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
height of tree
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- Brent@GMATPrepNow
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Height of tree on day 0 = 4When 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
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
- jervizeloy
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Hi Brent, please help me out with something...I've thought about solving this problem following the scheme detailed below:Brent@GMATPrepNow wrote:Height of tree on day 0 = 4When 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
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
Year 1: 4
Year 2: 4R2
.
.
.
.
Year 6: 5R5
What's the flaw of my thinking? Thanks in advance
- jervizeloy
- Junior | Next Rank: 30 Posts
- Posts: 13
- Joined: Mon Aug 08, 2016 3:05 pm
Hi Brent, please help me out with something...I've thought about solving this problem following the scheme detailed below:Brent@GMATPrepNow wrote:Height of tree on day 0 = 4When 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
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
Year 1: 4
Year 2: 4R2
.
.
.
.
Year 6: 5R5
What's the flaw of my approach? Thanks in advance
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
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Hi jervizeloy,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
Sorry, but I'm not sure what 4R2 and 5R5 mean. Can you elaborate on this?
Cheers,
Brent
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
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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
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