A rectangular floor is covered by a rug except fo a strip p meters alo

Question

A rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by n meteres, What is the area of the rug in square meters?

A) mn - p(m+n)
B) mn – 2p(m+n)
C) mn – p^2
D) (m - p)(n - p)
E) (m - 2p)(n - 2p)

gmate2010 · Accepted Answer

Please see the atahced figure:-

Area of rug = (m-2p)(n-2p)

BrentGMATPrepNow · Answer

When we sketch the given information, we get the following: 
 https://i.imgur.com/QFrXPMB.png

So, the area of the rectangular rug equals = (base)(height) = (  m - 2p  )(  n - 2p  )

Answer: E

Cheers,
Brent

varunmb · Answer

The answer must be E.

Plug in M 100 
N 50
P 10.

Correct me if I am wrong.

royQV · Answer

Answer is E - (m-2p)(n-2p)

Area of floor is m*n
Length of rug = m - 2p (Distance of p on each side)
Width of rug = n - 2p (Distance of p on each side)

Thus area of rug = (m-2p)(n-2p)

PareshGmat · Answer

Refer diagram below; we require to find area of the pink region

Answer = E

mejia401 · Answer

1. mn-p(m+n)  Depending on the size of  m , n , and  p , the number could be positive or negative. 
2. mn-2p(m+n)  Again, depending on the size of  m , n , and  p , the number could be positive or negative 
3. mn-p^2  This is only the area in the top corner 
4. (m-p)(n-p)  Trick answer. Selected if one's coasting through the problem. 
5.(m-2p)(n-2p)  True, since  p  surrounds all four edges of the rug

saroshgilani · Answer

Bunuel  , hi, where can i find some questions on similar triangles...?

Bunuel · Answer

Check GEOMETRY tags in our questions banks: viewforumtags.php Hope it helps.

EMPOWERgmatRichC · Answer

Hi All,

We're told that a rectangular floor (that is M meters by N meters) is covered by a rug EXCEPT for a strip P meters along EACH of the four edges. We're asked for the area of the rug in square meters. This question can be solved in a couple of different ways, including by TESTing VALUES.

IF.... M=5 and N=4, then we have a 5x4 floor.

IF.... P=1, then there is a 1 meter space around EACH of the 4 sides, meaning that the area of the rug is....

(5-1-1) = 3 meters by (4-1-1) = 2 meters 
Area of the rug is (3)(2) = 6 square meters

Based on the work I've done so far, you might recognize which answer is correct (since it's "formatted" almost identically to the above calculation). If you don't recognize it, then you just have to do enough work until you find the answer that equals 6 when you plug in M=5, N=4 and P=1... there's only one answer that matches. ..

Final Answer:  E

GMAT assassins aren't born, they're made, 
Rich

ScottTargetTestPrep · Answer

The area of the rug is:

x

(m - 2p)(n - 2p)

Answer: E

ak2121 · Answer

can someone pls explain why m-2p or n-2p

EMPOWERgmatRichC · Answer

Hi ak2121,

There are a number of explanations in this thread that define how to get to the correct answer. Is there a particular aspect of this question that you are finding difficult to understand?
 
GMAT assassins aren't born, they're made,
Rich

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A rectangular floor is covered by a rug except fo a strip p meters alo

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A rectangular floor is covered by a rug except fo a strip p meters alo

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards