The perimeter of a rectangular garden is 360 ft. What is the
This topic has expert replies

 Moderator
 Posts: 5769
 Joined: 07 Sep 2017
 Followed by:19 members
Timer
Your Answer
A
B
C
D
E
Global Stats
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
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 3008
 Joined: 22 Aug 2016
 Location: Grand Central / New York
 Thanked: 470 times
 Followed by:32 members
Timer
Your Answer
A
B
C
D
E
Global Stats
Say the length and the width of the rectangular garden is l and w, respectively.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
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
_________________
Manhattan Review GRE Prep
Locations: GMAT Classes Chicago  GRE Prep Course San Diego  GRE Prep Atlanta  TOEFL Prep Classes Houston  and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 15557
 Joined: 08 Dec 2008
 Location: Vancouver, BC
 Thanked: 5254 times
 Followed by:1266 members
 GMAT Score:770
Timer
Your Answer
A
B
C
D
E
Global Stats
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
 [email protected]
 GMAT Instructor
 Posts: 1449
 Joined: 09 Oct 2010
 Thanked: 59 times
 Followed by:33 members
Timer
Your Answer
A
B
C
D
E
Global Stats
Hi Brent,[email protected] wrote:To my testprep 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
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 3D analogous discussion.
Classic Elementary Geometry (Plane or Spatial) does not have any "orientationpreferences", like (for instance) when we are dealing with planar simpleclosed 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, thatÂ´s the way I see it!
Regards,
Fabio.
Englishspeakers :: https://www.gmath.net
Portuguesespeakers :: https://www.gmath.com.br
 [email protected]
 GMAT Instructor
 Posts: 1449
 Joined: 09 Oct 2010
 Thanked: 59 times
 Followed by:33 members
Timer
Your Answer
A
B
C
D
E
Global Stats
\[W + L = 180\,\,\,\left[ {{\text{ft}}} \right]\,\,\,\,\,\,\,\,\,\left( * \right)\]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
\[? = L\]
\[\left( 1 \right)\,\,\,\left\{ \begin{gathered}
\,L = 2k \hfill \\
\,W = k \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\left( {k > 0} \right)\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,3k = 180\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = L = 2k\,\,\,\,{\text{unique}}\]
\[\left( 2 \right)\,\,\left\{ \begin{gathered}
L  W = 60 \hfill \\
W + L = 180\,\,\,\,\left( * \right) \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\,2L = 240\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = L\,\,\,{\text{unique}}\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.
Englishspeakers :: https://www.gmath.net
Portuguesespeakers :: https://www.gmath.com.br
 GMATGuruNY
 GMAT Instructor
 Posts: 15533
 Joined: 25 May 2010
 Location: New York, NY
 Thanked: 13060 times
 Followed by:1898 members
 GMAT Score:790
Timer
Your Answer
A
B
C
D
E
Global Stats
Definitions of length:[email protected] wrote:To my testprep 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
MerriamWebster: The LONGER OR LONGEST dimension of an object.
American Heritage: The measurement of something along its GREATEST dimension.
Private Tutor for the GMAT and GRE
[email protected]
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and longdistance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 15557
 Joined: 08 Dec 2008
 Location: Vancouver, BC
 Thanked: 5254 times
 Followed by:1266 members
 GMAT Score:770
Timer
Your Answer
A
B
C
D
E
Global Stats
Interesting. I've never heard of that construct.GMATGuruNY wrote: Definitions of length:
MerriamWebster: The LONGER OR LONGEST dimension of an object.
American Heritage: The measurement of something along its GREATEST dimension.
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
 [email protected]
 GMAT Instructor
 Posts: 1449
 Joined: 09 Oct 2010
 Thanked: 59 times
 Followed by:33 members
Timer
Your Answer
A
B
C
D
E
Global Stats
(i) LANGUAGES dictionaries?GMATGuruNY wrote:Definitions of length:
MerriamWebster: The LONGER OR LONGEST dimension of an object.
American Heritage: The measurement of something along its GREATEST dimension.
(ii) LENGTH of what?
In my humble opinion, this is too generic and too nonmathematical 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 ... ightdepth
The problem here is another: they are usually materials taught by teachers who are NOT mathoriented (Education Studies x Mathematical Studies) and... for children.
Anyway, I will not go into this further. My explanations were presented previously.
Regards,
fskilnik.
Englishspeakers :: https://www.gmath.net
Portuguesespeakers :: https://www.gmath.com.br
 [email protected]
 GMAT Instructor
 Posts: 1449
 Joined: 09 Oct 2010
 Thanked: 59 times
 Followed by:33 members
Timer
Your Answer
A
B
C
D
E
Global Stats
EXACTLY.[email protected] 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.
Englishspeakers :: https://www.gmath.net
Portuguesespeakers :: https://www.gmath.com.br
 GMATGuruNY
 GMAT Instructor
 Posts: 15533
 Joined: 25 May 2010
 Location: New York, NY
 Thanked: 13060 times
 Followed by:1898 members
 GMAT Score:790
Timer
Your Answer
A
B
C
D
E
Global Stats
The GRE is administered by ETS, which also used to administer the GMAT.[email protected] wrote:Interesting. I've never heard of that construct.GMATGuruNY wrote: Definitions of length:
MerriamWebster: The LONGER OR LONGEST dimension of an object.
American Heritage: The measurement of something along its GREATEST dimension.
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 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
Private Tutor for the GMAT and GRE
[email protected]
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and longdistance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 15557
 Joined: 08 Dec 2008
 Location: Vancouver, BC
 Thanked: 5254 times
 Followed by:1266 members
 GMAT Score:770
Timer
Your Answer
A
B
C
D
E
Global Stats
Great research, Mitch!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 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
 [email protected]
 GMAT Instructor
 Posts: 1449
 Joined: 09 Oct 2010
 Thanked: 59 times
 Followed by:33 members
Timer
Your Answer
A
B
C
D
E
Global Stats
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.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
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 realworld 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.

ThatÂ´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.
Englishspeakers :: https://www.gmath.net
Portuguesespeakers :: https://www.gmath.com.br