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The perimeter of a rectangular garden is 360 ft. What is the

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The perimeter of a rectangular garden is 360 ft. What is the length of the garden?

1) the length of the garden is twice the width
2) the difference between the length and width of the garden is 60 ft

OA D

Source: Official Guide

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by Jay@ManhattanReview » Mon Sep 10, 2018 9:18 pm

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BTGmoderatorDC wrote:The perimeter of a rectangular garden is 360 ft. What is the length of the garden?

1) the length of the garden is twice the width
2) the difference between the length and width of the garden is 60 ft

OA D

Source: Official Guide
Say the length and the width of the rectangular garden is l and w, respectively.

Thus,

Perimeter of the rectangular garden = 2(l + w) = 360 => (l + w) = 180

We have to find out the length of the garden.

Let's take each statement one by one.

1) The length of the garden is twice the width.

=> l = 2w

Thus, from l + w = 180 and l = 2w, we have l = 120. Sufficient.

2) The difference between the length and width of the garden is 60 ft

=> l - w = 60

Thus, from l + w = 180 and l - w = 60, we have l = 120. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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by Brent@GMATPrepNow » Tue Sep 11, 2018 6:18 am

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To my test-prep colleagues.

I have to say that I'm a little surprised by the official answer (D).
For statement 2, it could be the case that length = 120 and width = 60, OR it could be the case that length = 60 and width = 120
The assumption here is that the length of a rectangle must be its longest side, but I've never seen anything in the Official Guide that confirms this.
If we say that the length must be longer than the width, how does all of this play out with a box with a length, width and height? Which dimension is the length? Is it the longest dimension?
To make things even murkier, let's say the box is floating in space (so that the height isn't implied)

Anyone care to weigh in?

Cheers,
Brent
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Brent@GMATPrepNow wrote:To my test-prep colleagues.

I have to say that I'm a little surprised by the official answer (D).
For statement 2, it could be the case that length = 120 and width = 60, OR it could be the case that length = 60 and width = 120
The assumption here is that the length of a rectangle must be its longest side, but I've never seen anything in the Official Guide that confirms this.
If we say that the length must be longer than the width, how does all of this play out with a box with a length, width and height? Which dimension is the length? Is it the longest dimension?
To make things even murkier, let's say the box is floating in space (so that the height isn't implied)

Anyone care to weigh in?

Cheers,
Brent
Hi Brent,

I will try to give my contribution to the discussion you (nicely) open.
There is not a convention like "the length of a rectangle must be its longest side (or anyone, if a square)", neither in Mathematics nor in the GMAT.
Length and width are common ways of mentioning two consecutive sides of a rectangle. "The box floating in space" is an excellent argument for the 3-D analogous discussion.
Classic Elementary Geometry (Plane or Spatial) does not have any "orientation-preferences", like (for instance) when we are dealing with planar simple-closed smooth curves (*).
(*) In this case, the positive orientation (by convention) is usually the one in which the bounded region is to the left of the "observer" moving along the trajectory of the curve.

All that put, why I believe the question stem is perfect for (D) as the right answer?
Because we must understand
2a) the difference between the length and width of the garden is 60 ft
as the same as
2b) the difference IN THAT ORDER between the length and width of the garden is 60 ft

On the other hand, your argument for (2) statement insufficiency would be perfect if we had
2c) the length and the width of the garden differ by 60 ft

Well, that´s the way I see it!

Regards,
Fabio.
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by fskilnik@GMATH » Tue Sep 11, 2018 10:35 am

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BTGmoderatorDC wrote:The perimeter of a rectangular garden is 360 ft. What is the length of the garden?

1) the length of the garden is twice the width
2) the difference between the length and width of the garden is 60 ft

Source: Official Guide
\[W + L = 180\,\,\,\left[ {{\text{ft}}} \right]\,\,\,\,\,\,\,\,\,\left( * \right)\]
\[? = L\]

\[\left( 1 \right)\,\,\,\left\{ \begin{gathered}
\,L = 2k \hfill \\
\,W = k \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\left( {k > 0} \right)\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,3k = 180\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = L = 2k\,\,\,\,{\text{unique}}\]

\[\left( 2 \right)\,\,\left\{ \begin{gathered}
L - W = 60 \hfill \\
W + L = 180\,\,\,\,\left( * \right) \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\,2L = 240\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = L\,\,\,{\text{unique}}\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
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by GMATGuruNY » Tue Sep 11, 2018 12:37 pm

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Brent@GMATPrepNow wrote:To my test-prep colleagues.

