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height of tree

This topic has 3 expert replies and 2 member replies
josh80 Senior | Next Rank: 100 Posts Default Avatar
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03 Nov 2013
Posted:
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1

height of tree

Post 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

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Post 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

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GMAT/MBA Expert

Post 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 – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

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GMAT/MBA Expert

Post Wed Dec 11, 2013 5:25 pm
Quote:
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 = 2/3 = D

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

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jervizeloy Junior | Next Rank: 30 Posts
Joined
08 Aug 2016
Posted:
13 messages
Post Wed Aug 24, 2016 1:57 pm
Brent@GMATPrepNow wrote:
Quote:
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 = 2/3 = 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

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jervizeloy Junior | Next Rank: 30 Posts
Joined
08 Aug 2016
Posted:
13 messages
Post Wed Aug 24, 2016 1:58 pm
Brent@GMATPrepNow wrote:
Quote:
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 = 2/3 = 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

  • +1 Upvote Post
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