates guide? Comes with a free 8-video course.

https://yourgmatcoach.podia.com/courses/how-to-beat-gmat-work-and-rates-problems
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4074
Re: When a certain tree was first planted, it was 4 feet tall  [#permalink]

### Show Tags

11 Dec 2017, 12:14
Top Contributor
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
_________________
Test confidently with gmatprepnow.com
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15489
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: When a certain tree was first planted, it was 4 feet tall  [#permalink]

### Show Tags

13 Jan 2018, 17:23
Hi All,

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:

Start = 4 ft
Yr. 1 = 4 1/2
Yr. 2 = 5
Yr. 3 = 5 1/2
Yr. 4 = 6
Yr. 5 = 6 1/2
Yr. 6 = 7

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…

Start = 4 ft
Yr. 1 = 4 2/3
Yr. 2 = 5 1/3
Yr. 3 = 6
Yr. 4 = 6 2/3
Yr. 5 = 7 1/3
Yr. 6 = 8

This comparison requires a bit more math, but isn't "crazy" by any definition.

6 2/3 = 20/3
8 = 24/3

Ignore the denominators….24 to 20….. 1/5 of 20 = 4…..24 IS 1/5 greater than 20.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15489
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: When a certain tree was first planted, it was 4 feet tall  [#permalink]

### Show Tags

28 May 2018, 22:13
Hi Nixondutta,

We're told that the height of the tree increases by a constant amount (for example, 3/10 of a foot per year). Interest rate formulas are based on percentages - NOT fixed values - so neither interest rate formula would be applicable here.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Joined: 30 May 2018
Posts: 88
GMAT 1: 620 Q42 V34
WE: Corporate Finance (Commercial Banking)
When a certain tree was first planted, it was 4 feet tall  [#permalink]

### Show Tags

12 Aug 2019, 10:48
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

I tried this and it worked for me.
Attachments

Untitled.png [ 19.48 KiB | Viewed 3433 times ]

Non-Human User
Joined: 09 Sep 2013
Posts: 13612
Re: When a certain tree was first planted, it was 4 feet tall,  [#permalink]

### Show Tags

09 Oct 2019, 04:54
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.
_________________
Re: When a certain tree was first planted, it was 4 feet tall,   [#permalink] 09 Oct 2019, 04:54
Display posts from previous: Sort by