I have to say that I'm a little surprised by the official answer (D).
For statement 2, it could be the case that length = 120 and width = 60, OR it could be the case that length = 60 and width = 120
The assumption here is that the length of a rectangle must be its longest side, but I've never seen anything in the Official Guide that confirms this.
If we say that the length must be longer than the width, how does all of this play out with a box with a length, width and height? Which dimension is the length? Is it the longest dimension?
To make things even murkier, let's say the box is floating in space (so that the height isn't implied)

Anyone care to weigh in?

Cheers,
Brent
Definitions of length:
Merriam-Webster: The LONGER OR LONGEST dimension of an object.
American Heritage: The measurement of something along its GREATEST dimension.
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by Brent@GMATPrepNow » Tue Sep 11, 2018 1:16 pm

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GMATGuruNY wrote: Definitions of length:
Merriam-Webster: The LONGER OR LONGEST dimension of an object.
American Heritage: The measurement of something along its GREATEST dimension.
Interesting. I've never heard of that construct.
So, for a box with dimensions 3 x 4 x 5, then the side with length 5 is the length?
Which dimension is the width?
What about cases when the terms base and height are used? Which one is the base?

In a way, this reminds me of the times when students (incorrectly) insist that the side of a triangle that's horizontal (and on the bottom) must be the base of the triangle.

Cheers,
Brent
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by fskilnik@GMATH » Tue Sep 11, 2018 1:48 pm

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GMATGuruNY wrote:Definitions of length:
Merriam-Webster: The LONGER OR LONGEST dimension of an object.
American Heritage: The measurement of something along its GREATEST dimension.
(i) LANGUAGES dictionaries?
(ii) LENGTH of what?

In my humble opinion, this is too generic and too non-mathematical to be taken into account in our context.

More on the matter:

01. I found no explicit definitions in the "Quantitative Review (Official Guide) 2017", but this official problem with the corresponding official solution (I believe) closes the issue.

02. There ARE some "math sites" in which you will find the very same definitions presented by the dictionaries, for example:
https://thinkmath.edc.org/resource/measu ... ight-depth

The problem here is another: they are usually materials taught by teachers who are NOT math-oriented (Education Studies x Mathematical Studies) and... for children.

Anyway, I will not go into this further. My explanations were presented previously.

Regards,
fskilnik.
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by fskilnik@GMATH » Tue Sep 11, 2018 1:49 pm

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Brent@GMATPrepNow wrote: So, for a box with dimensions 3 x 4 x 5, then the side with length 5 is the length?
Which dimension is the width?
What about cases when the terms base and height are used? Which one is the base?

In a way, this reminds me of the times when students (incorrectly) insist that the side of a triangle that's horizontal (and on the bottom) must be the base of the triangle.
EXACTLY.
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length and long

by GMATGuruNY » Tue Sep 11, 2018 2:18 pm

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Brent@GMATPrepNow wrote:
GMATGuruNY wrote: Definitions of length:
Merriam-Webster: The LONGER OR LONGEST dimension of an object.
American Heritage: The measurement of something along its GREATEST dimension.
Interesting. I've never heard of that construct.
So, for a box with dimensions 3 x 4 x 5, then the side with length 5 is the length?
Which dimension is the width?
What about cases when the terms base and height are used? Which one is the base?

In a way, this reminds me of the times when students (incorrectly) insist that the side of a triangle that's horizontal (and on the bottom) must be the base of the triangle.

Cheers,
Brent
The GRE is administered by ETS, which also used to administer the GMAT.
The GRE Quantitative Guide states that any side of a triangle or parallelogram can be used as a base.
The GMAT is likely to abide by this definition.

But the terms length and long seem to connote a different meaning when used to refer to a rectangle or a rectangular solid.

In PS99 in the OG18, the given figure shows length L as the longer dimension of a rectangle.
PS17 in the OG18:
A rectangular garden is to be twice as long as it is wide.
Here, the term long is used to refer to the greater dimension.
DS296 in the OG17:
The tabletop is 36 inches wide by 60 inches long.
Here again, the term long is used to refer to the greater dimension.

PS159 in the OG18:
The interior of a rectangular carton is designed to have a ratio of length to width to height of 3:2:2.
Here, the term length is used to refer to the greatest dimension.
DS34 in the OG12:
The inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high.
Here, the term long is used to refer to the greatest dimension.

