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by saadishah » Fri Jan 01, 2016 3:36 am
Happy New Year Guys!

I have come across this word problem with the solution. However, do not follow a few steps in the solution. May I request you to solve it for me with explanations on how to you are going about it.

Q: The length of a rectangular garden surrounded by a walkway is twice its width. If difference between the length and width of just the rectangular garden is 10 meters, what will be the width of the walkway if just the garden has width 6 meters?

Again, Happy New Year!
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by MartyMurray » Fri Jan 01, 2016 6:02 am
saadishah wrote:
Q: The length of a rectangular garden surrounded by a walkway is twice its width. If difference between the length and width of just the rectangular garden is 10 meters, what will be the width of the walkway if just the garden has width 6 meters?
Start with what we know. The width of just the garden is 6.

The length of just the garden is 6 + 10 = 16

The width of the walkway = x.

The walkway is on all sides, so it shows up twice in the length and the width.

Width of entire thing is 6 + 2x.

Length of entire thing is 16 + 2x.

The length of the entire thing is twice the width. Only one walkway width, x, will work.

16 + 2x = 2(6 + 2x)

16 + 2x = 12 + 4x

4 = 2x

2 = x = width of the walkway
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by Brent@GMATPrepNow » Fri Jan 01, 2016 11:01 am
This is actually a DS question. Here's the original wording:
What is the length in meters of a certain rectangular garden?

(1) The length of the garden is 6 meters more than twice the width.

(2) The length of the garden is 4 times the width
Let L = length of garden
Let W = width of garden

Target question: What is the value of L?

Statement 1: The length of the garden is 6 meters more than twice the width.
In other words, L = 2W + 6
Since this equation does not provide sufficient information to find the value of L, statement 1 is NOT SUFFICIENT

Statement 2: The length of the garden is 4 times the width
In other words, L = 4W
Since this equation does not provide sufficient information to find the value of L, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
We now know that:
L = 2W + 6
L = 4W
Since both equations equal L, we can write: 2W + 6 = 4W
Rearrange: 6 = 2W
Solve: 3 = W

If W = 3, then L = 12
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
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by Sci45 » Tue Jul 04, 2017 12:48 pm
Marty Murray wrote:
saadishah wrote:
Q: The length of a rectangular garden surrounded by a walkway is twice its width. If difference between the length and width of just the rectangular garden is 10 meters, what will be the width of the walkway if just the garden has width 6 meters?
Start with what we know. The width of just the garden is 6.

The length of just the garden is 6 + 10 = 16

The width of the walkway = x.

The walkway is on all sides, so it shows up twice in the length and the width.

Width of entire thing is 6 + 2x.

Length of entire thing is 16 + 2x.

The length of the entire thing is twice the width. Only one walkway width, x, will work.

16 + 2x = 2(6 + 2x)

16 + 2x = 12 + 4x

4 = 2x

2 = x = width of the walkway
I am struggling to understand what the heck is a walkway.... Anyone has a picture? Is it just another rectangle surrounding the garden? In that case, wouldn't the walkway's width and length be equal to the entire thing's w and l?

I m
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by Sci45 » Tue Jul 04, 2017 12:48 pm
Marty Murray wrote:
saadishah wrote:
Q: The length of a rectangular garden surrounded by a walkway is twice its width. If difference between the length and width of just the rectangular garden is 10 meters, what will be the width of the walkway if just the garden has width 6 meters?
Start with what we know. The width of just the garden is 6.

The length of just the garden is 6 + 10 = 16

The width of the walkway = x.

The walkway is on all sides, so it shows up twice in the length and the width.

Width of entire thing is 6 + 2x.

Length of entire thing is 16 + 2x.

The length of the entire thing is twice the width. Only one walkway width, x, will work.

16 + 2x = 2(6 + 2x)

16 + 2x = 12 + 4x

4 = 2x

2 = x = width of the walkway
I am struggling to understand what the heck is a walkway.... Anyone has a picture? Is it just another rectangle surrounding the garden? In that case, wouldn't the walkway's width and length be equal to the entire thing's w and l?
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by Jay@ManhattanReview » Tue Jul 04, 2017 9:39 pm
Sci45 wrote:
Marty Murray wrote:
saadishah wrote:
Q: The length of a rectangular garden surrounded by a walkway is twice its width. If difference between the length and width of just the rectangular garden is 10 meters, what will be the width of the walkway if just the garden has width 6 meters?
Start with what we know. The width of just the garden is 6.

The length of just the garden is 6 + 10 = 16

The width of the walkway = x.

The walkway is on all sides, so it shows up twice in the length and the width.

Width of entire thing is 6 + 2x.

Length of entire thing is 16 + 2x.

The length of the entire thing is twice the width. Only one walkway width, x, will work.

16 + 2x = 2(6 + 2x)

16 + 2x = 12 + 4x

4 = 2x

2 = x = width of the walkway
I am struggling to understand what the heck is a walkway.... Anyone has a picture? Is it just another rectangle surrounding the garden? In that case, wouldn't the walkway's width and length be equal to the entire thing's w and l?
Yes, it is just another rectangle surrounding the garden. The walkway's width and length be equal to the entire thing's w and l, where w = width of rectangular garden + 2*width of the walkway, and l = length of rectangular garden + 2*width of the walkway.

Hope it is clear. Pl. see the image attached.

-Jay
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by Matt@VeritasPrep » Wed Jul 05, 2017 1:10 am
Sci45 wrote:[
I am struggling to understand what the heck is a walkway.... Anyone has a picture? Is it just another rectangle surrounding the garden? In that case, wouldn't the walkway's width and length be equal to the entire thing's w and l?
Think of the frame around a painting. The frame is the walkway and the painting is the garden.
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by Sci45 » Fri Jul 07, 2017 1:19 pm
Thank you!
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