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Word problem problem - Tree height in 6 years

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by gdshamain » Tue May 13, 2014 9:07 am
When a certain tree was first plated 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 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase per year?

A) 3/10
B) 2/5
C) 1/2
D) 2/3
E) 6/5
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by Brent@GMATPrepNow » Tue May 13, 2014 9:24 am
gdshamain wrote:When a certain tree was first plated 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 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase per 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

---------------------
Here's a similar question to practice with: https://www.beatthegmat.com/linear-growt ... 73800.html

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Brent
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by gdshamain » Tue May 13, 2014 9:39 am
Thanks Brent. It is clear now.
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by [email protected] » Tue May 13, 2014 10:57 pm
Hi gdshamain,

This question can also be solved by TESTing THE ANSWERS.

We're told that a tree grows the same length in each year. It starts of at 4ft and grows for 6 years. At the end of the 6th year, the tree is EXACTLY 1/5 taller than it was at the end of the 4th year. We're asked for the growth per year, in feet.

If you tried answer C first, you'd have the following measurements (representing the starting value and each of the 6 years that follow:

Start = 4ft
Yr. 1 = 4.5ft
Yr. 2 = 5ft
Yr. 3 = 5.5ft
Yr. 4 = 6ft
Yr. 5 = 6.5ft
Yr. 6 = 7ft

Comparing Year 4 to Year 6, we see that the tree was 1/6 bigger, which is NOT what we're looking for. We need a bigger fraction (1/5), so we'll need to tree to grow faster.

Testing D, we'd have:

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

Now, comparing Year 4 to Year 6, we have (1 1/3) / (6 2/3) = (4/3)/(20/3) = 4/20 = 1/5. This is the exact match for what we're looking for.

Final Answer: D

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by sanju09 » Fri May 23, 2014 12:20 am
gdshamain wrote:When a certain tree was first plated 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 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase per year?

A) 3/10
B) 2/5
C) 1/2
D) 2/3
E) 6/5
Let's try plugging in the answers, starting from (C) as usual.

If the height of the tree increases @ ½ feet per year, then at the end of the 4th year, it would be 6 feet, and at the end of the 6th year, it would 7 feet. We can justify that 7 is not 1/5 taller than 6, it's even less in fact. This is because we picked a choice that is too small to make it true.

Eliminate (C) and the smaller choices, (A) and (B).

Take one more attempt, say try (D).

If the height of the tree increases @ 2/3 feet per year, then at the end of the 4th year, it would be 20/3 feet, and at the end of the 6th year, it would 24/3 feet. We can justify that 24/3 is 1/5 taller than 20/3, hence [spoiler](D)[/spoiler] is the right choice, take it!
The mind is everything. What you think you become. -Lord Buddha



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