When referring to a rectangle or a rectangular solid, the GMAT seems to reserve the terms length and long for the greater or greatest dimension.
This usage is supported not only by the dictionaries cited in my post above but also by Dr. Math:
https://mathforum.org/library/drmath/view/57801.html
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by Brent@GMATPrepNow » Tue Sep 11, 2018 2:31 pm

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GMATGuruNY wrote: The GRE is administered by ETS, which also used to administer the GMAT.
The GRE Quantitative Guide states that any side of a triangle or parallelogram can be used as a base.
The GMAT is likely to abide by this definition.

But the terms length and long seem to connote a different meaning when used to refer to a rectangle or a rectangular solid.

In PS99 in the OG18, the given figure shows length L as the longer dimension of a rectangle.
PS17 in the OG18:
A rectangular garden is to be twice as long as it is wide.
Here, the term long is used to refer to the greater dimension.
DS296 in the OG17:
The tabletop is 36 inches wide by 60 inches long.
Here again, the term long is used to refer to the greater dimension.

PS159 in the OG18:
The interior of a rectangular carton is designed to have a ratio of length to width to height of 3:2:2.
Here, the term length is used to refer to the greatest dimension.
DS34 in the OG12:
The inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high.
Here, the term long is used to refer to the greatest dimension.

When referring to a rectangle or a rectangular solid, the GMAT seems to reserve the terms length and long for the greater or greatest dimension.
This usage is supported not only by the dictionaries cited in my post above but also by Dr. Math:
https://mathforum.org/library/drmath/view/57801.html
Great research, Mitch!
I can't imagine there are many official questions that hinge entirely on that one (somewhat esoteric) construct.
I mean, for the every question you cited, it doesn't matter which side we call the length or the width. The correct answer is the same in all cases.
It's just this one DS question (in the original post) where the construct is crucial.

Cheers and thanks again,
Brent
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by fskilnik@GMATH » Tue Sep 11, 2018 2:44 pm

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GMATGuruNY wrote: The GRE is administered by ETS, which also used to administer the GMAT.
The GRE Quantitative Guide states that any side of a triangle or parallelogram can be used as a base.
The GMAT is likely to abide by this definition.

But the terms length and long seem to connote a different meaning when used to refer to a rectangle or a rectangular solid.

In PS99 in the OG18, the given figure shows length L as the longer dimension of a rectangle.
PS17 in the OG18:
A rectangular garden is to be twice as long as it is wide.
Here, the term long is used to refer to the greater dimension.
DS296 in the OG17:
The tabletop is 36 inches wide by 60 inches long.
Here again, the term long is used to refer to the greater dimension.

PS159 in the OG18:
The interior of a rectangular carton is designed to have a ratio of length to width to height of 3:2:2.
Here, the term length is used to refer to the greatest dimension.
DS34 in the OG12:
The inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high.
Here, the term long is used to refer to the greatest dimension.

When referring to a rectangle or a rectangular solid, the GMAT seems to reserve the terms length and long for the greater or greatest dimension.
This usage is supported not only by the dictionaries cited in my post above but also by Dr. Math:
https://mathforum.org/library/drmath/view/57801.html
I said I would not go further in the discussion, but I respect your research, Mitch, therefore I will give my LAST opinions on the matter.

Yes, in all examples you have provided the term "length of a rectangle" was used according to your arguments.
BUT this was not the case in the official question that started this discussion and, perhaps, in other official exercises that you did not find or did not mention.

As far as Dr. Math is concerned, it is easy to realize we are in a "children" and "Educational purposes" situation... even so, the blocks below are from the very link you have provided:

-----------------------------------------------------------------------------------------
In math, we try to avoid letting words depend on context, so in more
advanced fields we define special terms very carefully. In elementary
math, we don't have the freedom to choose our own terms, especially
when we deal with real-world applications, so we have to be all the
more careful.
-----------------------------------------------------------------------------------------

And, at the end,

-----------------------------------------------------------------------------------------
But since English lacks a general word without reference to relative
size or orientation, in math we often use "length and width" without
any distinction. For instance, in the formula for the area of a
rectangle, it makes no difference which is bigger, so "l" and "w" in
my mind are just arbitrary labels for the two dimensions.
-----------------------------------------------------------------------------------------

That´s it. Now I will really keep my promise and, with all due respect,
avoid coming back to this matter.

Thank you all for your understanding!

Regards,
fskilnik.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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