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by vrn2vw » Sun Nov 01, 2015 8:36 am
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount over 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

Someone mind helping me out with the above? The OA is D
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by theCEO » Sun Nov 01, 2015 9:38 am
vrn2vw wrote:When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount over 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

Someone mind helping me out with the above? The OA is D
Beginning of 1st year = 4
End of 1st year = 4 + x
End of 2nd year = 4 + x + x = 4 + 2x
End of 3rd year = 4 + x + x + x = 4 + 3x
End of 4th year = 4 + 4x
End of 5th year = 4 + 5x
End of 6th year = 4 + 6x

End of the 6th year is 1/5 taller than end of the 4th year
This means (4+4x) + 1/5 (4+4x) = 4+6x

5/5 *(4+4x) + 1/5 * (4+4x) = 4+6x
6/5 * (4+4x) = 4+6x
24/5 + 24x/5 = 20/5 + 30x/5
4/5 = 6x/5
x = 20/30 = 2/3

ans = d
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by [email protected] » Sun Nov 01, 2015 11:00 am
Hi vrn2vw,

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.

If we start with Answer C (1/2 foot growth per year), here's what we'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 (since E is SO much bigger), 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.

Final Answer: D

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by Brent@GMATPrepNow » Sun Nov 01, 2015 11:20 am
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 6th year, the tree was 1/5 taller than it was at the end of 4th year. By how many feet the height of the tree increase each year?

1) 3/10
2) 2/5
3) 1/2
4) 2/3
5) 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
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by jain2016 » Sat Dec 19, 2015 9:54 pm
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)

Why are we doing like this 4 + 6d = (4 + 4d) + 1/5(4 + 4d) , why not this 4 + 6d = 1/5(4 + 4d).


Please explain .

Thanks in advance.

SJ
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by [email protected] » Sun Dec 20, 2015 4:59 pm
Hi jain2016,

When using that algebraic approach, you have to create an equation that matches the information that you're given. We're told that, at the end of the 6th year, the tree is 1/5 TALLER than it was at the end of the 4th year.... this mean that the tree is TALLER than it was in the 4th year: the height in year 4 + 1/5 of that same height.

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