Last visit was: 22 Jun 2025, 14:07 It is currently 22 Jun 2025, 14:07
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
505-555 Level|   Geometry|                           
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 June 2025
Posts: 102,229
Own Kudos:
Given Kudos: 93,970
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,229
Kudos: 734,608
 [108]
5
Kudos
Add Kudos
103
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 3,003
Own Kudos:
7,864
 [49]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 3,003
Kudos: 7,864
 [49]
35
Kudos
Add Kudos
14
Bookmarks
Bookmark this Post
User avatar
VikashAlex
Joined: 22 Sep 2014
Last visit: 05 Jan 2016
Posts: 29
Own Kudos:
281
 [10]
Given Kudos: 12
Posts: 29
Kudos: 281
 [10]
6
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
General Discussion
avatar
wings.ap
Joined: 10 Aug 2015
Last visit: 29 Jun 2019
Posts: 20
Own Kudos:
58
 [1]
Given Kudos: 232
Location: India
GMAT 1: 700 Q48 V38
GPA: 3.5
WE:Consulting (Computer Software)
GMAT 1: 700 Q48 V38
Posts: 20
Kudos: 58
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
The rectangular rug shown in the figure above has an accent border. What is the area of the portion of the rug that excludes the border?

(1) The perimeter of the rug is 44 feet.
(2) The width of the border on all sides is 1 foot.


Kudos for a correct solution.

Attachment:
2015-10-25_2007.png

So from statement 1 we know perimeter = 44. Not sufficient to find area as we don't know individual sides.
from statement 2 we know border is of 1ft. Not sufficient to find area as we don't know individual sides.
Now combining both we know if the sides are x and y without the borders then 2{(x+2)+(y+2)} = 44
=> x+y = 18.
So x & y could be any possible combination that gives sum 18. So area will vary depending on the combination.

That's why answer is
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,082
Own Kudos:
18,661
 [8]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,082
Kudos: 18,661
 [8]
6
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
If we look at the original condition, we have to know the length and width of the rug. Also, we have to know width of the border. Hence, there are 3 variables in the original condition. In order to match the number of variables and the number of equations, we need to have 3 equations. The condition 1) and the condition 2) each has 1 equation. Hence, there is high chance E is the correct answer. In fact, we cannot know the width and the length of the rug even if we use the condition 1) and the condition 2). Hence the correct answer is E.

- For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
avatar
ReddyL
Joined: 03 Dec 2012
Last visit: 25 Sep 2017
Posts: 10
Own Kudos:
4
 [1]
Given Kudos: 43
Location: United Kingdom
Concentration: Finance, International Business
GPA: 3.57
Products:
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

The rectangular rug shown in the figure above has an accent border. What is the area of the portion of the rug that excludes the border?

(1) The perimeter of the rug is 44 feet.
(2) The width of the border on all sides is 1 foot.


Kudos for a correct solution.

Attachment:
2015-10-25_2007.png

1) It is given that the perimeter of the rug(Including the Border) is 44 feet.
Which means 2l+2w=44
l+w=22, So we have multiple possibilities for l & w, hence INSUFFICIENT

2)Here we are only provided with the width of the border and no other information is provided, hence INSUFFICIENT

1+2 Combining both the answers we still do not have enough information of length and width to calculate the area of the portion of rug excluding the border.
User avatar
shashank1tripathi
Joined: 12 Jun 2016
Last visit: 22 Nov 2017
Posts: 22
Own Kudos:
17
 [2]
Given Kudos: 18
Location: India
Concentration: Entrepreneurship, Finance
GPA: 3.76
WE:Information Technology (Computer Software)
Posts: 22
Kudos: 17
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Let us assume the length and width to be L and W respectively.

Statement 1: 2(L+W) = 44
L+W = 22
This statement does not provide information about individual length and width of rug. No information about border width. So, Insufficient.
Statement 2: Border width is 1 foot. But, no information about length and width of rug. Clearly, Insufficient.

Combining both: Still we can't deduce unique values for L and W. Hence, Insufficient.

Ans. E
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel

The rectangular rug shown in the figure above has an accent border. What is the area of the portion of the rug that excludes the border?

(1) The perimeter of the rug is 44 feet.
(2) The width of the border on all sides is 1 foot.

statement 1:
2l+2w=44
so, l+w=22
insufficient..

statement 2:
there is no info about length and width of rug. so, insufficient.

Combined (1)+(2)
length of rug=l-(1+1)=l-2,
width of rug=w-(1+1)=w-2
So, area of rug=(l-2)*(w-2)
we can not find the are of rug for this unknown variable.
So, insufficient...
Is my explanation correct Bunuel?
Thanks...
User avatar
kuvshah
Joined: 05 Jan 2017
Last visit: 17 Feb 2022
Posts: 18
Own Kudos:
5
 [1]
Given Kudos: 19
Location: India
GMAT 1: 540 Q35 V29
GMAT 1: 540 Q35 V29
Posts: 18
Kudos: 5
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
just tweak the problem and make Rug square - than may be possible to find the numbers.
User avatar
Nunuboy1994
Joined: 12 Nov 2016
Last visit: 24 Apr 2019
Posts: 559
Own Kudos:
122
 [1]
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
Posts: 559
Kudos: 122
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This question asks us to find the area of the white rectangle- as interpreted by the stimulus.

