BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

height of tree

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 72
Joined: Sun Nov 03, 2013 9:29 am
Thanked: 1 times
by josh80 » Wed Dec 11, 2013 5:20 pm
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 the 6th year, the tree was 1/5th taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?

- 3/10
- 2/5
- 1/2
- 2/3
- 6/5
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Wed Dec 11, 2013 5:25 pm
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a certain amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th 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 = [spoiler]2/3[/spoiler] = D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Mon Aug 08, 2016 3:05 pm

by jervizeloy » Wed Aug 24, 2016 1:57 pm
Brent@GMATPrepNow wrote:
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a certain amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th 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 = [spoiler]2/3[/spoiler] = D

Cheers,
Brent
Hi Brent, please help me out with something...I've thought about solving this problem following the scheme detailed below:

Year 1: 4
Year 2: 4R2
.
.
.
.
Year 6: 5R5

What's the flaw of my thinking? Thanks in advance
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Mon Aug 08, 2016 3:05 pm

by jervizeloy » Wed Aug 24, 2016 1:58 pm
Brent@GMATPrepNow wrote:
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a certain amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th 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 = [spoiler]2/3[/spoiler] = D

Cheers,
Brent
Hi Brent, please help me out with something...I've thought about solving this problem following the scheme detailed below:

Year 1: 4
Year 2: 4R2
.
.
.
.
Year 6: 5R5

What's the flaw of my approach? Thanks in advance
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Wed Aug 24, 2016 2:40 pm
jervizeloy wrote: Hi Brent, please help me out with something...I've thought about solving this problem following the scheme detailed below:

Year 1: 4
Year 2: 4R2
.
.
.
.
Year 6: 5R5

What's the flaw of my approach? Thanks in advance
Hi jervizeloy,

Sorry, but I'm not sure what 4R2 and 5R5 mean. Can you elaborate on this?

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8138
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

by Scott@TargetTestPrep » Thu Aug 25, 2016 4:07 pm
josh80 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 the 6th year, the tree was 1/5th taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?

- 3/10
- 2/5
- 1/2
- 2/3
- 6/5

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 label the growth by year where 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 is 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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1