The rectangular rug shown in the figure above has an accent border.

Solution:

We are given a rectangular rug with a uniform border. Let’s begin by sketching and labeling the dimensions of the rug and the rug’s border below.



We must determine the area of the rug that excludes the border. Thus, according to our diagram above, we must determine the product of W and L.

Note that the entire length of the rug is (L + 2x) and the entire width of the rug is (W + 2x).

Statement One Alone:

The perimeter of the rug is 44 feet.

We will use the formula for the perimeter of a rectangle, which is P = 2W + 2L. Using the information in statement one, we can now create the following equation for the perimeter of the rug:

2(W + 2x) + 2(L + 2x) = 44

2W + 4x + 2L + 4x = 44

2W + 2L + 8x = 44

We see that we do not have enough information to determine the value of WL. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The width of the border on all sides is 1 foot.

We know x = 1, but we still don’t know the value of either W or L. Thus, the information in statement two is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information in statements one and two we know that 2W + 2L + 8x = 44 and that x = 1. So,

2W + 2L + 8(1) = 44

2W + 2L = 36

W + L = 18

Since there are many pairs of numbers that add up to 18, we can’t determine the exact values of W and L. Thus, we still do not have enough information to determine the value of WL.

Answer: E
_________________

Will go with answer E

Statement 1: does not provide the length or width individually. Length and width could be different. For example L = 22 and W = 2, or L = 11 and w = 4. So the area will vary. Not sufficient.

Statement 2: only the width of the border is given i.e 1 foot. Can not possible to calculate area. Not sufficient

Combine: Combining both will also not possible as its the same thing the area will be changing because we don't know specific value of length and width. Not sufficient.

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

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.

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.

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

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...
_________________

just tweak the problem and make Rug square - than may be possible to find the numbers.

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.

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.

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

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

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.

Answer: Option E

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub

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

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

Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

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.
_________________