The rectangular rug shown in the figure above has an accent border. What is the area of the portion of the rug that excludes the border?

(1) The perimeter of the rug is 44 feet.
(2) The width of the border on all sides is 1 foot.


Statement (1) tells us that the perimeter of the rug is 44 feet; though, we do know the ratio of the side lengths and therefore there are multiple possibilities for the width and length. For example, you could have a length of 12 and width of 10. I almost tried to be creative with this question and had this impulse to find some reason to apply the Pythagorean theorem; though, there is no need to because even if you did that you would not be able to calculate the length and width of the rectangle within the black rectangle. Insufficient.

Statement (2) tells us that the width of the border on all sides is 1 foot- however, we run into the same dilemma as statement one. Insufficient.

Hence, both statements taken together are insufficient.
avatar
inandout
Joined: 12 May 2017
Last visit: 16 May 2017
Posts: 5
Own Kudos:
Given Kudos: 7
Location: United States (CA)
Concentration: Real Estate, Nonprofit
GPA: 3.85
Posts: 5
Kudos: 25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
it took me less than 5 secs to react to the right answer of this question. Of course, it is E, no information given to calculate the requirement of the question.
avatar
SudhindraBhat
Joined: 03 Jun 2019
Last visit: 15 Oct 2021
Posts: 7
Own Kudos:
Given Kudos: 41
Concentration: Strategy, Marketing
GMAT 1: 680 Q48 V35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I understand why Condition 1 and 2 individually doesn't give us an answer. However I'm unable to understand how a combination will not help us with an answer. Have provided below my answer on combination.

On combination, we can say that the area of the shaded region = 44*1 - 4 * (1^2). The reduction is on account of duplication at the corners. It would be great if somebody can help me understand why this approach is wrong.

Posted from my mobile device
User avatar
LoneSurvivor
Joined: 23 Nov 2016
Last visit: 18 Jul 2021
Posts: 306
Own Kudos:
Given Kudos: 156
GMAT 1: 690 Q50 V33
Products:
GMAT 1: 690 Q50 V33
Posts: 306
Kudos: 743
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can someone please clarify when we are saying "The perimeter of the rug is 44 feet" are we considering ,

1. Perimeter including the border
2. Perimeter excluding the border

Because if we consider 1 then ans is E
if we consider 2 then ans is C
User avatar
Sneha2021
Joined: 20 Dec 2020
Last visit: 10 Jun 2025
Posts: 319
Own Kudos:
35
 [1]
Given Kudos: 525
Location: India
Posts: 319
Kudos: 35
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I am confused why option C is incorrect

L+B=22

Inside area = (L-2)(B-2)

Area of rug (Area of the portion of the rug that excludes the border) = Area of Outside Rectangle including width - Area of inside rectangle
= (L*B) - (L-2)(B-2)
=2(L+B)-4
=2(22)-4

Is my approach correct @Brunuel,@MathRevolution?
Can you please help?

Thanks in advance.
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 22 Jun 2025
Posts: 6,349
Own Kudos:
15,483
 [2]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,349
Kudos: 15,483
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel

The rectangular rug shown in the figure above has an accent border. What is the area of the portion of the rug that excludes the border?

(1) The perimeter of the rug is 44 feet.
(2) The width of the border on all sides is 1 foot.
Answer: Option E

Video solution by GMATinsight

User avatar
RamseyGooner
User avatar
Current Student
Joined: 29 Feb 2020
Last visit: 03 Oct 2022
Posts: 55
Own Kudos:
42
 [2]
Given Kudos: 56
Location: India
GMAT 1: 720 Q49 V40
GPA: 3.5
GMAT 1: 720 Q49 V40
Posts: 55
Kudos: 42
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
My answer was C initially, because I misread the question and thought we need to find the area that is taken by the border but in reality, the question asks us to find the area of the smaller rectangle.

Because of the mistake, I learnt that the area of the border could be found without the values for L and B, but if the question asks to get the value for either the bigger or smaller rectangle, we definitely need to know either L or B.

Cheers,
R
avatar
kashika101
Joined: 27 Feb 2020
Last visit: 22 Mar 2022
Posts: 2
Own Kudos:
Given Kudos: 3
Location: India
Posts: 2
Kudos: 1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi, I am getting (C) as my answer.
could someone help me with what is wrong with my reasoning?

Let the length of the rug = l
breath of the rug = b,
and the width of the border = x.

therefore, the length of the rug with border = l+2x
similarly, the breath of rug without border = b+2x

to find :
area of the rug without border =
{(l+2x)(b+2x)}-lb = (2l+2b)x+4x^2

given,
option 1 ---
p = 44
=> 2(l+b) = 44
inconclusive.

option 2 ---
x=1
inconclusive

together:
(2l+2b)x+4x^2 = 44(1)+4(1)^2 = 48
User avatar
avigutman
Joined: 17 Jul 2019
Last visit: 09 Jun 2025
Posts: 1,295
Own Kudos:
1,896
 [2]
Given Kudos: 66
Location: Canada
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert
Expert reply
GMAT 3: 770 Q50 V45
Posts: 1,295
Kudos: 1,896
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,251
Own Kudos:
Posts: 37,251
Kudos: 1,002
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Math Expert
102229 posts
425 posts